Question:
Assets: BTC-USD, VNQI
BTC-USD: annualized_mean_return=2.0412, daily_std=0.0276
VNQI: annualized_mean_return=-0.2772, daily_std=0.0087
Minimum required portfolio return (annualized): -0.1054
Market regime: bull

Compute portfolio weights (w_BTC-USD, w_VNQI) that minimize portfolio variance while satisfying the minimum return constraint. Constraints: all weights >= 0, weights sum to 1. Report as: w_BTC-USD=X.XXXX, w_VNQI=X.XXXX

Answer: w_BTC-USD=0.1310, w_VNQI=0.8690

Explanation:
Analytic min-variance formula:
  w1* = (σ2² - σ12) / (σ1² + σ2² - 2σ12)
  = (0.000076 - -0.000046) / (0.000763 + 0.000076 - -0.000092)
  Unconstrained: w_BTC-USD=0.1310
  After long-only clamp: w_BTC-USD=0.1310, w_VNQI=0.8690.


Question:
Assets: DOT-USD, DBB
DOT-USD: annualized_mean_return=1.2600, daily_std=0.0418
DBB: annualized_mean_return=0.0252, daily_std=0.0131
Minimum required portfolio return (annualized): 0.1113
Market regime: sideways

Compute portfolio weights (w_DOT-USD, w_DBB) that minimize portfolio variance while satisfying the minimum return constraint. Constraints: all weights >= 0, weights sum to 1. Report as: w_DOT-USD=X.XXXX, w_DBB=X.XXXX

Answer: w_DOT-USD=0.0972, w_DBB=0.9028

Explanation:
Analytic min-variance formula:
  w1* = (σ2² - σ12) / (σ1² + σ2² - 2σ12)
  = (0.000171 - -0.000019) / (0.001748 + 0.000171 - -0.000037)
  Unconstrained: w_DOT-USD=0.0970
  After long-only clamp: w_DOT-USD=0.0970, w_DBB=0.9030.


Question:
Assets: XLF, REZ
XLF: annualized_mean_return=0.3276, daily_std=0.0113
REZ: annualized_mean_return=0.3024, daily_std=0.0142
Minimum required portfolio return (annualized): 0.3163
Market regime: sideways

Compute portfolio weights (w_XLF, w_REZ) that minimize portfolio variance while satisfying the minimum return constraint. Constraints: all weights >= 0, weights sum to 1. Report as: w_XLF=X.XXXX, w_REZ=X.XXXX

Answer: w_XLF=0.9059, w_REZ=0.0941

Explanation:
Analytic min-variance formula:
  w1* = (σ2² - σ12) / (σ1² + σ2² - 2σ12)
  = (0.000201 - 0.000118) / (0.000127 + 0.000201 - 0.000236)
  Unconstrained: w_XLF=0.9065
  After long-only clamp: w_XLF=0.9065, w_REZ=0.0935.


MATIC-USD σ=0.0334, ICSH σ=0.0005, ρ=0.023. Min-variance weights: MATIC-USD=0.000, ICSH=1.000.

Question:
Assets: MATIC-USD, ICSH
MATIC-USD: annualized_mean_return=-2.0916, daily_std=0.0334
ICSH: annualized_mean_return=0.0252, daily_std=0.0005
Minimum required portfolio return (annualized): -1.1678
Market regime: sideways

Compute portfolio weights (w_MATIC-USD, w_ICSH) that minimize portfolio variance while satisfying the minimum return constraint. Constraints: all weights >= 0, weights sum to 1. Report as: w_MATIC-USD=X.XXXX, w_ICSH=X.XXXX

Answer: w_MATIC-USD=0.0002, w_ICSH=0.9998

Explanation:
Analytic min-variance formula:
  w1* = (σ2² - σ12) / (σ1² + σ2² - 2σ12)
  = (0.000000 - 0.000000) / (0.001117 + 0.000000 - 0.000001)
  Unconstrained: w_MATIC-USD=-0.0001
  After long-only clamp: w_MATIC-USD=0.0000, w_ICSH=1.0000.


Question:
Assets: LINK-USD, DBB
LINK-USD: annualized_mean_return=1.1340, daily_std=0.0381
DBB: annualized_mean_return=0.0504, daily_std=0.0086
Minimum required portfolio return (annualized): 0.1117
Market regime: sideways

Compute portfolio weights (w_LINK-USD, w_DBB) that minimize portfolio variance while satisfying the minimum return constraint. Constraints: all weights >= 0, weights sum to 1. Report as: w_LINK-USD=X.XXXX, w_DBB=X.XXXX

Answer: w_LINK-USD=0.0725, w_DBB=0.9275

Explanation:
Analytic min-variance formula:
  w1* = (σ2² - σ12) / (σ1² + σ2² - 2σ12)
  = (0.000074 - -0.000043) / (0.001455 + 0.000074 - -0.000085)
  Unconstrained: w_LINK-USD=0.0723
  After long-only clamp: w_LINK-USD=0.0723, w_DBB=0.9277.


Question:
Assets: LINK-USD, BIL
LINK-USD: annualized_mean_return=-0.9072, daily_std=0.0280
BIL: annualized_mean_return=0.0504, daily_std=0.0002
Minimum required portfolio return (annualized): -0.4043
Market regime: sideways

Compute portfolio weights (w_LINK-USD, w_BIL) that minimize portfolio variance while satisfying the minimum return constraint. Constraints: all weights >= 0, weights sum to 1. Report as: w_LINK-USD=X.XXXX, w_BIL=X.XXXX

Answer: w_LINK-USD=0.0000, w_BIL=1.0000

Explanation:
Analytic min-variance formula:
  w1* = (σ2² - σ12) / (σ1² + σ2² - 2σ12)
  = (0.000000 - -0.000000) / (0.000783 + 0.000000 - -0.000000)
  Unconstrained: w_LINK-USD=0.0003
  After long-only clamp: w_LINK-USD=0.0003, w_BIL=0.9997.


Question:
Assets: XLU, TLH
XLU: annualized_mean_return=-0.0000, daily_std=0.0115
TLH: annualized_mean_return=-0.0756, daily_std=0.0085
Minimum required portfolio return (annualized): -0.0104
Market regime: sideways

Compute portfolio weights (w_XLU, w_TLH) that minimize portfolio variance while satisfying the minimum return constraint. Constraints: all weights >= 0, weights sum to 1. Report as: w_XLU=X.XXXX, w_TLH=X.XXXX

Answer: w_XLU=0.8624, w_TLH=0.1376

Explanation:
Analytic min-variance formula:
  w1* = (σ2² - σ12) / (σ1² + σ2² - 2σ12)
  = (0.000073 - -0.000011) / (0.000133 + 0.000073 - -0.000022)
  Unconstrained: w_XLU=0.3685
  After long-only clamp: w_XLU=0.3685, w_TLH=0.6315.


Question:
Assets: FXI, SCHH
FXI: annualized_mean_return=0.2772, daily_std=0.0128
SCHH: annualized_mean_return=0.7308, daily_std=0.0087
Minimum required portfolio return (annualized): 0.6991
Market regime: sideways

Compute portfolio weights (w_FXI, w_SCHH) that minimize portfolio variance while satisfying the minimum return constraint. Constraints: all weights >= 0, weights sum to 1. Report as: w_FXI=X.XXXX, w_SCHH=X.XXXX

Answer: w_FXI=0.0699, w_SCHH=0.9301

Explanation:
Analytic min-variance formula:
  w1* = (σ2² - σ12) / (σ1² + σ2² - 2σ12)
  = (0.000075 - 0.000017) / (0.000163 + 0.000075 - 0.000035)
  Unconstrained: w_FXI=0.2856
  After long-only clamp: w_FXI=0.2856, w_SCHH=0.7144.


Question:
Assets: EEM, CSHI
EEM: annualized_mean_return=0.1764, daily_std=0.0096
CSHI: annualized_mean_return=0.0504, daily_std=0.0003
Minimum required portfolio return (annualized): 0.0505
Market regime: sideways

Compute portfolio weights (w_EEM, w_CSHI) that minimize portfolio variance while satisfying the minimum return constraint. Constraints: all weights >= 0, weights sum to 1. Report as: w_EEM=X.XXXX, w_CSHI=X.XXXX

Answer: w_EEM=0.0010, w_CSHI=0.9990

Explanation:
Analytic min-variance formula:
  w1* = (σ2² - σ12) / (σ1² + σ2² - 2σ12)
  = (0.000000 - -0.000000) / (0.000093 + 0.000000 - -0.000000)
  Unconstrained: w_EEM=0.0016
  After long-only clamp: w_EEM=0.0016, w_CSHI=0.9984.


Question:
Assets: BTC-USD, ITB
BTC-USD: annualized_mean_return=0.9072, daily_std=0.0312
ITB: annualized_mean_return=0.3780, daily_std=0.0155
Minimum required portfolio return (annualized): 0.4618
Market regime: sideways

Compute portfolio weights (w_BTC-USD, w_ITB) that minimize portfolio variance while satisfying the minimum return constraint. Constraints: all weights >= 0, weights sum to 1. Report as: w_BTC-USD=X.XXXX, w_ITB=X.XXXX

Answer: w_BTC-USD=0.2156, w_ITB=0.7844

Explanation:
Analytic min-variance formula:
  w1* = (σ2² - σ12) / (σ1² + σ2² - 2σ12)
  = (0.000241 - -0.000035) / (0.000971 + 0.000241 - -0.000071)
  Unconstrained: w_BTC-USD=0.2157
  After long-only clamp: w_BTC-USD=0.2157, w_ITB=0.7843.


AVAX-USD σ=0.0394, HYG σ=0.0032, ρ=0.050. Min-variance weights: AVAX-USD=0.002, HYG=0.998.

Question:
Assets: AVAX-USD, HYG
AVAX-USD: annualized_mean_return=-1.0584, daily_std=0.0394
HYG: annualized_mean_return=0.0504, daily_std=0.0032
Minimum required portfolio return (annualized): -0.3188
Market regime: sideways

Compute portfolio weights (w_AVAX-USD, w_HYG) that minimize portfolio variance while satisfying the minimum return constraint. Constraints: all weights >= 0, weights sum to 1. Report as: w_AVAX-USD=X.XXXX, w_HYG=X.XXXX

Answer: w_AVAX-USD=0.0026, w_HYG=0.9974

Explanation:
Analytic min-variance formula:
  w1* = (σ2² - σ12) / (σ1² + σ2² - 2σ12)
  = (0.000010 - 0.000006) / (0.001548 + 0.000010 - 0.000013)
  Unconstrained: w_AVAX-USD=0.0024
  After long-only clamp: w_AVAX-USD=0.0024, w_HYG=0.9976.


Question:
Assets: XLY, CSHI
XLY: annualized_mean_return=-0.2016, daily_std=0.0094
CSHI: annualized_mean_return=0.0504, daily_std=0.0004
Minimum required portfolio return (annualized): -0.0812
Market regime: sideways

Compute portfolio weights (w_XLY, w_CSHI) that minimize portfolio variance while satisfying the minimum return constraint. Constraints: all weights >= 0, weights sum to 1. Report as: w_XLY=X.XXXX, w_CSHI=X.XXXX

Answer: w_XLY=0.0020, w_CSHI=0.9980

Explanation:
Analytic min-variance formula:
  w1* = (σ2² - σ12) / (σ1² + σ2² - 2σ12)
  = (0.000000 - 0.000000) / (0.000089 + 0.000000 - 0.000000)
  Unconstrained: w_XLY=0.0016
  After long-only clamp: w_XLY=0.0016, w_CSHI=0.9984.


Question:
Assets: BNB-USD, ITB
BNB-USD: annualized_mean_return=0.0756, daily_std=0.0178
ITB: annualized_mean_return=0.6048, daily_std=0.0134
Minimum required portfolio return (annualized): 0.4863
Market regime: sideways

Compute portfolio weights (w_BNB-USD, w_ITB) that minimize portfolio variance while satisfying the minimum return constraint. Constraints: all weights >= 0, weights sum to 1. Report as: w_BNB-USD=X.XXXX, w_ITB=X.XXXX

Answer: w_BNB-USD=0.2239, w_ITB=0.7761

Explanation:
Analytic min-variance formula:
  w1* = (σ2² - σ12) / (σ1² + σ2² - 2σ12)
  = (0.000178 - -0.000011) / (0.000317 + 0.000178 - -0.000021)
  Unconstrained: w_BNB-USD=0.3659
  After long-only clamp: w_BNB-USD=0.3659, w_ITB=0.6341.


MATIC-USD σ=0.0367, ^VIX σ=0.0506, ρ=0.093. Min-variance weights: MATIC-USD=0.670, ^VIX=0.330.

Question:
Assets: MATIC-USD, ^VIX
MATIC-USD: annualized_mean_return=-0.5292, daily_std=0.0367
^VIX: annualized_mean_return=-0.4788, daily_std=0.0506
Minimum required portfolio return (annualized): -0.4935
Market regime: sideways

Compute portfolio weights (w_MATIC-USD, w_^VIX) that minimize portfolio variance while satisfying the minimum return constraint. Constraints: all weights >= 0, weights sum to 1. Report as: w_MATIC-USD=X.XXXX, w_^VIX=X.XXXX

Answer: w_MATIC-USD=0.2917, w_^VIX=0.7083

Explanation:
Analytic min-variance formula:
  w1* = (σ2² - σ12) / (σ1² + σ2² - 2σ12)
  = (0.002561 - 0.000172) / (0.001347 + 0.002561 - 0.000344)
  Unconstrained: w_MATIC-USD=0.6703
  After long-only clamp: w_MATIC-USD=0.6703, w_^VIX=0.3297.


Question:
Assets: XRP-USD, XLE
XRP-USD: annualized_mean_return=0.6552, daily_std=0.0429
XLE: annualized_mean_return=-0.4032, daily_std=0.0175
Minimum required portfolio return (annualized): 0.2524
Market regime: sideways

Compute portfolio weights (w_XRP-USD, w_XLE) that minimize portfolio variance while satisfying the minimum return constraint. Constraints: all weights >= 0, weights sum to 1. Report as: w_XRP-USD=X.XXXX, w_XLE=X.XXXX

Answer: w_XRP-USD=0.6194, w_XLE=0.3806

Explanation:
Analytic min-variance formula:
  w1* = (σ2² - σ12) / (σ1² + σ2² - 2σ12)
  = (0.000305 - 0.000159) / (0.001841 + 0.000305 - 0.000317)
  Unconstrained: w_XRP-USD=0.0798
  After long-only clamp: w_XRP-USD=0.0798, w_XLE=0.9202.


Question:
Assets: QQQ, EMB
QQQ: annualized_mean_return=0.2772, daily_std=0.0101
EMB: annualized_mean_return=-0.0504, daily_std=0.0049
Minimum required portfolio return (annualized): -0.0153
Market regime: sideways

Compute portfolio weights (w_QQQ, w_EMB) that minimize portfolio variance while satisfying the minimum return constraint. Constraints: all weights >= 0, weights sum to 1. Report as: w_QQQ=X.XXXX, w_EMB=X.XXXX

Answer: w_QQQ=0.1627, w_EMB=0.8373

Explanation:
Analytic min-variance formula:
  w1* = (σ2² - σ12) / (σ1² + σ2² - 2σ12)
  = (0.000024 - 0.000005) / (0.000102 + 0.000024 - 0.000009)
  Unconstrained: w_QQQ=0.1649
  After long-only clamp: w_QQQ=0.1649, w_EMB=0.8351.


Question:
Assets: ACWI, CSHI
ACWI: annualized_mean_return=0.2016, daily_std=0.0066
CSHI: annualized_mean_return=0.0252, daily_std=0.0005
Minimum required portfolio return (annualized): 0.0259
Market regime: bull

Compute portfolio weights (w_ACWI, w_CSHI) that minimize portfolio variance while satisfying the minimum return constraint. Constraints: all weights >= 0, weights sum to 1. Report as: w_ACWI=X.XXXX, w_CSHI=X.XXXX

Answer: w_ACWI=0.0049, w_CSHI=0.9951

Explanation:
Analytic min-variance formula:
  w1* = (σ2² - σ12) / (σ1² + σ2² - 2σ12)
  = (0.000000 - -0.000000) / (0.000044 + 0.000000 - -0.000001)
  Unconstrained: w_ACWI=0.0136
  After long-only clamp: w_ACWI=0.0136, w_CSHI=0.9864.


Question:
Assets: XLP, GLD
XLP: annualized_mean_return=0.3528, daily_std=0.0098
GLD: annualized_mean_return=0.5544, daily_std=0.0097
Minimum required portfolio return (annualized): 0.4038
Market regime: sideways

Compute portfolio weights (w_XLP, w_GLD) that minimize portfolio variance while satisfying the minimum return constraint. Constraints: all weights >= 0, weights sum to 1. Report as: w_XLP=X.XXXX, w_GLD=X.XXXX

Answer: w_XLP=0.4957, w_GLD=0.5043

Explanation:
Analytic min-variance formula:
  w1* = (σ2² - σ12) / (σ1² + σ2² - 2σ12)
  = (0.000094 - 0.000007) / (0.000096 + 0.000094 - 0.000013)
  Unconstrained: w_XLP=0.4958
  After long-only clamp: w_XLP=0.4958, w_GLD=0.5042.


Question:
Assets: SPY, BNDX
SPY: annualized_mean_return=0.2772, daily_std=0.0076
BNDX: annualized_mean_return=0.0000, daily_std=0.0020
Minimum required portfolio return (annualized): 0.0091
Market regime: sideways

Compute portfolio weights (w_SPY, w_BNDX) that minimize portfolio variance while satisfying the minimum return constraint. Constraints: all weights >= 0, weights sum to 1. Report as: w_SPY=X.XXXX, w_BNDX=X.XXXX

Answer: w_SPY=0.0769, w_BNDX=0.9231

Explanation:
Analytic min-variance formula:
  w1* = (σ2² - σ12) / (σ1² + σ2² - 2σ12)
  = (0.000004 - -0.000001) / (0.000058 + 0.000004 - -0.000002)
  Unconstrained: w_SPY=0.0748
  After long-only clamp: w_SPY=0.0748, w_BNDX=0.9252.


LINK-USD σ=0.0380, SOYB σ=0.0094, ρ=-0.130. Min-variance weights: LINK-USD=0.083, SOYB=0.917.

Question:
Assets: LINK-USD, SOYB
LINK-USD: annualized_mean_return=-0.1260, daily_std=0.0380
SOYB: annualized_mean_return=-0.3528, daily_std=0.0094
Minimum required portfolio return (annualized): -0.3391
Market regime: bull

Compute portfolio weights (w_LINK-USD, w_SOYB) that minimize portfolio variance while satisfying the minimum return constraint. Constraints: all weights >= 0, weights sum to 1. Report as: w_LINK-USD=X.XXXX, w_SOYB=X.XXXX

Answer: w_LINK-USD=0.0831, w_SOYB=0.9169

Explanation:
Analytic min-variance formula:
  w1* = (σ2² - σ12) / (σ1² + σ2² - 2σ12)
  = (0.000088 - -0.000047) / (0.001447 + 0.000088 - -0.000093)
  Unconstrained: w_LINK-USD=0.0829
  After long-only clamp: w_LINK-USD=0.0829, w_SOYB=0.9171.


Question:
Assets: ETH-USD, LQD
ETH-USD: annualized_mean_return=0.1008, daily_std=0.0258
LQD: annualized_mean_return=-0.0504, daily_std=0.0036
Minimum required portfolio return (annualized): -0.0470
Market regime: sideways

Compute portfolio weights (w_ETH-USD, w_LQD) that minimize portfolio variance while satisfying the minimum return constraint. Constraints: all weights >= 0, weights sum to 1. Report as: w_ETH-USD=X.XXXX, w_LQD=X.XXXX

Answer: w_ETH-USD=0.0232, w_LQD=0.9768

Explanation:
Analytic min-variance formula:
  w1* = (σ2² - σ12) / (σ1² + σ2² - 2σ12)
  = (0.000013 - -0.000003) / (0.000665 + 0.000013 - -0.000006)
  Unconstrained: w_ETH-USD=0.0235
  After long-only clamp: w_ETH-USD=0.0235, w_LQD=0.9765.


Question:
Assets: XRP-USD, CSHI
XRP-USD: annualized_mean_return=0.4788, daily_std=0.0277
CSHI: annualized_mean_return=0.0756, daily_std=0.0008
Minimum required portfolio return (annualized): 0.1838
Market regime: sideways

Compute portfolio weights (w_XRP-USD, w_CSHI) that minimize portfolio variance while satisfying the minimum return constraint. Constraints: all weights >= 0, weights sum to 1. Report as: w_XRP-USD=X.XXXX, w_CSHI=X.XXXX

Answer: w_XRP-USD=0.2684, w_CSHI=0.7316

Explanation:
Analytic min-variance formula:
  w1* = (σ2² - σ12) / (σ1² + σ2² - 2σ12)
  = (0.000001 - -0.000001) / (0.000770 + 0.000001 - -0.000001)
  Unconstrained: w_XRP-USD=0.0016
  After long-only clamp: w_XRP-USD=0.0016, w_CSHI=0.9984.


Question:
Assets: IVV, IGOV
IVV: annualized_mean_return=0.0252, daily_std=0.0082
IGOV: annualized_mean_return=0.1764, daily_std=0.0052
Minimum required portfolio return (annualized): 0.0672
Market regime: sideways

Compute portfolio weights (w_IVV, w_IGOV) that minimize portfolio variance while satisfying the minimum return constraint. Constraints: all weights >= 0, weights sum to 1. Report as: w_IVV=X.XXXX, w_IGOV=X.XXXX

Answer: w_IVV=0.3082, w_IGOV=0.6918

Explanation:
Analytic min-variance formula:
  w1* = (σ2² - σ12) / (σ1² + σ2² - 2σ12)
  = (0.000027 - -0.000006) / (0.000067 + 0.000027 - -0.000012)
  Unconstrained: w_IVV=0.3079
  After long-only clamp: w_IVV=0.3079, w_IGOV=0.6921.


Question:
Assets: AVAX-USD, GLD
AVAX-USD: annualized_mean_return=1.3104, daily_std=0.0385
GLD: annualized_mean_return=0.4536, daily_std=0.0082
Minimum required portfolio return (annualized): 0.4975
Market regime: sideways

Compute portfolio weights (w_AVAX-USD, w_GLD) that minimize portfolio variance while satisfying the minimum return constraint. Constraints: all weights >= 0, weights sum to 1. Report as: w_AVAX-USD=X.XXXX, w_GLD=X.XXXX

Answer: w_AVAX-USD=0.0572, w_GLD=0.9428

Explanation:
Analytic min-variance formula:
  w1* = (σ2² - σ12) / (σ1² + σ2² - 2σ12)
  = (0.000067 - -0.000024) / (0.001483 + 0.000067 - -0.000048)
  Unconstrained: w_AVAX-USD=0.0571
  After long-only clamp: w_AVAX-USD=0.0571, w_GLD=0.9429.


Question:
Assets: VEA, ICSH
VEA: annualized_mean_return=0.3780, daily_std=0.0075
ICSH: annualized_mean_return=0.0504, daily_std=0.0003
Minimum required portfolio return (annualized): 0.0564
Market regime: sideways

Compute portfolio weights (w_VEA, w_ICSH) that minimize portfolio variance while satisfying the minimum return constraint. Constraints: all weights >= 0, weights sum to 1. Report as: w_VEA=X.XXXX, w_ICSH=X.XXXX

Answer: w_VEA=0.0188, w_ICSH=0.9812

Explanation:
Analytic min-variance formula:
  w1* = (σ2² - σ12) / (σ1² + σ2² - 2σ12)
  = (0.000000 - -0.000001) / (0.000056 + 0.000000 - -0.000001)
  Unconstrained: w_VEA=0.0111
  After long-only clamp: w_VEA=0.0111, w_ICSH=0.9889.


Question:
Assets: ACWI, ICSH
ACWI: annualized_mean_return=0.2016, daily_std=0.0063
ICSH: annualized_mean_return=0.0504, daily_std=0.0002
Minimum required portfolio return (annualized): 0.0506
Market regime: sideways

Compute portfolio weights (w_ACWI, w_ICSH) that minimize portfolio variance while satisfying the minimum return constraint. Constraints: all weights >= 0, weights sum to 1. Report as: w_ACWI=X.XXXX, w_ICSH=X.XXXX

Answer: w_ACWI=0.0014, w_ICSH=0.9986

Explanation:
Analytic min-variance formula:
  w1* = (σ2² - σ12) / (σ1² + σ2² - 2σ12)
  = (0.000000 - 0.000000) / (0.000040 + 0.000000 - 0.000001)
  Unconstrained: w_ACWI=-0.0079
  After long-only clamp: w_ACWI=0.0000, w_ICSH=1.0000.


Question:
Assets: XLB, BIL
XLB: annualized_mean_return=0.3528, daily_std=0.0084
BIL: annualized_mean_return=0.0504, daily_std=0.0001
Minimum required portfolio return (annualized): 0.2195
Market regime: sideways

Compute portfolio weights (w_XLB, w_BIL) that minimize portfolio variance while satisfying the minimum return constraint. Constraints: all weights >= 0, weights sum to 1. Report as: w_XLB=X.XXXX, w_BIL=X.XXXX

Answer: w_XLB=0.5592, w_BIL=0.4408

Explanation:
Analytic min-variance formula:
  w1* = (σ2² - σ12) / (σ1² + σ2² - 2σ12)
  = (0.000000 - -0.000000) / (0.000070 + 0.000000 - -0.000001)
  Unconstrained: w_XLB=0.0047
  After long-only clamp: w_XLB=0.0047, w_BIL=0.9953.


Question:
Assets: XLU, PPLT
XLU: annualized_mean_return=0.2772, daily_std=0.0092
PPLT: annualized_mean_return=0.3780, daily_std=0.0168
Minimum required portfolio return (annualized): 0.3453
Market regime: sideways

Compute portfolio weights (w_XLU, w_PPLT) that minimize portfolio variance while satisfying the minimum return constraint. Constraints: all weights >= 0, weights sum to 1. Report as: w_XLU=X.XXXX, w_PPLT=X.XXXX

Answer: w_XLU=0.3244, w_PPLT=0.6756

Explanation:
Analytic min-variance formula:
  w1* = (σ2² - σ12) / (σ1² + σ2² - 2σ12)
  = (0.000283 - 0.000014) / (0.000085 + 0.000283 - 0.000027)
  Unconstrained: w_XLU=0.7909
  After long-only clamp: w_XLU=0.7909, w_PPLT=0.2091.


Question:
Assets: EFA, IYR
EFA: annualized_mean_return=0.5292, daily_std=0.0117
IYR: annualized_mean_return=0.2016, daily_std=0.0144
Minimum required portfolio return (annualized): 0.5265
Market regime: sideways

Compute portfolio weights (w_EFA, w_IYR) that minimize portfolio variance while satisfying the minimum return constraint. Constraints: all weights >= 0, weights sum to 1. Report as: w_EFA=X.XXXX, w_IYR=X.XXXX

Answer: w_EFA=0.9918, w_IYR=0.0082

Explanation:
Analytic min-variance formula:
  w1* = (σ2² - σ12) / (σ1² + σ2² - 2σ12)
  = (0.000207 - 0.000135) / (0.000136 + 0.000207 - 0.000269)
  Unconstrained: w_EFA=0.9842
  After long-only clamp: w_EFA=0.9842, w_IYR=0.0158.


Question:
Assets: XLB, DBA
XLB: annualized_mean_return=0.1260, daily_std=0.0103
DBA: annualized_mean_return=0.2772, daily_std=0.0080
Minimum required portfolio return (annualized): 0.1867
Market regime: sideways

Compute portfolio weights (w_XLB, w_DBA) that minimize portfolio variance while satisfying the minimum return constraint. Constraints: all weights >= 0, weights sum to 1. Report as: w_XLB=X.XXXX, w_DBA=X.XXXX

Answer: w_XLB=0.3816, w_DBA=0.6184

Explanation:
Analytic min-variance formula:
  w1* = (σ2² - σ12) / (σ1² + σ2² - 2σ12)
  = (0.000064 - -0.000003) / (0.000106 + 0.000064 - -0.000007)
  Unconstrained: w_XLB=0.3820
  After long-only clamp: w_XLB=0.3820, w_DBA=0.6180.


Question:
Assets: EFA, SHV
EFA: annualized_mean_return=0.1260, daily_std=0.0089
SHV: annualized_mean_return=0.0504, daily_std=0.0002
Minimum required portfolio return (annualized): 0.0862
Market regime: sideways

Compute portfolio weights (w_EFA, w_SHV) that minimize portfolio variance while satisfying the minimum return constraint. Constraints: all weights >= 0, weights sum to 1. Report as: w_EFA=X.XXXX, w_SHV=X.XXXX

Answer: w_EFA=0.4735, w_SHV=0.5265

Explanation:
Analytic min-variance formula:
  w1* = (σ2² - σ12) / (σ1² + σ2² - 2σ12)
  = (0.000000 - 0.000000) / (0.000080 + 0.000000 - 0.000001)
  Unconstrained: w_EFA=-0.0040
  After long-only clamp: w_EFA=0.0000, w_SHV=1.0000.


Question:
Assets: EWJ, CSHI
EWJ: annualized_mean_return=-0.2520, daily_std=0.0091
CSHI: annualized_mean_return=0.1008, daily_std=0.0006
Minimum required portfolio return (annualized): 0.1003
Market regime: sideways

Compute portfolio weights (w_EWJ, w_CSHI) that minimize portfolio variance while satisfying the minimum return constraint. Constraints: all weights >= 0, weights sum to 1. Report as: w_EWJ=X.XXXX, w_CSHI=X.XXXX

Answer: w_EWJ=0.0014, w_CSHI=0.9986

Explanation:
Analytic min-variance formula:
  w1* = (σ2² - σ12) / (σ1² + σ2² - 2σ12)
  = (0.000000 - 0.000000) / (0.000082 + 0.000000 - 0.000001)
  Unconstrained: w_EWJ=-0.0006
  After long-only clamp: w_EWJ=0.0000, w_CSHI=1.0000.


Question:
Assets: XLU, CSHI
XLU: annualized_mean_return=-0.0504, daily_std=0.0122
CSHI: annualized_mean_return=0.0504, daily_std=0.0005
Minimum required portfolio return (annualized): 0.0158
Market regime: sideways

Compute portfolio weights (w_XLU, w_CSHI) that minimize portfolio variance while satisfying the minimum return constraint. Constraints: all weights >= 0, weights sum to 1. Report as: w_XLU=X.XXXX, w_CSHI=X.XXXX

Answer: w_XLU=0.0000, w_CSHI=1.0000

Explanation:
Analytic min-variance formula:
  w1* = (σ2² - σ12) / (σ1² + σ2² - 2σ12)
  = (0.000000 - 0.000001) / (0.000149 + 0.000000 - 0.000003)
  Unconstrained: w_XLU=-0.0073
  After long-only clamp: w_XLU=0.0000, w_CSHI=1.0000.


Question:
Assets: XLP, TIP
XLP: annualized_mean_return=0.0756, daily_std=0.0080
TIP: annualized_mean_return=0.0756, daily_std=0.0022
Minimum required portfolio return (annualized): 0.0756
Market regime: sideways

Compute portfolio weights (w_XLP, w_TIP) that minimize portfolio variance while satisfying the minimum return constraint. Constraints: all weights >= 0, weights sum to 1. Report as: w_XLP=X.XXXX, w_TIP=X.XXXX

Answer: w_XLP=0.0705, w_TIP=0.9295

Explanation:
Analytic min-variance formula:
  w1* = (σ2² - σ12) / (σ1² + σ2² - 2σ12)
  = (0.000005 - 0.000000) / (0.000065 + 0.000005 - 0.000000)
  Unconstrained: w_XLP=0.0688
  After long-only clamp: w_XLP=0.0688, w_TIP=0.9312.


Question:
Assets: XRP-USD, IYR
XRP-USD: annualized_mean_return=0.2268, daily_std=0.0255
IYR: annualized_mean_return=0.1512, daily_std=0.0123
Minimum required portfolio return (annualized): 0.1832
Market regime: sideways

Compute portfolio weights (w_XRP-USD, w_IYR) that minimize portfolio variance while satisfying the minimum return constraint. Constraints: all weights >= 0, weights sum to 1. Report as: w_XRP-USD=X.XXXX, w_IYR=X.XXXX

Answer: w_XRP-USD=0.4233, w_IYR=0.5767

Explanation:
Analytic min-variance formula:
  w1* = (σ2² - σ12) / (σ1² + σ2² - 2σ12)
  = (0.000150 - 0.000018) / (0.000650 + 0.000150 - 0.000035)
  Unconstrained: w_XRP-USD=0.1734
  After long-only clamp: w_XRP-USD=0.1734, w_IYR=0.8266.


Question:
Assets: XRP-USD, IVV
XRP-USD: annualized_mean_return=0.2016, daily_std=0.0244
IVV: annualized_mean_return=0.3024, daily_std=0.0075
Minimum required portfolio return (annualized): 0.2957
Market regime: sideways

Compute portfolio weights (w_XRP-USD, w_IVV) that minimize portfolio variance while satisfying the minimum return constraint. Constraints: all weights >= 0, weights sum to 1. Report as: w_XRP-USD=X.XXXX, w_IVV=X.XXXX

Answer: w_XRP-USD=0.0665, w_IVV=0.9335

Explanation:
Analytic min-variance formula:
  w1* = (σ2² - σ12) / (σ1² + σ2² - 2σ12)
  = (0.000056 - -0.000008) / (0.000597 + 0.000056 - -0.000016)
  Unconstrained: w_XRP-USD=0.0961
  After long-only clamp: w_XRP-USD=0.0961, w_IVV=0.9039.


MATIC-USD σ=0.0471, PDBC σ=0.0066, ρ=-0.367. Min-variance weights: MATIC-USD=0.063, PDBC=0.937.

Question:
Assets: MATIC-USD, PDBC
MATIC-USD: annualized_mean_return=-1.7640, daily_std=0.0471
PDBC: annualized_mean_return=0.2268, daily_std=0.0066
Minimum required portfolio return (annualized): 0.1597
Market regime: sideways

Compute portfolio weights (w_MATIC-USD, w_PDBC) that minimize portfolio variance while satisfying the minimum return constraint. Constraints: all weights >= 0, weights sum to 1. Report as: w_MATIC-USD=X.XXXX, w_PDBC=X.XXXX

Answer: w_MATIC-USD=0.0337, w_PDBC=0.9663

Explanation:
Analytic min-variance formula:
  w1* = (σ2² - σ12) / (σ1² + σ2² - 2σ12)
  = (0.000043 - -0.000114) / (0.002218 + 0.000043 - -0.000228)
  Unconstrained: w_MATIC-USD=0.0632
  After long-only clamp: w_MATIC-USD=0.0632, w_PDBC=0.9368.


Question:
Assets: XLY, SCHH
XLY: annualized_mean_return=0.6552, daily_std=0.0116
SCHH: annualized_mean_return=0.3276, daily_std=0.0076
Minimum required portfolio return (annualized): 0.5777
Market regime: sideways

Compute portfolio weights (w_XLY, w_SCHH) that minimize portfolio variance while satisfying the minimum return constraint. Constraints: all weights >= 0, weights sum to 1. Report as: w_XLY=X.XXXX, w_SCHH=X.XXXX

Answer: w_XLY=0.7634, w_SCHH=0.2366

Explanation:
Analytic min-variance formula:
  w1* = (σ2² - σ12) / (σ1² + σ2² - 2σ12)
  = (0.000058 - 0.000030) / (0.000135 + 0.000058 - 0.000060)
  Unconstrained: w_XLY=0.2103
  After long-only clamp: w_XLY=0.2103, w_SCHH=0.7897.


Question:
Assets: FXI, BNDX
FXI: annualized_mean_return=-0.0756, daily_std=0.0193
BNDX: annualized_mean_return=0.0504, daily_std=0.0039
Minimum required portfolio return (annualized): 0.0491
Market regime: sideways

Compute portfolio weights (w_FXI, w_BNDX) that minimize portfolio variance while satisfying the minimum return constraint. Constraints: all weights >= 0, weights sum to 1. Report as: w_FXI=X.XXXX, w_BNDX=X.XXXX

Answer: w_FXI=0.0103, w_BNDX=0.9897

Explanation:
Analytic min-variance formula:
  w1* = (σ2² - σ12) / (σ1² + σ2² - 2σ12)
  = (0.000015 - -0.000000) / (0.000373 + 0.000015 - -0.000000)
  Unconstrained: w_FXI=0.0387
  After long-only clamp: w_FXI=0.0387, w_BNDX=0.9613.


LINK-USD σ=0.0473, CSHI σ=0.0005, ρ=-0.117. Min-variance weights: LINK-USD=0.001, CSHI=0.999.

Question:
Assets: LINK-USD, CSHI
LINK-USD: annualized_mean_return=2.0664, daily_std=0.0473
CSHI: annualized_mean_return=0.0504, daily_std=0.0005
Minimum required portfolio return (annualized): 0.0533
Market regime: sideways

Compute portfolio weights (w_LINK-USD, w_CSHI) that minimize portfolio variance while satisfying the minimum return constraint. Constraints: all weights >= 0, weights sum to 1. Report as: w_LINK-USD=X.XXXX, w_CSHI=X.XXXX

Answer: w_LINK-USD=0.0015, w_CSHI=0.9985

Explanation:
Analytic min-variance formula:
  w1* = (σ2² - σ12) / (σ1² + σ2² - 2σ12)
  = (0.000000 - -0.000003) / (0.002235 + 0.000000 - -0.000006)
  Unconstrained: w_LINK-USD=0.0014
  After long-only clamp: w_LINK-USD=0.0014, w_CSHI=0.9986.


Question:
Assets: BNB-USD, XLU
BNB-USD: annualized_mean_return=1.2852, daily_std=0.0283
XLU: annualized_mean_return=0.2772, daily_std=0.0116
Minimum required portfolio return (annualized): 1.0986
Market regime: sideways

Compute portfolio weights (w_BNB-USD, w_XLU) that minimize portfolio variance while satisfying the minimum return constraint. Constraints: all weights >= 0, weights sum to 1. Report as: w_BNB-USD=X.XXXX, w_XLU=X.XXXX

Answer: w_BNB-USD=0.8149, w_XLU=0.1851

Explanation:
Analytic min-variance formula:
  w1* = (σ2² - σ12) / (σ1² + σ2² - 2σ12)
  = (0.000135 - 0.000005) / (0.000798 + 0.000135 - 0.000010)
  Unconstrained: w_BNB-USD=0.1410
  After long-only clamp: w_BNB-USD=0.1410, w_XLU=0.8590.


Question:
Assets: FXI, SLV
FXI: annualized_mean_return=-0.1512, daily_std=0.0161
SLV: annualized_mean_return=0.3780, daily_std=0.0151
Minimum required portfolio return (annualized): -0.0009
Market regime: sideways

Compute portfolio weights (w_FXI, w_SLV) that minimize portfolio variance while satisfying the minimum return constraint. Constraints: all weights >= 0, weights sum to 1. Report as: w_FXI=X.XXXX, w_SLV=X.XXXX

Answer: w_FXI=0.4699, w_SLV=0.5301

Explanation:
Analytic min-variance formula:
  w1* = (σ2² - σ12) / (σ1² + σ2² - 2σ12)
  = (0.000229 - -0.000005) / (0.000259 + 0.000229 - -0.000010)
  Unconstrained: w_FXI=0.4699
  After long-only clamp: w_FXI=0.4699, w_SLV=0.5301.


Question:
Assets: DOT-USD, DBC
DOT-USD: annualized_mean_return=1.8144, daily_std=0.0333
DBC: annualized_mean_return=0.0252, daily_std=0.0071
Minimum required portfolio return (annualized): 0.5686
Market regime: sideways

Compute portfolio weights (w_DOT-USD, w_DBC) that minimize portfolio variance while satisfying the minimum return constraint. Constraints: all weights >= 0, weights sum to 1. Report as: w_DOT-USD=X.XXXX, w_DBC=X.XXXX

Answer: w_DOT-USD=0.3037, w_DBC=0.6963

Explanation:
Analytic min-variance formula:
  w1* = (σ2² - σ12) / (σ1² + σ2² - 2σ12)
  = (0.000050 - 0.000054) / (0.001111 + 0.000050 - 0.000108)
  Unconstrained: w_DOT-USD=-0.0037
  After long-only clamp: w_DOT-USD=0.0000, w_DBC=1.0000.


Question:
Assets: XLK, DBA
XLK: annualized_mean_return=1.0080, daily_std=0.0095
DBA: annualized_mean_return=-0.0252, daily_std=0.0079
Minimum required portfolio return (annualized): 0.6548
Market regime: sideways

Compute portfolio weights (w_XLK, w_DBA) that minimize portfolio variance while satisfying the minimum return constraint. Constraints: all weights >= 0, weights sum to 1. Report as: w_XLK=X.XXXX, w_DBA=X.XXXX

Answer: w_XLK=0.6581, w_DBA=0.3419

Explanation:
Analytic min-variance formula:
  w1* = (σ2² - σ12) / (σ1² + σ2² - 2σ12)
  = (0.000062 - 0.000021) / (0.000089 + 0.000062 - 0.000041)
  Unconstrained: w_XLK=0.3753
  After long-only clamp: w_XLK=0.3753, w_DBA=0.6247.


AVAX-USD σ=0.0445, BNO σ=0.0230, ρ=0.031. Min-variance weights: AVAX-USD=0.203, BNO=0.797.

Question:
Assets: AVAX-USD, BNO
AVAX-USD: annualized_mean_return=1.3860, daily_std=0.0445
BNO: annualized_mean_return=-0.1008, daily_std=0.0230
Minimum required portfolio return (annualized): 1.0884
Market regime: sideways

Compute portfolio weights (w_AVAX-USD, w_BNO) that minimize portfolio variance while satisfying the minimum return constraint. Constraints: all weights >= 0, weights sum to 1. Report as: w_AVAX-USD=X.XXXX, w_BNO=X.XXXX

Answer: w_AVAX-USD=0.7998, w_BNO=0.2002

Explanation:
Analytic min-variance formula:
  w1* = (σ2² - σ12) / (σ1² + σ2² - 2σ12)
  = (0.000529 - 0.000031) / (0.001980 + 0.000529 - 0.000063)
  Unconstrained: w_AVAX-USD=0.2034
  After long-only clamp: w_AVAX-USD=0.2034, w_BNO=0.7966.


Question:
Assets: ADA-USD, XLU
ADA-USD: annualized_mean_return=0.1008, daily_std=0.0295
XLU: annualized_mean_return=0.4284, daily_std=0.0120
Minimum required portfolio return (annualized): 0.2881
Market regime: sideways

Compute portfolio weights (w_ADA-USD, w_XLU) that minimize portfolio variance while satisfying the minimum return constraint. Constraints: all weights >= 0, weights sum to 1. Report as: w_ADA-USD=X.XXXX, w_XLU=X.XXXX

Answer: w_ADA-USD=0.0614, w_XLU=0.9386

Explanation:
Analytic min-variance formula:
  w1* = (σ2² - σ12) / (σ1² + σ2² - 2σ12)
  = (0.000144 - 0.000093) / (0.000870 + 0.000144 - 0.000186)
  Unconstrained: w_ADA-USD=0.0612
  After long-only clamp: w_ADA-USD=0.0612, w_XLU=0.9388.


EEM σ=0.0118, LINK-USD σ=0.0433, ρ=0.024. Min-variance weights: EEM=0.936, LINK-USD=0.064.

Question:
Assets: EEM, LINK-USD
EEM: annualized_mean_return=-0.0504, daily_std=0.0118
LINK-USD: annualized_mean_return=1.1340, daily_std=0.0433
Minimum required portfolio return (annualized): 0.0014
Market regime: sideways

Compute portfolio weights (w_EEM, w_LINK-USD) that minimize portfolio variance while satisfying the minimum return constraint. Constraints: all weights >= 0, weights sum to 1. Report as: w_EEM=X.XXXX, w_LINK-USD=X.XXXX

Answer: w_EEM=0.9360, w_LINK-USD=0.0640

Explanation:
Analytic min-variance formula:
  w1* = (σ2² - σ12) / (σ1² + σ2² - 2σ12)
  = (0.001878 - 0.000012) / (0.000140 + 0.001878 - 0.000025)
  Unconstrained: w_EEM=0.9362
  After long-only clamp: w_EEM=0.9362, w_LINK-USD=0.0638.


Question:
Assets: XRP-USD, VNQI
XRP-USD: annualized_mean_return=-0.2520, daily_std=0.0452
VNQI: annualized_mean_return=0.0000, daily_std=0.0083
Minimum required portfolio return (annualized): -0.0948
Market regime: sideways

Compute portfolio weights (w_XRP-USD, w_VNQI) that minimize portfolio variance while satisfying the minimum return constraint. Constraints: all weights >= 0, weights sum to 1. Report as: w_XRP-USD=X.XXXX, w_VNQI=X.XXXX

Answer: w_XRP-USD=0.0498, w_VNQI=0.9502

Explanation:
Analytic min-variance formula:
  w1* = (σ2² - σ12) / (σ1² + σ2² - 2σ12)
  = (0.000069 - -0.000040) / (0.002041 + 0.000069 - -0.000081)
  Unconstrained: w_XRP-USD=0.0499
  After long-only clamp: w_XRP-USD=0.0499, w_VNQI=0.9501.


Question:
Assets: ADA-USD, VNQI
ADA-USD: annualized_mean_return=3.5532, daily_std=0.0462
VNQI: annualized_mean_return=0.4032, daily_std=0.0108
Minimum required portfolio return (annualized): 1.5900
Market regime: sideways

Compute portfolio weights (w_ADA-USD, w_VNQI) that minimize portfolio variance while satisfying the minimum return constraint. Constraints: all weights >= 0, weights sum to 1. Report as: w_ADA-USD=X.XXXX, w_VNQI=X.XXXX

Answer: w_ADA-USD=0.3768, w_VNQI=0.6232

Explanation:
Analytic min-variance formula:
  w1* = (σ2² - σ12) / (σ1² + σ2² - 2σ12)
  = (0.000116 - -0.000091) / (0.002131 + 0.000116 - -0.000181)
  Unconstrained: w_ADA-USD=0.0850
  After long-only clamp: w_ADA-USD=0.0850, w_VNQI=0.9150.


Question:
Assets: VTI, ICSH
VTI: annualized_mean_return=0.2016, daily_std=0.0103
ICSH: annualized_mean_return=0.0756, daily_std=0.0003
Minimum required portfolio return (annualized): 0.1578
Market regime: sideways

Compute portfolio weights (w_VTI, w_ICSH) that minimize portfolio variance while satisfying the minimum return constraint. Constraints: all weights >= 0, weights sum to 1. Report as: w_VTI=X.XXXX, w_ICSH=X.XXXX

Answer: w_VTI=0.6524, w_ICSH=0.3476

Explanation:
Analytic min-variance formula:
  w1* = (σ2² - σ12) / (σ1² + σ2² - 2σ12)
  = (0.000000 - 0.000000) / (0.000106 + 0.000000 - 0.000001)
  Unconstrained: w_VTI=-0.0034
  After long-only clamp: w_VTI=0.0000, w_ICSH=1.0000.


Question:
Assets: VEA, CSHI
VEA: annualized_mean_return=0.2016, daily_std=0.0103
CSHI: annualized_mean_return=0.0504, daily_std=0.0012
Minimum required portfolio return (annualized): 0.0940
Market regime: sideways

Compute portfolio weights (w_VEA, w_CSHI) that minimize portfolio variance while satisfying the minimum return constraint. Constraints: all weights >= 0, weights sum to 1. Report as: w_VEA=X.XXXX, w_CSHI=X.XXXX

Answer: w_VEA=0.2884, w_CSHI=0.7116

Explanation:
Analytic min-variance formula:
  w1* = (σ2² - σ12) / (σ1² + σ2² - 2σ12)
  = (0.000001 - 0.000003) / (0.000107 + 0.000001 - 0.000005)
  Unconstrained: w_VEA=-0.0109
  After long-only clamp: w_VEA=0.0000, w_CSHI=1.0000.


Question:
Assets: SOL-USD, HYG
SOL-USD: annualized_mean_return=-1.6632, daily_std=0.0352
HYG: annualized_mean_return=0.2016, daily_std=0.0044
Minimum required portfolio return (annualized): -0.2829
Market regime: sideways

Compute portfolio weights (w_SOL-USD, w_HYG) that minimize portfolio variance while satisfying the minimum return constraint. Constraints: all weights >= 0, weights sum to 1. Report as: w_SOL-USD=X.XXXX, w_HYG=X.XXXX

Answer: w_SOL-USD=0.0268, w_HYG=0.9732

Explanation:
Analytic min-variance formula:
  w1* = (σ2² - σ12) / (σ1² + σ2² - 2σ12)
  = (0.000020 - -0.000015) / (0.001243 + 0.000020 - -0.000031)
  Unconstrained: w_SOL-USD=0.0271
  After long-only clamp: w_SOL-USD=0.0271, w_HYG=0.9729.


Question:
Assets: IVV, XRP-USD
IVV: annualized_mean_return=-0.2016, daily_std=0.0070
XRP-USD: annualized_mean_return=-0.6300, daily_std=0.0261
Minimum required portfolio return (annualized): -0.2148
Market regime: sideways

Compute portfolio weights (w_IVV, w_XRP-USD) that minimize portfolio variance while satisfying the minimum return constraint. Constraints: all weights >= 0, weights sum to 1. Report as: w_IVV=X.XXXX, w_XRP-USD=X.XXXX

Answer: w_IVV=0.9692, w_XRP-USD=0.0308

Explanation:
Analytic min-variance formula:
  w1* = (σ2² - σ12) / (σ1² + σ2² - 2σ12)
  = (0.000683 - 0.000011) / (0.000049 + 0.000683 - 0.000023)
  Unconstrained: w_IVV=0.9473
  After long-only clamp: w_IVV=0.9473, w_XRP-USD=0.0527.


Question:
Assets: BNB-USD, DBA
BNB-USD: annualized_mean_return=-0.4536, daily_std=0.0143
DBA: annualized_mean_return=-0.0252, daily_std=0.0071
Minimum required portfolio return (annualized): -0.2350
Market regime: sideways

Compute portfolio weights (w_BNB-USD, w_DBA) that minimize portfolio variance while satisfying the minimum return constraint. Constraints: all weights >= 0, weights sum to 1. Report as: w_BNB-USD=X.XXXX, w_DBA=X.XXXX

Answer: w_BNB-USD=0.1927, w_DBA=0.8073

Explanation:
Analytic min-variance formula:
  w1* = (σ2² - σ12) / (σ1² + σ2² - 2σ12)
  = (0.000051 - 0.000002) / (0.000205 + 0.000051 - 0.000003)
  Unconstrained: w_BNB-USD=0.1933
  After long-only clamp: w_BNB-USD=0.1933, w_DBA=0.8067.


Question:
Assets: EEM, HYG
EEM: annualized_mean_return=0.0756, daily_std=0.0095
HYG: annualized_mean_return=0.2016, daily_std=0.0046
Minimum required portfolio return (annualized): 0.1720
Market regime: sideways

Compute portfolio weights (w_EEM, w_HYG) that minimize portfolio variance while satisfying the minimum return constraint. Constraints: all weights >= 0, weights sum to 1. Report as: w_EEM=X.XXXX, w_HYG=X.XXXX

Answer: w_EEM=0.1566, w_HYG=0.8434

Explanation:
Analytic min-variance formula:
  w1* = (σ2² - σ12) / (σ1² + σ2² - 2σ12)
  = (0.000021 - 0.000005) / (0.000090 + 0.000021 - 0.000009)
  Unconstrained: w_EEM=0.1597
  After long-only clamp: w_EEM=0.1597, w_HYG=0.8403.


Question:
Assets: SOL-USD, VNQ
SOL-USD: annualized_mean_return=-0.7308, daily_std=0.0505
VNQ: annualized_mean_return=0.0504, daily_std=0.0103
Minimum required portfolio return (annualized): -0.1310
Market regime: bull

Compute portfolio weights (w_SOL-USD, w_VNQ) that minimize portfolio variance while satisfying the minimum return constraint. Constraints: all weights >= 0, weights sum to 1. Report as: w_SOL-USD=X.XXXX, w_VNQ=X.XXXX

Answer: w_SOL-USD=0.0366, w_VNQ=0.9634

Explanation:
Analytic min-variance formula:
  w1* = (σ2² - σ12) / (σ1² + σ2² - 2σ12)
  = (0.000105 - 0.000009) / (0.002547 + 0.000105 - 0.000018)
  Unconstrained: w_SOL-USD=0.0367
  After long-only clamp: w_SOL-USD=0.0367, w_VNQ=0.9633.


Question:
Assets: FXI, UNG
FXI: annualized_mean_return=0.0504, daily_std=0.0180
UNG: annualized_mean_return=0.6048, daily_std=0.0304
Minimum required portfolio return (annualized): 0.1857
Market regime: sideways

Compute portfolio weights (w_FXI, w_UNG) that minimize portfolio variance while satisfying the minimum return constraint. Constraints: all weights >= 0, weights sum to 1. Report as: w_FXI=X.XXXX, w_UNG=X.XXXX

Answer: w_FXI=0.7326, w_UNG=0.2674

Explanation:
Analytic min-variance formula:
  w1* = (σ2² - σ12) / (σ1² + σ2² - 2σ12)
  = (0.000922 - -0.000019) / (0.000324 + 0.000922 - -0.000037)
  Unconstrained: w_FXI=0.7327
  After long-only clamp: w_FXI=0.7327, w_UNG=0.2673.


Question:
Assets: ETH-USD, WEAT
ETH-USD: annualized_mean_return=0.0252, daily_std=0.0238
WEAT: annualized_mean_return=-0.4032, daily_std=0.0181
Minimum required portfolio return (annualized): -0.3289
Market regime: sideways

Compute portfolio weights (w_ETH-USD, w_WEAT) that minimize portfolio variance while satisfying the minimum return constraint. Constraints: all weights >= 0, weights sum to 1. Report as: w_ETH-USD=X.XXXX, w_WEAT=X.XXXX

Answer: w_ETH-USD=0.3731, w_WEAT=0.6269

Explanation:
Analytic min-variance formula:
  w1* = (σ2² - σ12) / (σ1² + σ2² - 2σ12)
  = (0.000327 - -0.000023) / (0.000566 + 0.000327 - -0.000047)
  Unconstrained: w_ETH-USD=0.3732
  After long-only clamp: w_ETH-USD=0.3732, w_WEAT=0.6268.


MATIC-USD σ=0.0449, HAUZ σ=0.0097, ρ=0.110. Min-variance weights: MATIC-USD=0.023, HAUZ=0.977.

Question:
Assets: MATIC-USD, HAUZ
MATIC-USD: annualized_mean_return=-0.9072, daily_std=0.0449
HAUZ: annualized_mean_return=-0.1008, daily_std=0.0097
Minimum required portfolio return (annualized): -0.1102
Market regime: sideways

Compute portfolio weights (w_MATIC-USD, w_HAUZ) that minimize portfolio variance while satisfying the minimum return constraint. Constraints: all weights >= 0, weights sum to 1. Report as: w_MATIC-USD=X.XXXX, w_HAUZ=X.XXXX

Answer: w_MATIC-USD=0.0117, w_HAUZ=0.9883

Explanation:
Analytic min-variance formula:
  w1* = (σ2² - σ12) / (σ1² + σ2² - 2σ12)
  = (0.000095 - 0.000048) / (0.002018 + 0.000095 - 0.000096)
  Unconstrained: w_MATIC-USD=0.0230
  After long-only clamp: w_MATIC-USD=0.0230, w_HAUZ=0.9770.


Question:
Assets: MTUM, XHB
MTUM: annualized_mean_return=0.2268, daily_std=0.0080
XHB: annualized_mean_return=0.6300, daily_std=0.0136
Minimum required portfolio return (annualized): 0.2416
Market regime: sideways

Compute portfolio weights (w_MTUM, w_XHB) that minimize portfolio variance while satisfying the minimum return constraint. Constraints: all weights >= 0, weights sum to 1. Report as: w_MTUM=X.XXXX, w_XHB=X.XXXX

Answer: w_MTUM=0.9130, w_XHB=0.0870

Explanation:
Analytic min-variance formula:
  w1* = (σ2² - σ12) / (σ1² + σ2² - 2σ12)
  = (0.000184 - 0.000052) / (0.000065 + 0.000184 - 0.000104)
  Unconstrained: w_MTUM=0.9143
  After long-only clamp: w_MTUM=0.9143, w_XHB=0.0857.


Question:
Assets: IWM, CORN
IWM: annualized_mean_return=0.0756, daily_std=0.0130
CORN: annualized_mean_return=0.0000, daily_std=0.0098
Minimum required portfolio return (annualized): 0.0472
Market regime: sideways

Compute portfolio weights (w_IWM, w_CORN) that minimize portfolio variance while satisfying the minimum return constraint. Constraints: all weights >= 0, weights sum to 1. Report as: w_IWM=X.XXXX, w_CORN=X.XXXX

Answer: w_IWM=0.6243, w_CORN=0.3757

Explanation:
Analytic min-variance formula:
  w1* = (σ2² - σ12) / (σ1² + σ2² - 2σ12)
  = (0.000096 - 0.000019) / (0.000168 + 0.000096 - 0.000038)
  Unconstrained: w_IWM=0.3416
  After long-only clamp: w_IWM=0.3416, w_CORN=0.6584.


Question:
Assets: ADA-USD, DBA
ADA-USD: annualized_mean_return=-0.7812, daily_std=0.0371
DBA: annualized_mean_return=0.4788, daily_std=0.0121
Minimum required portfolio return (annualized): 0.4159
Market regime: bull

Compute portfolio weights (w_ADA-USD, w_DBA) that minimize portfolio variance while satisfying the minimum return constraint. Constraints: all weights >= 0, weights sum to 1. Report as: w_ADA-USD=X.XXXX, w_DBA=X.XXXX

Answer: w_ADA-USD=0.0499, w_DBA=0.9501

Explanation:
Analytic min-variance formula:
  w1* = (σ2² - σ12) / (σ1² + σ2² - 2σ12)
  = (0.000147 - -0.000018) / (0.001380 + 0.000147 - -0.000036)
  Unconstrained: w_ADA-USD=0.1053
  After long-only clamp: w_ADA-USD=0.1053, w_DBA=0.8947.


BNB-USD σ=0.0200, STIP σ=0.0021, ρ=0.155. Min-variance weights: BNB-USD=0.000, STIP=1.000.

Question:
Assets: BNB-USD, STIP
BNB-USD: annualized_mean_return=-0.1512, daily_std=0.0200
STIP: annualized_mean_return=0.0756, daily_std=0.0021
Minimum required portfolio return (annualized): -0.0257
Market regime: sideways

Compute portfolio weights (w_BNB-USD, w_STIP) that minimize portfolio variance while satisfying the minimum return constraint. Constraints: all weights >= 0, weights sum to 1. Report as: w_BNB-USD=X.XXXX, w_STIP=X.XXXX

Answer: w_BNB-USD=0.0000, w_STIP=1.0000

Explanation:
Analytic min-variance formula:
  w1* = (σ2² - σ12) / (σ1² + σ2² - 2σ12)
  = (0.000005 - 0.000007) / (0.000400 + 0.000005 - 0.000013)
  Unconstrained: w_BNB-USD=-0.0053
  After long-only clamp: w_BNB-USD=0.0000, w_STIP=1.0000.


Question:
Assets: XLK, JNK
XLK: annualized_mean_return=0.3024, daily_std=0.0121
JNK: annualized_mean_return=0.1008, daily_std=0.0054
Minimum required portfolio return (annualized): 0.1912
Market regime: sideways

Compute portfolio weights (w_XLK, w_JNK) that minimize portfolio variance while satisfying the minimum return constraint. Constraints: all weights >= 0, weights sum to 1. Report as: w_XLK=X.XXXX, w_JNK=X.XXXX

Answer: w_XLK=0.4484, w_JNK=0.5516

Explanation:
Analytic min-variance formula:
  w1* = (σ2² - σ12) / (σ1² + σ2² - 2σ12)
  = (0.000029 - -0.000000) / (0.000147 + 0.000029 - -0.000000)
  Unconstrained: w_XLK=0.1646
  After long-only clamp: w_XLK=0.1646, w_JNK=0.8354.


Question:
Assets: IVV, ICSH
IVV: annualized_mean_return=0.6048, daily_std=0.0071
ICSH: annualized_mean_return=0.0756, daily_std=0.0003
Minimum required portfolio return (annualized): 0.0764
Market regime: sideways

Compute portfolio weights (w_IVV, w_ICSH) that minimize portfolio variance while satisfying the minimum return constraint. Constraints: all weights >= 0, weights sum to 1. Report as: w_IVV=X.XXXX, w_ICSH=X.XXXX

Answer: w_IVV=0.0019, w_ICSH=0.9981

Explanation:
Analytic min-variance formula:
  w1* = (σ2² - σ12) / (σ1² + σ2² - 2σ12)
  = (0.000000 - -0.000000) / (0.000051 + 0.000000 - -0.000000)
  Unconstrained: w_IVV=0.0068
  After long-only clamp: w_IVV=0.0068, w_ICSH=0.9932.


Question:
Assets: ETH-USD, BIL
ETH-USD: annualized_mean_return=-1.0080, daily_std=0.0389
BIL: annualized_mean_return=0.0756, daily_std=0.0002
Minimum required portfolio return (annualized): -0.1064
Market regime: bull

Compute portfolio weights (w_ETH-USD, w_BIL) that minimize portfolio variance while satisfying the minimum return constraint. Constraints: all weights >= 0, weights sum to 1. Report as: w_ETH-USD=X.XXXX, w_BIL=X.XXXX

Answer: w_ETH-USD=0.0000, w_BIL=1.0000

Explanation:
Analytic min-variance formula:
  w1* = (σ2² - σ12) / (σ1² + σ2² - 2σ12)
  = (0.000000 - -0.000000) / (0.001516 + 0.000000 - -0.000000)
  Unconstrained: w_ETH-USD=0.0000
  After long-only clamp: w_ETH-USD=0.0000, w_BIL=1.0000.


Question:
Assets: DOT-USD, PPLT
DOT-USD: annualized_mean_return=0.9072, daily_std=0.0349
PPLT: annualized_mean_return=-0.1764, daily_std=0.0169
Minimum required portfolio return (annualized): -0.0110
Market regime: sideways

Compute portfolio weights (w_DOT-USD, w_PPLT) that minimize portfolio variance while satisfying the minimum return constraint. Constraints: all weights >= 0, weights sum to 1. Report as: w_DOT-USD=X.XXXX, w_PPLT=X.XXXX

Answer: w_DOT-USD=0.2001, w_PPLT=0.7999

Explanation:
Analytic min-variance formula:
  w1* = (σ2² - σ12) / (σ1² + σ2² - 2σ12)
  = (0.000286 - -0.000025) / (0.001219 + 0.000286 - -0.000049)
  Unconstrained: w_DOT-USD=0.2000
  After long-only clamp: w_DOT-USD=0.2000, w_PPLT=0.8000.


Question:
Assets: IVV, HYG
IVV: annualized_mean_return=0.2016, daily_std=0.0065
HYG: annualized_mean_return=0.0504, daily_std=0.0039
Minimum required portfolio return (annualized): 0.1329
Market regime: sideways

Compute portfolio weights (w_IVV, w_HYG) that minimize portfolio variance while satisfying the minimum return constraint. Constraints: all weights >= 0, weights sum to 1. Report as: w_IVV=X.XXXX, w_HYG=X.XXXX

Answer: w_IVV=0.5456, w_HYG=0.4544

Explanation:
Analytic min-variance formula:
  w1* = (σ2² - σ12) / (σ1² + σ2² - 2σ12)
  = (0.000015 - -0.000001) / (0.000043 + 0.000015 - -0.000001)
  Unconstrained: w_IVV=0.2690
  After long-only clamp: w_IVV=0.2690, w_HYG=0.7310.


Question:
Assets: XLRE, TIP
XLRE: annualized_mean_return=-0.3528, daily_std=0.0102
TIP: annualized_mean_return=0.0000, daily_std=0.0015
Minimum required portfolio return (annualized): -0.0021
Market regime: sideways

Compute portfolio weights (w_XLRE, w_TIP) that minimize portfolio variance while satisfying the minimum return constraint. Constraints: all weights >= 0, weights sum to 1. Report as: w_XLRE=X.XXXX, w_TIP=X.XXXX

Answer: w_XLRE=0.0060, w_TIP=0.9940

Explanation:
Analytic min-variance formula:
  w1* = (σ2² - σ12) / (σ1² + σ2² - 2σ12)
  = (0.000002 - 0.000001) / (0.000103 + 0.000002 - 0.000003)
  Unconstrained: w_XLRE=0.0065
  After long-only clamp: w_XLRE=0.0065, w_TIP=0.9935.


Question:
Assets: LINK-USD, HYG
LINK-USD: annualized_mean_return=0.1512, daily_std=0.0410
HYG: annualized_mean_return=0.0252, daily_std=0.0038
Minimum required portfolio return (annualized): 0.1122
Market regime: sideways

Compute portfolio weights (w_LINK-USD, w_HYG) that minimize portfolio variance while satisfying the minimum return constraint. Constraints: all weights >= 0, weights sum to 1. Report as: w_LINK-USD=X.XXXX, w_HYG=X.XXXX

Answer: w_LINK-USD=0.6905, w_HYG=0.3095

Explanation:
Analytic min-variance formula:
  w1* = (σ2² - σ12) / (σ1² + σ2² - 2σ12)
  = (0.000014 - -0.000037) / (0.001680 + 0.000014 - -0.000074)
  Unconstrained: w_LINK-USD=0.0290
  After long-only clamp: w_LINK-USD=0.0290, w_HYG=0.9710.


Question:
Assets: EEM, BTC-USD
EEM: annualized_mean_return=-0.4536, daily_std=0.0093
BTC-USD: annualized_mean_return=0.4284, daily_std=0.0167
Minimum required portfolio return (annualized): -0.0374
Market regime: sideways

Compute portfolio weights (w_EEM, w_BTC-USD) that minimize portfolio variance while satisfying the minimum return constraint. Constraints: all weights >= 0, weights sum to 1. Report as: w_EEM=X.XXXX, w_BTC-USD=X.XXXX

Answer: w_EEM=0.5281, w_BTC-USD=0.4719

Explanation:
Analytic min-variance formula:
  w1* = (σ2² - σ12) / (σ1² + σ2² - 2σ12)
  = (0.000279 - -0.000008) / (0.000086 + 0.000279 - -0.000016)
  Unconstrained: w_EEM=0.7537
  After long-only clamp: w_EEM=0.7537, w_BTC-USD=0.2463.


Question:
Assets: ETH-USD, SCHH
ETH-USD: annualized_mean_return=-1.0836, daily_std=0.0387
SCHH: annualized_mean_return=0.6300, daily_std=0.0087
Minimum required portfolio return (annualized): 0.5438
Market regime: sideways

Compute portfolio weights (w_ETH-USD, w_SCHH) that minimize portfolio variance while satisfying the minimum return constraint. Constraints: all weights >= 0, weights sum to 1. Report as: w_ETH-USD=X.XXXX, w_SCHH=X.XXXX

Answer: w_ETH-USD=0.0503, w_SCHH=0.9497

Explanation:
Analytic min-variance formula:
  w1* = (σ2² - σ12) / (σ1² + σ2² - 2σ12)
  = (0.000075 - -0.000041) / (0.001501 + 0.000075 - -0.000082)
  Unconstrained: w_ETH-USD=0.0699
  After long-only clamp: w_ETH-USD=0.0699, w_SCHH=0.9301.


Question:
Assets: XLU, ICSH
XLU: annualized_mean_return=-0.1008, daily_std=0.0108
ICSH: annualized_mean_return=0.0504, daily_std=0.0003
Minimum required portfolio return (annualized): 0.0503
Market regime: sideways

Compute portfolio weights (w_XLU, w_ICSH) that minimize portfolio variance while satisfying the minimum return constraint. Constraints: all weights >= 0, weights sum to 1. Report as: w_XLU=X.XXXX, w_ICSH=X.XXXX

Answer: w_XLU=0.0007, w_ICSH=0.9993

Explanation:
Analytic min-variance formula:
  w1* = (σ2² - σ12) / (σ1² + σ2² - 2σ12)
  = (0.000000 - 0.000000) / (0.000117 + 0.000000 - 0.000000)
  Unconstrained: w_XLU=0.0006
  After long-only clamp: w_XLU=0.0006, w_ICSH=0.9994.


Question:
Assets: ETH-USD, JNK
ETH-USD: annualized_mean_return=0.0756, daily_std=0.0204
JNK: annualized_mean_return=0.0252, daily_std=0.0036
Minimum required portfolio return (annualized): 0.0252
Market regime: sideways

Compute portfolio weights (w_ETH-USD, w_JNK) that minimize portfolio variance while satisfying the minimum return constraint. Constraints: all weights >= 0, weights sum to 1. Report as: w_ETH-USD=X.XXXX, w_JNK=X.XXXX

Answer: w_ETH-USD=0.0000, w_JNK=1.0000

Explanation:
Analytic min-variance formula:
  w1* = (σ2² - σ12) / (σ1² + σ2² - 2σ12)
  = (0.000013 - 0.000015) / (0.000415 + 0.000013 - 0.000030)
  Unconstrained: w_ETH-USD=-0.0045
  After long-only clamp: w_ETH-USD=0.0000, w_JNK=1.0000.


Question:
Assets: BNB-USD, INDS
BNB-USD: annualized_mean_return=-0.0504, daily_std=0.0132
INDS: annualized_mean_return=-0.4788, daily_std=0.0109
Minimum required portfolio return (annualized): -0.1808
Market regime: sideways

Compute portfolio weights (w_BNB-USD, w_INDS) that minimize portfolio variance while satisfying the minimum return constraint. Constraints: all weights >= 0, weights sum to 1. Report as: w_BNB-USD=X.XXXX, w_INDS=X.XXXX

Answer: w_BNB-USD=0.6956, w_INDS=0.3044

Explanation:
Analytic min-variance formula:
  w1* = (σ2² - σ12) / (σ1² + σ2² - 2σ12)
  = (0.000118 - -0.000013) / (0.000175 + 0.000118 - -0.000026)
  Unconstrained: w_BNB-USD=0.4115
  After long-only clamp: w_BNB-USD=0.4115, w_INDS=0.5885.


Question:
Assets: SOL-USD, BIL
SOL-USD: annualized_mean_return=1.3356, daily_std=0.0304
BIL: annualized_mean_return=0.0756, daily_std=0.0002
Minimum required portfolio return (annualized): 0.0767
Market regime: sideways

Compute portfolio weights (w_SOL-USD, w_BIL) that minimize portfolio variance while satisfying the minimum return constraint. Constraints: all weights >= 0, weights sum to 1. Report as: w_SOL-USD=X.XXXX, w_BIL=X.XXXX

Answer: w_SOL-USD=0.0011, w_BIL=0.9989

Explanation:
Analytic min-variance formula:
  w1* = (σ2² - σ12) / (σ1² + σ2² - 2σ12)
  = (0.000000 - -0.000001) / (0.000924 + 0.000000 - -0.000001)
  Unconstrained: w_SOL-USD=0.0007
  After long-only clamp: w_SOL-USD=0.0007, w_BIL=0.9993.


Question:
Assets: VEA, SGOV
VEA: annualized_mean_return=0.2016, daily_std=0.0073
SGOV: annualized_mean_return=0.0504, daily_std=0.0001
Minimum required portfolio return (annualized): 0.0888
Market regime: sideways

Compute portfolio weights (w_VEA, w_SGOV) that minimize portfolio variance while satisfying the minimum return constraint. Constraints: all weights >= 0, weights sum to 1. Report as: w_VEA=X.XXXX, w_SGOV=X.XXXX

Answer: w_VEA=0.2540, w_SGOV=0.7460

Explanation:
Analytic min-variance formula:
  w1* = (σ2² - σ12) / (σ1² + σ2² - 2σ12)
  = (0.000000 - -0.000000) / (0.000053 + 0.000000 - -0.000000)
  Unconstrained: w_VEA=0.0009
  After long-only clamp: w_VEA=0.0009, w_SGOV=0.9991.


Question:
Assets: SOL-USD, ITB
SOL-USD: annualized_mean_return=-0.1764, daily_std=0.0332
ITB: annualized_mean_return=0.6804, daily_std=0.0118
Minimum required portfolio return (annualized): 0.4445
Market regime: sideways

Compute portfolio weights (w_SOL-USD, w_ITB) that minimize portfolio variance while satisfying the minimum return constraint. Constraints: all weights >= 0, weights sum to 1. Report as: w_SOL-USD=X.XXXX, w_ITB=X.XXXX

Answer: w_SOL-USD=0.0835, w_ITB=0.9165

Explanation:
Analytic min-variance formula:
  w1* = (σ2² - σ12) / (σ1² + σ2² - 2σ12)
  = (0.000139 - 0.000042) / (0.001103 + 0.000139 - 0.000083)
  Unconstrained: w_SOL-USD=0.0839
  After long-only clamp: w_SOL-USD=0.0839, w_ITB=0.9161.


Question:
Assets: BTC-USD, SHY
BTC-USD: annualized_mean_return=0.4032, daily_std=0.0166
SHY: annualized_mean_return=0.0000, daily_std=0.0010
Minimum required portfolio return (annualized): 0.0020
Market regime: sideways

Compute portfolio weights (w_BTC-USD, w_SHY) that minimize portfolio variance while satisfying the minimum return constraint. Constraints: all weights >= 0, weights sum to 1. Report as: w_BTC-USD=X.XXXX, w_SHY=X.XXXX

Answer: w_BTC-USD=0.0074, w_SHY=0.9926

Explanation:
Analytic min-variance formula:
  w1* = (σ2² - σ12) / (σ1² + σ2² - 2σ12)
  = (0.000001 - -0.000001) / (0.000276 + 0.000001 - -0.000001)
  Unconstrained: w_BTC-USD=0.0062
  After long-only clamp: w_BTC-USD=0.0062, w_SHY=0.9938.


AVAX-USD σ=0.0457, ICSH σ=0.0003, ρ=-0.193. Min-variance weights: AVAX-USD=0.001, ICSH=0.999.

Question:
Assets: AVAX-USD, ICSH
AVAX-USD: annualized_mean_return=0.5796, daily_std=0.0457
ICSH: annualized_mean_return=0.0756, daily_std=0.0003
Minimum required portfolio return (annualized): 0.0763
Market regime: sideways

Compute portfolio weights (w_AVAX-USD, w_ICSH) that minimize portfolio variance while satisfying the minimum return constraint. Constraints: all weights >= 0, weights sum to 1. Report as: w_AVAX-USD=X.XXXX, w_ICSH=X.XXXX

Answer: w_AVAX-USD=0.0015, w_ICSH=0.9985

Explanation:
Analytic min-variance formula:
  w1* = (σ2² - σ12) / (σ1² + σ2² - 2σ12)
  = (0.000000 - -0.000003) / (0.002092 + 0.000000 - -0.000005)
  Unconstrained: w_AVAX-USD=0.0013
  After long-only clamp: w_AVAX-USD=0.0013, w_ICSH=0.9987.


Question:
Assets: LINK-USD, SLV
LINK-USD: annualized_mean_return=-0.3528, daily_std=0.0265
SLV: annualized_mean_return=0.4032, daily_std=0.0163
Minimum required portfolio return (annualized): 0.3553
Market regime: sideways

Compute portfolio weights (w_LINK-USD, w_SLV) that minimize portfolio variance while satisfying the minimum return constraint. Constraints: all weights >= 0, weights sum to 1. Report as: w_LINK-USD=X.XXXX, w_SLV=X.XXXX

Answer: w_LINK-USD=0.0634, w_SLV=0.9366

Explanation:
Analytic min-variance formula:
  w1* = (σ2² - σ12) / (σ1² + σ2² - 2σ12)
  = (0.000266 - -0.000059) / (0.000705 + 0.000266 - -0.000118)
  Unconstrained: w_LINK-USD=0.2988
  After long-only clamp: w_LINK-USD=0.2988, w_SLV=0.7012.


Question:
Assets: EEM, DBB
EEM: annualized_mean_return=0.1512, daily_std=0.0084
DBB: annualized_mean_return=0.3024, daily_std=0.0115
Minimum required portfolio return (annualized): 0.1853
Market regime: bull

Compute portfolio weights (w_EEM, w_DBB) that minimize portfolio variance while satisfying the minimum return constraint. Constraints: all weights >= 0, weights sum to 1. Report as: w_EEM=X.XXXX, w_DBB=X.XXXX

Answer: w_EEM=0.6293, w_DBB=0.3707

Explanation:
Analytic min-variance formula:
  w1* = (σ2² - σ12) / (σ1² + σ2² - 2σ12)
  = (0.000131 - -0.000018) / (0.000070 + 0.000131 - -0.000036)
  Unconstrained: w_EEM=0.6290
  After long-only clamp: w_EEM=0.6290, w_DBB=0.3710.


Question:
Assets: QQQ, MORT
QQQ: annualized_mean_return=0.2268, daily_std=0.0148
MORT: annualized_mean_return=0.0252, daily_std=0.0149
Minimum required portfolio return (annualized): 0.1258
Market regime: sideways

Compute portfolio weights (w_QQQ, w_MORT) that minimize portfolio variance while satisfying the minimum return constraint. Constraints: all weights >= 0, weights sum to 1. Report as: w_QQQ=X.XXXX, w_MORT=X.XXXX

Answer: w_QQQ=0.5088, w_MORT=0.4912

Explanation:
Analytic min-variance formula:
  w1* = (σ2² - σ12) / (σ1² + σ2² - 2σ12)
  = (0.000222 - 0.000158) / (0.000220 + 0.000222 - 0.000317)
  Unconstrained: w_QQQ=0.5089
  After long-only clamp: w_QQQ=0.5089, w_MORT=0.4911.


Question:
Assets: XLE, LQD
XLE: annualized_mean_return=0.1260, daily_std=0.0171
LQD: annualized_mean_return=0.3276, daily_std=0.0069
Minimum required portfolio return (annualized): 0.2173
Market regime: sideways

Compute portfolio weights (w_XLE, w_LQD) that minimize portfolio variance while satisfying the minimum return constraint. Constraints: all weights >= 0, weights sum to 1. Report as: w_XLE=X.XXXX, w_LQD=X.XXXX

Answer: w_XLE=0.1073, w_LQD=0.8927

Explanation:
Analytic min-variance formula:
  w1* = (σ2² - σ12) / (σ1² + σ2² - 2σ12)
  = (0.000048 - 0.000015) / (0.000291 + 0.000048 - 0.000029)
  Unconstrained: w_XLE=0.1085
  After long-only clamp: w_XLE=0.1085, w_LQD=0.8915.


Question:
Assets: EEM, ICSH
EEM: annualized_mean_return=0.3024, daily_std=0.0078
ICSH: annualized_mean_return=0.0504, daily_std=0.0002
Minimum required portfolio return (annualized): 0.1014
Market regime: bull

Compute portfolio weights (w_EEM, w_ICSH) that minimize portfolio variance while satisfying the minimum return constraint. Constraints: all weights >= 0, weights sum to 1. Report as: w_EEM=X.XXXX, w_ICSH=X.XXXX

Answer: w_EEM=0.2024, w_ICSH=0.7976

Explanation:
Analytic min-variance formula:
  w1* = (σ2² - σ12) / (σ1² + σ2² - 2σ12)
  = (0.000000 - 0.000000) / (0.000061 + 0.000000 - 0.000001)
  Unconstrained: w_EEM=-0.0035
  After long-only clamp: w_EEM=0.0000, w_ICSH=1.0000.


LINK-USD σ=0.0364, DBA σ=0.0110, ρ=0.059. Min-variance weights: LINK-USD=0.070, DBA=0.930.

Question:
Assets: LINK-USD, DBA
LINK-USD: annualized_mean_return=-1.2096, daily_std=0.0364
DBA: annualized_mean_return=0.0756, daily_std=0.0110
Minimum required portfolio return (annualized): 0.0140
Market regime: sideways

Compute portfolio weights (w_LINK-USD, w_DBA) that minimize portfolio variance while satisfying the minimum return constraint. Constraints: all weights >= 0, weights sum to 1. Report as: w_LINK-USD=X.XXXX, w_DBA=X.XXXX

Answer: w_LINK-USD=0.0479, w_DBA=0.9521

Explanation:
Analytic min-variance formula:
  w1* = (σ2² - σ12) / (σ1² + σ2² - 2σ12)
  = (0.000122 - 0.000024) / (0.001325 + 0.000122 - 0.000048)
  Unconstrained: w_LINK-USD=0.0701
  After long-only clamp: w_LINK-USD=0.0701, w_DBA=0.9299.


Question:
Assets: ADA-USD, CPER
ADA-USD: annualized_mean_return=-0.4536, daily_std=0.0189
CPER: annualized_mean_return=-0.1764, daily_std=0.0114
Minimum required portfolio return (annualized): -0.2684
Market regime: sideways

Compute portfolio weights (w_ADA-USD, w_CPER) that minimize portfolio variance while satisfying the minimum return constraint. Constraints: all weights >= 0, weights sum to 1. Report as: w_ADA-USD=X.XXXX, w_CPER=X.XXXX

Answer: w_ADA-USD=0.3081, w_CPER=0.6919

Explanation:
Analytic min-variance formula:
  w1* = (σ2² - σ12) / (σ1² + σ2² - 2σ12)
  = (0.000131 - -0.000051) / (0.000357 + 0.000131 - -0.000101)
  Unconstrained: w_ADA-USD=0.3078
  After long-only clamp: w_ADA-USD=0.3078, w_CPER=0.6922.


LINK-USD σ=0.0402, CORN σ=0.0199, ρ=-0.072. Min-variance weights: LINK-USD=0.213, CORN=0.787.

Question:
Assets: LINK-USD, CORN
LINK-USD: annualized_mean_return=-0.3528, daily_std=0.0402
CORN: annualized_mean_return=-0.1512, daily_std=0.0199
Minimum required portfolio return (annualized): -0.1690
Market regime: sideways

Compute portfolio weights (w_LINK-USD, w_CORN) that minimize portfolio variance while satisfying the minimum return constraint. Constraints: all weights >= 0, weights sum to 1. Report as: w_LINK-USD=X.XXXX, w_CORN=X.XXXX

Answer: w_LINK-USD=0.0883, w_CORN=0.9117

Explanation:
Analytic min-variance formula:
  w1* = (σ2² - σ12) / (σ1² + σ2² - 2σ12)
  = (0.000395 - -0.000057) / (0.001615 + 0.000395 - -0.000115)
  Unconstrained: w_LINK-USD=0.2129
  After long-only clamp: w_LINK-USD=0.2129, w_CORN=0.7871.


Question:
Assets: EEM, SGOV
EEM: annualized_mean_return=-0.0252, daily_std=0.0095
SGOV: annualized_mean_return=0.0504, daily_std=0.0002
Minimum required portfolio return (annualized): 0.0488
Market regime: sideways

Compute portfolio weights (w_EEM, w_SGOV) that minimize portfolio variance while satisfying the minimum return constraint. Constraints: all weights >= 0, weights sum to 1. Report as: w_EEM=X.XXXX, w_SGOV=X.XXXX

Answer: w_EEM=0.0003, w_SGOV=0.9997

Explanation:
Analytic min-variance formula:
  w1* = (σ2² - σ12) / (σ1² + σ2² - 2σ12)
  = (0.000000 - 0.000000) / (0.000090 + 0.000000 - 0.000000)
  Unconstrained: w_EEM=-0.0017
  After long-only clamp: w_EEM=0.0000, w_SGOV=1.0000.


Question:
Assets: XLI, DBC
XLI: annualized_mean_return=0.2520, daily_std=0.0068
DBC: annualized_mean_return=0.2772, daily_std=0.0065
Minimum required portfolio return (annualized): 0.2685
Market regime: bull

Compute portfolio weights (w_XLI, w_DBC) that minimize portfolio variance while satisfying the minimum return constraint. Constraints: all weights >= 0, weights sum to 1. Report as: w_XLI=X.XXXX, w_DBC=X.XXXX

Answer: w_XLI=0.3452, w_DBC=0.6548

Explanation:
Analytic min-variance formula:
  w1* = (σ2² - σ12) / (σ1² + σ2² - 2σ12)
  = (0.000042 - 0.000008) / (0.000046 + 0.000042 - 0.000017)
  Unconstrained: w_XLI=0.4723
  After long-only clamp: w_XLI=0.4723, w_DBC=0.5277.


Question:
Assets: XLK, CORN
XLK: annualized_mean_return=0.6804, daily_std=0.0117
CORN: annualized_mean_return=-0.1008, daily_std=0.0179
Minimum required portfolio return (annualized): 0.3093
Market regime: sideways

Compute portfolio weights (w_XLK, w_CORN) that minimize portfolio variance while satisfying the minimum return constraint. Constraints: all weights >= 0, weights sum to 1. Report as: w_XLK=X.XXXX, w_CORN=X.XXXX

Answer: w_XLK=0.7336, w_CORN=0.2664

Explanation:
Analytic min-variance formula:
  w1* = (σ2² - σ12) / (σ1² + σ2² - 2σ12)
  = (0.000322 - 0.000031) / (0.000137 + 0.000322 - 0.000062)
  Unconstrained: w_XLK=0.7338
  After long-only clamp: w_XLK=0.7338, w_CORN=0.2662.


Question:
Assets: XLY, TLT
XLY: annualized_mean_return=0.4788, daily_std=0.0120
TLT: annualized_mean_return=0.5544, daily_std=0.0135
Minimum required portfolio return (annualized): 0.5096
Market regime: sideways

Compute portfolio weights (w_XLY, w_TLT) that minimize portfolio variance while satisfying the minimum return constraint. Constraints: all weights >= 0, weights sum to 1. Report as: w_XLY=X.XXXX, w_TLT=X.XXXX

Answer: w_XLY=0.5597, w_TLT=0.4403

Explanation:
Analytic min-variance formula:
  w1* = (σ2² - σ12) / (σ1² + σ2² - 2σ12)
  = (0.000183 - -0.000001) / (0.000144 + 0.000183 - -0.000002)
  Unconstrained: w_XLY=0.5597
  After long-only clamp: w_XLY=0.5597, w_TLT=0.4403.


Question:
Assets: MTUM, STIP
MTUM: annualized_mean_return=0.5544, daily_std=0.0089
STIP: annualized_mean_return=0.1008, daily_std=0.0016
Minimum required portfolio return (annualized): 0.1033
Market regime: sideways

Compute portfolio weights (w_MTUM, w_STIP) that minimize portfolio variance while satisfying the minimum return constraint. Constraints: all weights >= 0, weights sum to 1. Report as: w_MTUM=X.XXXX, w_STIP=X.XXXX

Answer: w_MTUM=0.0075, w_STIP=0.9925

Explanation:
Analytic min-variance formula:
  w1* = (σ2² - σ12) / (σ1² + σ2² - 2σ12)
  = (0.000003 - 0.000002) / (0.000079 + 0.000003 - 0.000004)
  Unconstrained: w_MTUM=0.0088
  After long-only clamp: w_MTUM=0.0088, w_STIP=0.9912.


Question:
Assets: BTC-USD, XLE
BTC-USD: annualized_mean_return=0.0000, daily_std=0.0285
XLE: annualized_mean_return=0.2772, daily_std=0.0089
Minimum required portfolio return (annualized): 0.2678
Market regime: sideways

Compute portfolio weights (w_BTC-USD, w_XLE) that minimize portfolio variance while satisfying the minimum return constraint. Constraints: all weights >= 0, weights sum to 1. Report as: w_BTC-USD=X.XXXX, w_XLE=X.XXXX

Answer: w_BTC-USD=0.0339, w_XLE=0.9661

Explanation:
Analytic min-variance formula:
  w1* = (σ2² - σ12) / (σ1² + σ2² - 2σ12)
  = (0.000080 - 0.000028) / (0.000812 + 0.000080 - 0.000055)
  Unconstrained: w_BTC-USD=0.0624
  After long-only clamp: w_BTC-USD=0.0624, w_XLE=0.9376.


Question:
Assets: QUAL, REZ
QUAL: annualized_mean_return=0.2268, daily_std=0.0113
REZ: annualized_mean_return=-0.0504, daily_std=0.0149
Minimum required portfolio return (annualized): 0.0717
Market regime: sideways

Compute portfolio weights (w_QUAL, w_REZ) that minimize portfolio variance while satisfying the minimum return constraint. Constraints: all weights >= 0, weights sum to 1. Report as: w_QUAL=X.XXXX, w_REZ=X.XXXX

Answer: w_QUAL=1.0000, w_REZ=0.0000

Explanation:
Analytic min-variance formula:
  w1* = (σ2² - σ12) / (σ1² + σ2² - 2σ12)
  = (0.000222 - 0.000129) / (0.000129 + 0.000222 - 0.000259)
  Unconstrained: w_QUAL=1.0083
  After long-only clamp: w_QUAL=1.0000, w_REZ=0.0000.


Question:
Assets: ADA-USD, INDS
ADA-USD: annualized_mean_return=-0.1260, daily_std=0.0368
INDS: annualized_mean_return=-0.1008, daily_std=0.0102
Minimum required portfolio return (annualized): -0.1030
Market regime: sideways

Compute portfolio weights (w_ADA-USD, w_INDS) that minimize portfolio variance while satisfying the minimum return constraint. Constraints: all weights >= 0, weights sum to 1. Report as: w_ADA-USD=X.XXXX, w_INDS=X.XXXX

Answer: w_ADA-USD=0.0873, w_INDS=0.9127

Explanation:
Analytic min-variance formula:
  w1* = (σ2² - σ12) / (σ1² + σ2² - 2σ12)
  = (0.000104 - -0.000071) / (0.001353 + 0.000104 - -0.000141)
  Unconstrained: w_ADA-USD=0.1092
  After long-only clamp: w_ADA-USD=0.1092, w_INDS=0.8908.


Question:
Assets: FXI, XHB
FXI: annualized_mean_return=1.2852, daily_std=0.0259
XHB: annualized_mean_return=0.6300, daily_std=0.0185
Minimum required portfolio return (annualized): 1.1610
Market regime: sideways

Compute portfolio weights (w_FXI, w_XHB) that minimize portfolio variance while satisfying the minimum return constraint. Constraints: all weights >= 0, weights sum to 1. Report as: w_FXI=X.XXXX, w_XHB=X.XXXX

Answer: w_FXI=0.8104, w_XHB=0.1896

Explanation:
Analytic min-variance formula:
  w1* = (σ2² - σ12) / (σ1² + σ2² - 2σ12)
  = (0.000343 - 0.000178) / (0.000673 + 0.000343 - 0.000356)
  Unconstrained: w_FXI=0.2495
  After long-only clamp: w_FXI=0.2495, w_XHB=0.7505.


Question:
Assets: IWM, REZ
IWM: annualized_mean_return=0.0000, daily_std=0.0108
REZ: annualized_mean_return=0.3024, daily_std=0.0107
Minimum required portfolio return (annualized): 0.2631
Market regime: sideways

Compute portfolio weights (w_IWM, w_REZ) that minimize portfolio variance while satisfying the minimum return constraint. Constraints: all weights >= 0, weights sum to 1. Report as: w_IWM=X.XXXX, w_REZ=X.XXXX

Answer: w_IWM=0.1300, w_REZ=0.8700

Explanation:
Analytic min-variance formula:
  w1* = (σ2² - σ12) / (σ1² + σ2² - 2σ12)
  = (0.000115 - 0.000090) / (0.000116 + 0.000115 - 0.000180)
  Unconstrained: w_IWM=0.4953
  After long-only clamp: w_IWM=0.4953, w_REZ=0.5047.


Question:
Assets: BNB-USD, IYR
BNB-USD: annualized_mean_return=0.1008, daily_std=0.0294
IYR: annualized_mean_return=0.6804, daily_std=0.0089
Minimum required portfolio return (annualized): 0.6702
Market regime: sideways

Compute portfolio weights (w_BNB-USD, w_IYR) that minimize portfolio variance while satisfying the minimum return constraint. Constraints: all weights >= 0, weights sum to 1. Report as: w_BNB-USD=X.XXXX, w_IYR=X.XXXX

Answer: w_BNB-USD=0.0176, w_IYR=0.9824

Explanation:
Analytic min-variance formula:
  w1* = (σ2² - σ12) / (σ1² + σ2² - 2σ12)
  = (0.000080 - 0.000010) / (0.000862 + 0.000080 - 0.000019)
  Unconstrained: w_BNB-USD=0.0760
  After long-only clamp: w_BNB-USD=0.0760, w_IYR=0.9240.


Question:
Assets: AVAX-USD, DBC
AVAX-USD: annualized_mean_return=1.7640, daily_std=0.0493
DBC: annualized_mean_return=0.0504, daily_std=0.0115
Minimum required portfolio return (annualized): 0.4776
Market regime: sideways

Compute portfolio weights (w_AVAX-USD, w_DBC) that minimize portfolio variance while satisfying the minimum return constraint. Constraints: all weights >= 0, weights sum to 1. Report as: w_AVAX-USD=X.XXXX, w_DBC=X.XXXX

Answer: w_AVAX-USD=0.2493, w_DBC=0.7507

Explanation:
Analytic min-variance formula:
  w1* = (σ2² - σ12) / (σ1² + σ2² - 2σ12)
  = (0.000133 - -0.000005) / (0.002429 + 0.000133 - -0.000011)
  Unconstrained: w_AVAX-USD=0.0539
  After long-only clamp: w_AVAX-USD=0.0539, w_DBC=0.9461.


BTC-USD σ=0.0275, HAUZ σ=0.0092, ρ=0.214. Min-variance weights: BTC-USD=0.042, HAUZ=0.958.

Question:
Assets: BTC-USD, HAUZ
BTC-USD: annualized_mean_return=1.6884, daily_std=0.0275
HAUZ: annualized_mean_return=-0.1512, daily_std=0.0092
Minimum required portfolio return (annualized): -0.0926
Market regime: bull

Compute portfolio weights (w_BTC-USD, w_HAUZ) that minimize portfolio variance while satisfying the minimum return constraint. Constraints: all weights >= 0, weights sum to 1. Report as: w_BTC-USD=X.XXXX, w_HAUZ=X.XXXX

Answer: w_BTC-USD=0.0422, w_HAUZ=0.9578

Explanation:
Analytic min-variance formula:
  w1* = (σ2² - σ12) / (σ1² + σ2² - 2σ12)
  = (0.000085 - 0.000054) / (0.000759 + 0.000085 - 0.000109)
  Unconstrained: w_BTC-USD=0.0418
  After long-only clamp: w_BTC-USD=0.0418, w_HAUZ=0.9582.


Question:
Assets: BNB-USD, HYG
BNB-USD: annualized_mean_return=-0.9576, daily_std=0.0425
HYG: annualized_mean_return=0.1008, daily_std=0.0072
Minimum required portfolio return (annualized): -0.4052
Market regime: sideways

Compute portfolio weights (w_BNB-USD, w_HYG) that minimize portfolio variance while satisfying the minimum return constraint. Constraints: all weights >= 0, weights sum to 1. Report as: w_BNB-USD=X.XXXX, w_HYG=X.XXXX

Answer: w_BNB-USD=0.0426, w_HYG=0.9574

Explanation:
Analytic min-variance formula:
  w1* = (σ2² - σ12) / (σ1² + σ2² - 2σ12)
  = (0.000052 - -0.000030) / (0.001809 + 0.000052 - -0.000059)
  Unconstrained: w_BNB-USD=0.0425
  After long-only clamp: w_BNB-USD=0.0425, w_HYG=0.9575.


Question:
Assets: USMV, HYG
USMV: annualized_mean_return=0.1008, daily_std=0.0070
HYG: annualized_mean_return=0.0504, daily_std=0.0058
Minimum required portfolio return (annualized): 0.0655
Market regime: sideways

Compute portfolio weights (w_USMV, w_HYG) that minimize portfolio variance while satisfying the minimum return constraint. Constraints: all weights >= 0, weights sum to 1. Report as: w_USMV=X.XXXX, w_HYG=X.XXXX

Answer: w_USMV=0.3981, w_HYG=0.6019

Explanation:
Analytic min-variance formula:
  w1* = (σ2² - σ12) / (σ1² + σ2² - 2σ12)
  = (0.000034 - 0.000004) / (0.000049 + 0.000034 - 0.000009)
  Unconstrained: w_USMV=0.3974
  After long-only clamp: w_USMV=0.3974, w_HYG=0.6026.


DOT-USD σ=0.0661, SCHH σ=0.0094, ρ=0.057. Min-variance weights: DOT-USD=0.012, SCHH=0.988.

Question:
Assets: DOT-USD, SCHH
DOT-USD: annualized_mean_return=2.8476, daily_std=0.0661
SCHH: annualized_mean_return=-0.3780, daily_std=0.0094
Minimum required portfolio return (annualized): 0.5337
Market regime: sideways

Compute portfolio weights (w_DOT-USD, w_SCHH) that minimize portfolio variance while satisfying the minimum return constraint. Constraints: all weights >= 0, weights sum to 1. Report as: w_DOT-USD=X.XXXX, w_SCHH=X.XXXX

Answer: w_DOT-USD=0.2826, w_SCHH=0.7174

Explanation:
Analytic min-variance formula:
  w1* = (σ2² - σ12) / (σ1² + σ2² - 2σ12)
  = (0.000089 - 0.000035) / (0.004368 + 0.000089 - 0.000071)
  Unconstrained: w_DOT-USD=0.0122
  After long-only clamp: w_DOT-USD=0.0122, w_SCHH=0.9878.


Question:
Assets: SOL-USD, LQD
SOL-USD: annualized_mean_return=0.0504, daily_std=0.0402
LQD: annualized_mean_return=0.0756, daily_std=0.0053
Minimum required portfolio return (annualized): 0.0752
Market regime: sideways

Compute portfolio weights (w_SOL-USD, w_LQD) that minimize portfolio variance while satisfying the minimum return constraint. Constraints: all weights >= 0, weights sum to 1. Report as: w_SOL-USD=X.XXXX, w_LQD=X.XXXX

Answer: w_SOL-USD=0.0159, w_LQD=0.9841

Explanation:
Analytic min-variance formula:
  w1* = (σ2² - σ12) / (σ1² + σ2² - 2σ12)
  = (0.000028 - -0.000030) / (0.001619 + 0.000028 - -0.000060)
  Unconstrained: w_SOL-USD=0.0338
  After long-only clamp: w_SOL-USD=0.0338, w_LQD=0.9662.


Question:
Assets: XLI, IEF
XLI: annualized_mean_return=-0.1260, daily_std=0.0089
IEF: annualized_mean_return=-0.0756, daily_std=0.0055
Minimum required portfolio return (annualized): -0.0798
Market regime: sideways

Compute portfolio weights (w_XLI, w_IEF) that minimize portfolio variance while satisfying the minimum return constraint. Constraints: all weights >= 0, weights sum to 1. Report as: w_XLI=X.XXXX, w_IEF=X.XXXX

Answer: w_XLI=0.0833, w_IEF=0.9167

Explanation:
Analytic min-variance formula:
  w1* = (σ2² - σ12) / (σ1² + σ2² - 2σ12)
  = (0.000030 - 0.000011) / (0.000079 + 0.000030 - 0.000022)
  Unconstrained: w_XLI=0.2183
  After long-only clamp: w_XLI=0.2183, w_IEF=0.7817.


Question:
Assets: BTC-USD, USMV
BTC-USD: annualized_mean_return=1.2852, daily_std=0.0189
USMV: annualized_mean_return=-0.1512, daily_std=0.0058
Minimum required portfolio return (annualized): 0.6296
Market regime: sideways

Compute portfolio weights (w_BTC-USD, w_USMV) that minimize portfolio variance while satisfying the minimum return constraint. Constraints: all weights >= 0, weights sum to 1. Report as: w_BTC-USD=X.XXXX, w_USMV=X.XXXX

Answer: w_BTC-USD=0.5436, w_USMV=0.4564

Explanation:
Analytic min-variance formula:
  w1* = (σ2² - σ12) / (σ1² + σ2² - 2σ12)
  = (0.000033 - -0.000011) / (0.000358 + 0.000033 - -0.000023)
  Unconstrained: w_BTC-USD=0.1082
  After long-only clamp: w_BTC-USD=0.1082, w_USMV=0.8918.


Question:
Assets: XLRE, CSHI
XLRE: annualized_mean_return=0.6048, daily_std=0.0125
CSHI: annualized_mean_return=0.0252, daily_std=0.0004
Minimum required portfolio return (annualized): 0.1495
Market regime: sideways

Compute portfolio weights (w_XLRE, w_CSHI) that minimize portfolio variance while satisfying the minimum return constraint. Constraints: all weights >= 0, weights sum to 1. Report as: w_XLRE=X.XXXX, w_CSHI=X.XXXX

Answer: w_XLRE=0.2145, w_CSHI=0.7855

Explanation:
Analytic min-variance formula:
  w1* = (σ2² - σ12) / (σ1² + σ2² - 2σ12)
  = (0.000000 - -0.000000) / (0.000156 + 0.000000 - -0.000000)
  Unconstrained: w_XLRE=0.0015
  After long-only clamp: w_XLRE=0.0015, w_CSHI=0.9985.


Question:
Assets: ^VIX, SLV
^VIX: annualized_mean_return=-0.3024, daily_std=0.0535
SLV: annualized_mean_return=1.0332, daily_std=0.0171
Minimum required portfolio return (annualized): 0.9901
Market regime: sideways

Compute portfolio weights (w_^VIX, w_SLV) that minimize portfolio variance while satisfying the minimum return constraint. Constraints: all weights >= 0, weights sum to 1. Report as: w_^VIX=X.XXXX, w_SLV=X.XXXX

Answer: w_^VIX=0.0323, w_SLV=0.9677

Explanation:
Analytic min-variance formula:
  w1* = (σ2² - σ12) / (σ1² + σ2² - 2σ12)
  = (0.000293 - 0.000008) / (0.002863 + 0.000293 - 0.000016)
  Unconstrained: w_^VIX=0.0908
  After long-only clamp: w_^VIX=0.0908, w_SLV=0.9092.


Question:
Assets: SOL-USD, VNQI
SOL-USD: annualized_mean_return=0.5544, daily_std=0.0535
VNQI: annualized_mean_return=-0.1260, daily_std=0.0098
Minimum required portfolio return (annualized): 0.2149
Market regime: sideways

Compute portfolio weights (w_SOL-USD, w_VNQI) that minimize portfolio variance while satisfying the minimum return constraint. Constraints: all weights >= 0, weights sum to 1. Report as: w_SOL-USD=X.XXXX, w_VNQI=X.XXXX

Answer: w_SOL-USD=0.5010, w_VNQI=0.4990

Explanation:
Analytic min-variance formula:
  w1* = (σ2² - σ12) / (σ1² + σ2² - 2σ12)
  = (0.000097 - -0.000073) / (0.002860 + 0.000097 - -0.000146)
  Unconstrained: w_SOL-USD=0.0547
  After long-only clamp: w_SOL-USD=0.0547, w_VNQI=0.9453.


Question:
Assets: XLY, XHB
XLY: annualized_mean_return=0.6048, daily_std=0.0110
XHB: annualized_mean_return=0.7560, daily_std=0.0125
Minimum required portfolio return (annualized): 0.6791
Market regime: sideways

Compute portfolio weights (w_XLY, w_XHB) that minimize portfolio variance while satisfying the minimum return constraint. Constraints: all weights >= 0, weights sum to 1. Report as: w_XLY=X.XXXX, w_XHB=X.XXXX

Answer: w_XLY=0.5086, w_XHB=0.4914

Explanation:
Analytic min-variance formula:
  w1* = (σ2² - σ12) / (σ1² + σ2² - 2σ12)
  = (0.000156 - 0.000085) / (0.000122 + 0.000156 - 0.000170)
  Unconstrained: w_XLY=0.6577
  After long-only clamp: w_XLY=0.6577, w_XHB=0.3423.


SOL-USD σ=0.0502, CORN σ=0.0075, ρ=0.036. Min-variance weights: SOL-USD=0.017, CORN=0.983.

Question:
Assets: SOL-USD, CORN
SOL-USD: annualized_mean_return=2.2680, daily_std=0.0502
CORN: annualized_mean_return=-0.5796, daily_std=0.0075
Minimum required portfolio return (annualized): 1.1975
Market regime: sideways

Compute portfolio weights (w_SOL-USD, w_CORN) that minimize portfolio variance while satisfying the minimum return constraint. Constraints: all weights >= 0, weights sum to 1. Report as: w_SOL-USD=X.XXXX, w_CORN=X.XXXX

Answer: w_SOL-USD=0.6241, w_CORN=0.3759

Explanation:
Analytic min-variance formula:
  w1* = (σ2² - σ12) / (σ1² + σ2² - 2σ12)
  = (0.000057 - 0.000014) / (0.002523 + 0.000057 - 0.000027)
  Unconstrained: w_SOL-USD=0.0169
  After long-only clamp: w_SOL-USD=0.0169, w_CORN=0.9831.


MATIC-USD σ=0.0461, ICSH σ=0.0003, ρ=0.070. Min-variance weights: MATIC-USD=0.000, ICSH=1.000.

Question:
Assets: MATIC-USD, ICSH
MATIC-USD: annualized_mean_return=0.7812, daily_std=0.0461
ICSH: annualized_mean_return=0.0504, daily_std=0.0003
Minimum required portfolio return (annualized): 0.3931
Market regime: sideways

Compute portfolio weights (w_MATIC-USD, w_ICSH) that minimize portfolio variance while satisfying the minimum return constraint. Constraints: all weights >= 0, weights sum to 1. Report as: w_MATIC-USD=X.XXXX, w_ICSH=X.XXXX

Answer: w_MATIC-USD=0.4689, w_ICSH=0.5311

Explanation:
Analytic min-variance formula:
  w1* = (σ2² - σ12) / (σ1² + σ2² - 2σ12)
  = (0.000000 - 0.000001) / (0.002128 + 0.000000 - 0.000002)
  Unconstrained: w_MATIC-USD=-0.0004
  After long-only clamp: w_MATIC-USD=0.0000, w_ICSH=1.0000.


Question:
Assets: USMV, SCHP
USMV: annualized_mean_return=0.0504, daily_std=0.0052
SCHP: annualized_mean_return=0.1008, daily_std=0.0029
Minimum required portfolio return (annualized): 0.0942
Market regime: sideways

Compute portfolio weights (w_USMV, w_SCHP) that minimize portfolio variance while satisfying the minimum return constraint. Constraints: all weights >= 0, weights sum to 1. Report as: w_USMV=X.XXXX, w_SCHP=X.XXXX

Answer: w_USMV=0.1310, w_SCHP=0.8690

Explanation:
Analytic min-variance formula:
  w1* = (σ2² - σ12) / (σ1² + σ2² - 2σ12)
  = (0.000008 - 0.000002) / (0.000027 + 0.000008 - 0.000004)
  Unconstrained: w_USMV=0.1994
  After long-only clamp: w_USMV=0.1994, w_SCHP=0.8006.


LINK-USD σ=0.0424, QUAL σ=0.0100, ρ=0.197. Min-variance weights: LINK-USD=0.010, QUAL=0.990.

Question:
Assets: LINK-USD, QUAL
LINK-USD: annualized_mean_return=-0.9576, daily_std=0.0424
QUAL: annualized_mean_return=0.1260, daily_std=0.0100
Minimum required portfolio return (annualized): -0.1140
Market regime: sideways

Compute portfolio weights (w_LINK-USD, w_QUAL) that minimize portfolio variance while satisfying the minimum return constraint. Constraints: all weights >= 0, weights sum to 1. Report as: w_LINK-USD=X.XXXX, w_QUAL=X.XXXX

Answer: w_LINK-USD=0.0098, w_QUAL=0.9902

Explanation:
Analytic min-variance formula:
  w1* = (σ2² - σ12) / (σ1² + σ2² - 2σ12)
  = (0.000101 - 0.000084) / (0.001801 + 0.000101 - 0.000168)
  Unconstrained: w_LINK-USD=0.0098
  After long-only clamp: w_LINK-USD=0.0098, w_QUAL=0.9902.


Question:
Assets: ADA-USD, VNQ
ADA-USD: annualized_mean_return=1.5876, daily_std=0.0356
VNQ: annualized_mean_return=-0.0252, daily_std=0.0129
Minimum required portfolio return (annualized): 1.0957
Market regime: sideways

Compute portfolio weights (w_ADA-USD, w_VNQ) that minimize portfolio variance while satisfying the minimum return constraint. Constraints: all weights >= 0, weights sum to 1. Report as: w_ADA-USD=X.XXXX, w_VNQ=X.XXXX

Answer: w_ADA-USD=0.6950, w_VNQ=0.3050

Explanation:
Analytic min-variance formula:
  w1* = (σ2² - σ12) / (σ1² + σ2² - 2σ12)
  = (0.000166 - 0.000007) / (0.001266 + 0.000166 - 0.000014)
  Unconstrained: w_ADA-USD=0.1119
  After long-only clamp: w_ADA-USD=0.1119, w_VNQ=0.8881.


Question:
Assets: XLB, INDS
XLB: annualized_mean_return=0.4536, daily_std=0.0082
INDS: annualized_mean_return=-0.2016, daily_std=0.0099
Minimum required portfolio return (annualized): 0.2595
Market regime: sideways

Compute portfolio weights (w_XLB, w_INDS) that minimize portfolio variance while satisfying the minimum return constraint. Constraints: all weights >= 0, weights sum to 1. Report as: w_XLB=X.XXXX, w_INDS=X.XXXX

Answer: w_XLB=0.7628, w_INDS=0.2372

Explanation:
Analytic min-variance formula:
  w1* = (σ2² - σ12) / (σ1² + σ2² - 2σ12)
  = (0.000098 - 0.000054) / (0.000068 + 0.000098 - 0.000108)
  Unconstrained: w_XLB=0.7640
  After long-only clamp: w_XLB=0.7640, w_INDS=0.2360.


Question:
Assets: VTI, SHV
VTI: annualized_mean_return=0.3276, daily_std=0.0080
SHV: annualized_mean_return=0.0504, daily_std=0.0002
Minimum required portfolio return (annualized): 0.0505
Market regime: sideways

Compute portfolio weights (w_VTI, w_SHV) that minimize portfolio variance while satisfying the minimum return constraint. Constraints: all weights >= 0, weights sum to 1. Report as: w_VTI=X.XXXX, w_SHV=X.XXXX

Answer: w_VTI=0.0004, w_SHV=0.9996

Explanation:
Analytic min-variance formula:
  w1* = (σ2² - σ12) / (σ1² + σ2² - 2σ12)
  = (0.000000 - -0.000000) / (0.000064 + 0.000000 - -0.000000)
  Unconstrained: w_VTI=0.0016
  After long-only clamp: w_VTI=0.0016, w_SHV=0.9984.


Question:
Assets: XLI, TIP
XLI: annualized_mean_return=-0.0252, daily_std=0.0069
TIP: annualized_mean_return=0.0252, daily_std=0.0016
Minimum required portfolio return (annualized): 0.0198
Market regime: sideways

Compute portfolio weights (w_XLI, w_TIP) that minimize portfolio variance while satisfying the minimum return constraint. Constraints: all weights >= 0, weights sum to 1. Report as: w_XLI=X.XXXX, w_TIP=X.XXXX

Answer: w_XLI=0.0498, w_TIP=0.9502

Explanation:
Analytic min-variance formula:
  w1* = (σ2² - σ12) / (σ1² + σ2² - 2σ12)
  = (0.000002 - 0.000000) / (0.000047 + 0.000002 - 0.000000)
  Unconstrained: w_XLI=0.0474
  After long-only clamp: w_XLI=0.0474, w_TIP=0.9526.


Question:
Assets: EFA, SOL-USD
EFA: annualized_mean_return=0.1512, daily_std=0.0088
SOL-USD: annualized_mean_return=3.8304, daily_std=0.0701
Minimum required portfolio return (annualized): 0.1925
Market regime: sideways

Compute portfolio weights (w_EFA, w_SOL-USD) that minimize portfolio variance while satisfying the minimum return constraint. Constraints: all weights >= 0, weights sum to 1. Report as: w_EFA=X.XXXX, w_SOL-USD=X.XXXX

Answer: w_EFA=0.9765, w_SOL-USD=0.0235

Explanation:
Analytic min-variance formula:
  w1* = (σ2² - σ12) / (σ1² + σ2² - 2σ12)
  = (0.004912 - -0.000041) / (0.000078 + 0.004912 - -0.000082)
  Unconstrained: w_EFA=0.9765
  After long-only clamp: w_EFA=0.9765, w_SOL-USD=0.0235.


Question:
Assets: USMV, XHB
USMV: annualized_mean_return=0.1512, daily_std=0.0047
XHB: annualized_mean_return=-0.1764, daily_std=0.0137
Minimum required portfolio return (annualized): 0.0603
Market regime: sideways

Compute portfolio weights (w_USMV, w_XHB) that minimize portfolio variance while satisfying the minimum return constraint. Constraints: all weights >= 0, weights sum to 1. Report as: w_USMV=X.XXXX, w_XHB=X.XXXX

Answer: w_USMV=1.0000, w_XHB=0.0000

Explanation:
Analytic min-variance formula:
  w1* = (σ2² - σ12) / (σ1² + σ2² - 2σ12)
  = (0.000187 - 0.000027) / (0.000022 + 0.000187 - 0.000053)
  Unconstrained: w_USMV=1.0264
  After long-only clamp: w_USMV=1.0000, w_XHB=0.0000.


QUAL σ=0.0074, BTC-USD σ=0.0293, ρ=0.240. Min-variance weights: QUAL=0.996, BTC-USD=0.004.

Question:
Assets: QUAL, BTC-USD
QUAL: annualized_mean_return=0.5544, daily_std=0.0074
BTC-USD: annualized_mean_return=1.8144, daily_std=0.0293
Minimum required portfolio return (annualized): 0.5579
Market regime: sideways

Compute portfolio weights (w_QUAL, w_BTC-USD) that minimize portfolio variance while satisfying the minimum return constraint. Constraints: all weights >= 0, weights sum to 1. Report as: w_QUAL=X.XXXX, w_BTC-USD=X.XXXX

Answer: w_QUAL=0.9963, w_BTC-USD=0.0037

Explanation:
Analytic min-variance formula:
  w1* = (σ2² - σ12) / (σ1² + σ2² - 2σ12)
  = (0.000856 - 0.000052) / (0.000055 + 0.000856 - 0.000104)
  Unconstrained: w_QUAL=0.9964
  After long-only clamp: w_QUAL=0.9964, w_BTC-USD=0.0036.


MATIC-USD σ=0.0271, VNQ σ=0.0105, ρ=-0.399. Min-variance weights: MATIC-USD=0.209, VNQ=0.791.

Question:
Assets: MATIC-USD, VNQ
MATIC-USD: annualized_mean_return=0.6552, daily_std=0.0271
VNQ: annualized_mean_return=-0.6300, daily_std=0.0105
Minimum required portfolio return (annualized): -0.5114
Market regime: sideways

Compute portfolio weights (w_MATIC-USD, w_VNQ) that minimize portfolio variance while satisfying the minimum return constraint. Constraints: all weights >= 0, weights sum to 1. Report as: w_MATIC-USD=X.XXXX, w_VNQ=X.XXXX

Answer: w_MATIC-USD=0.2088, w_VNQ=0.7912

Explanation:
Analytic min-variance formula:
  w1* = (σ2² - σ12) / (σ1² + σ2² - 2σ12)
  = (0.000110 - -0.000113) / (0.000732 + 0.000110 - -0.000227)
  Unconstrained: w_MATIC-USD=0.2090
  After long-only clamp: w_MATIC-USD=0.2090, w_VNQ=0.7910.


Question:
Assets: QQQ, GLD
QQQ: annualized_mean_return=0.1260, daily_std=0.0105
GLD: annualized_mean_return=0.1512, daily_std=0.0083
Minimum required portfolio return (annualized): 0.1396
Market regime: sideways

Compute portfolio weights (w_QQQ, w_GLD) that minimize portfolio variance while satisfying the minimum return constraint. Constraints: all weights >= 0, weights sum to 1. Report as: w_QQQ=X.XXXX, w_GLD=X.XXXX

Answer: w_QQQ=0.3821, w_GLD=0.6179

Explanation:
Analytic min-variance formula:
  w1* = (σ2² - σ12) / (σ1² + σ2² - 2σ12)
  = (0.000069 - 0.000004) / (0.000110 + 0.000069 - 0.000008)
  Unconstrained: w_QQQ=0.3821
  After long-only clamp: w_QQQ=0.3821, w_GLD=0.6179.


Question:
Assets: BNB-USD, IYR
BNB-USD: annualized_mean_return=0.3024, daily_std=0.0260
IYR: annualized_mean_return=0.2016, daily_std=0.0137
Minimum required portfolio return (annualized): 0.2190
Market regime: sideways

Compute portfolio weights (w_BNB-USD, w_IYR) that minimize portfolio variance while satisfying the minimum return constraint. Constraints: all weights >= 0, weights sum to 1. Report as: w_BNB-USD=X.XXXX, w_IYR=X.XXXX

Answer: w_BNB-USD=0.2169, w_IYR=0.7831

Explanation:
Analytic min-variance formula:
  w1* = (σ2² - σ12) / (σ1² + σ2² - 2σ12)
  = (0.000188 - 0.000002) / (0.000674 + 0.000188 - 0.000004)
  Unconstrained: w_BNB-USD=0.2169
  After long-only clamp: w_BNB-USD=0.2169, w_IYR=0.7831.


Question:
Assets: BTC-USD, SHV
BTC-USD: annualized_mean_return=2.0412, daily_std=0.0266
SHV: annualized_mean_return=0.0504, daily_std=0.0002
Minimum required portfolio return (annualized): 0.0505
Market regime: bull

Compute portfolio weights (w_BTC-USD, w_SHV) that minimize portfolio variance while satisfying the minimum return constraint. Constraints: all weights >= 0, weights sum to 1. Report as: w_BTC-USD=X.XXXX, w_SHV=X.XXXX

Answer: w_BTC-USD=0.0000, w_SHV=1.0000

Explanation:
Analytic min-variance formula:
  w1* = (σ2² - σ12) / (σ1² + σ2² - 2σ12)
  = (0.000000 - 0.000000) / (0.000709 + 0.000000 - 0.000000)
  Unconstrained: w_BTC-USD=-0.0002
  After long-only clamp: w_BTC-USD=0.0000, w_SHV=1.0000.


Question:
Assets: XLK, BIL
XLK: annualized_mean_return=0.1764, daily_std=0.0116
BIL: annualized_mean_return=0.0504, daily_std=0.0002
Minimum required portfolio return (annualized): 0.0504
Market regime: sideways

Compute portfolio weights (w_XLK, w_BIL) that minimize portfolio variance while satisfying the minimum return constraint. Constraints: all weights >= 0, weights sum to 1. Report as: w_XLK=X.XXXX, w_BIL=X.XXXX

Answer: w_XLK=0.0002, w_BIL=0.9998

Explanation:
Analytic min-variance formula:
  w1* = (σ2² - σ12) / (σ1² + σ2² - 2σ12)
  = (0.000000 - -0.000000) / (0.000134 + 0.000000 - -0.000000)
  Unconstrained: w_XLK=0.0013
  After long-only clamp: w_XLK=0.0013, w_BIL=0.9987.


MATIC-USD σ=0.0227, SGOV σ=0.0001, ρ=-0.010. Min-variance weights: MATIC-USD=0.000, SGOV=1.000.

Question:
Assets: MATIC-USD, SGOV
MATIC-USD: annualized_mean_return=-1.4616, daily_std=0.0227
SGOV: annualized_mean_return=0.0504, daily_std=0.0001
Minimum required portfolio return (annualized): 0.0504
Market regime: sideways

Compute portfolio weights (w_MATIC-USD, w_SGOV) that minimize portfolio variance while satisfying the minimum return constraint. Constraints: all weights >= 0, weights sum to 1. Report as: w_MATIC-USD=X.XXXX, w_SGOV=X.XXXX

Answer: w_MATIC-USD=-0.0000, w_SGOV=1.0000

Explanation:
Analytic min-variance formula:
  w1* = (σ2² - σ12) / (σ1² + σ2² - 2σ12)
  = (0.000000 - -0.000000) / (0.000517 + 0.000000 - -0.000000)
  Unconstrained: w_MATIC-USD=0.0001
  After long-only clamp: w_MATIC-USD=0.0001, w_SGOV=0.9999.


Question:
Assets: FXI, BIL
FXI: annualized_mean_return=0.4788, daily_std=0.0141
BIL: annualized_mean_return=0.0504, daily_std=0.0001
Minimum required portfolio return (annualized): 0.0504
Market regime: bull

Compute portfolio weights (w_FXI, w_BIL) that minimize portfolio variance while satisfying the minimum return constraint. Constraints: all weights >= 0, weights sum to 1. Report as: w_FXI=X.XXXX, w_BIL=X.XXXX

Answer: w_FXI=0.0001, w_BIL=0.9999

Explanation:
Analytic min-variance formula:
  w1* = (σ2² - σ12) / (σ1² + σ2² - 2σ12)
  = (0.000000 - 0.000000) / (0.000199 + 0.000000 - 0.000001)
  Unconstrained: w_FXI=-0.0014
  After long-only clamp: w_FXI=0.0000, w_BIL=1.0000.


Question:
Assets: XLK, ICSH
XLK: annualized_mean_return=0.6300, daily_std=0.0113
ICSH: annualized_mean_return=0.0504, daily_std=0.0002
Minimum required portfolio return (annualized): 0.0506
Market regime: bull

Compute portfolio weights (w_XLK, w_ICSH) that minimize portfolio variance while satisfying the minimum return constraint. Constraints: all weights >= 0, weights sum to 1. Report as: w_XLK=X.XXXX, w_ICSH=X.XXXX

Answer: w_XLK=0.0005, w_ICSH=0.9995

Explanation:
Analytic min-variance formula:
  w1* = (σ2² - σ12) / (σ1² + σ2² - 2σ12)
  = (0.000000 - 0.000000) / (0.000128 + 0.000000 - 0.000001)
  Unconstrained: w_XLK=-0.0020
  After long-only clamp: w_XLK=0.0000, w_ICSH=1.0000.


Question:
Assets: MTUM, BNO
MTUM: annualized_mean_return=0.2520, daily_std=0.0096
BNO: annualized_mean_return=-0.3780, daily_std=0.0212
Minimum required portfolio return (annualized): -0.1640
Market regime: sideways

Compute portfolio weights (w_MTUM, w_BNO) that minimize portfolio variance while satisfying the minimum return constraint. Constraints: all weights >= 0, weights sum to 1. Report as: w_MTUM=X.XXXX, w_BNO=X.XXXX

Answer: w_MTUM=0.8314, w_BNO=0.1686

Explanation:
Analytic min-variance formula:
  w1* = (σ2² - σ12) / (σ1² + σ2² - 2σ12)
  = (0.000448 - 0.000001) / (0.000092 + 0.000448 - 0.000002)
  Unconstrained: w_MTUM=0.8313
  After long-only clamp: w_MTUM=0.8313, w_BNO=0.1687.


Question:
Assets: XRP-USD, VTI
XRP-USD: annualized_mean_return=0.4284, daily_std=0.0513
VTI: annualized_mean_return=0.5292, daily_std=0.0067
Minimum required portfolio return (annualized): 0.4831
Market regime: sideways

Compute portfolio weights (w_XRP-USD, w_VTI) that minimize portfolio variance while satisfying the minimum return constraint. Constraints: all weights >= 0, weights sum to 1. Report as: w_XRP-USD=X.XXXX, w_VTI=X.XXXX

Answer: w_XRP-USD=0.0063, w_VTI=0.9937

Explanation:
Analytic min-variance formula:
  w1* = (σ2² - σ12) / (σ1² + σ2² - 2σ12)
  = (0.000044 - 0.000028) / (0.002628 + 0.000044 - 0.000057)
  Unconstrained: w_XRP-USD=0.0062
  After long-only clamp: w_XRP-USD=0.0062, w_VTI=0.9938.


Question:
Assets: VEA, SHY
VEA: annualized_mean_return=0.1764, daily_std=0.0099
SHY: annualized_mean_return=0.0000, daily_std=0.0016
Minimum required portfolio return (annualized): 0.0073
Market regime: sideways

Compute portfolio weights (w_VEA, w_SHY) that minimize portfolio variance while satisfying the minimum return constraint. Constraints: all weights >= 0, weights sum to 1. Report as: w_VEA=X.XXXX, w_SHY=X.XXXX

Answer: w_VEA=0.0599, w_SHY=0.9401

Explanation:
Analytic min-variance formula:
  w1* = (σ2² - σ12) / (σ1² + σ2² - 2σ12)
  = (0.000003 - -0.000004) / (0.000098 + 0.000003 - -0.000007)
  Unconstrained: w_VEA=0.0568
  After long-only clamp: w_VEA=0.0568, w_SHY=0.9432.


Question:
Assets: SOL-USD, ITB
SOL-USD: annualized_mean_return=1.3356, daily_std=0.0526
ITB: annualized_mean_return=0.2016, daily_std=0.0150
Minimum required portfolio return (annualized): 0.2346
Market regime: sideways

Compute portfolio weights (w_SOL-USD, w_ITB) that minimize portfolio variance while satisfying the minimum return constraint. Constraints: all weights >= 0, weights sum to 1. Report as: w_SOL-USD=X.XXXX, w_ITB=X.XXXX

Answer: w_SOL-USD=0.0494, w_ITB=0.9506

Explanation:
Analytic min-variance formula:
  w1* = (σ2² - σ12) / (σ1² + σ2² - 2σ12)
  = (0.000224 - 0.000085) / (0.002771 + 0.000224 - 0.000170)
  Unconstrained: w_SOL-USD=0.0494
  After long-only clamp: w_SOL-USD=0.0494, w_ITB=0.9506.


Question:
Assets: XRP-USD, USMV
XRP-USD: annualized_mean_return=-0.6804, daily_std=0.0250
USMV: annualized_mean_return=0.4788, daily_std=0.0051
Minimum required portfolio return (annualized): 0.3356
Market regime: sideways

Compute portfolio weights (w_XRP-USD, w_USMV) that minimize portfolio variance while satisfying the minimum return constraint. Constraints: all weights >= 0, weights sum to 1. Report as: w_XRP-USD=X.XXXX, w_USMV=X.XXXX

Answer: w_XRP-USD=0.0446, w_USMV=0.9554

Explanation:
Analytic min-variance formula:
  w1* = (σ2² - σ12) / (σ1² + σ2² - 2σ12)
  = (0.000026 - -0.000003) / (0.000623 + 0.000026 - -0.000006)
  Unconstrained: w_XRP-USD=0.0443
  After long-only clamp: w_XRP-USD=0.0443, w_USMV=0.9557.


Question:
Assets: EWJ, ETH-USD
EWJ: annualized_mean_return=0.2520, daily_std=0.0098
ETH-USD: annualized_mean_return=1.4868, daily_std=0.0260
Minimum required portfolio return (annualized): 0.3788
Market regime: sideways

Compute portfolio weights (w_EWJ, w_ETH-USD) that minimize portfolio variance while satisfying the minimum return constraint. Constraints: all weights >= 0, weights sum to 1. Report as: w_EWJ=X.XXXX, w_ETH-USD=X.XXXX

Answer: w_EWJ=0.8809, w_ETH-USD=0.1191

Explanation:
Analytic min-variance formula:
  w1* = (σ2² - σ12) / (σ1² + σ2² - 2σ12)
  = (0.000674 - 0.000006) / (0.000096 + 0.000674 - 0.000012)
  Unconstrained: w_EWJ=0.8808
  After long-only clamp: w_EWJ=0.8808, w_ETH-USD=0.1192.


Question:
Assets: USMV, HAUZ
USMV: annualized_mean_return=0.3276, daily_std=0.0052
HAUZ: annualized_mean_return=0.1260, daily_std=0.0102
Minimum required portfolio return (annualized): 0.3092
Market regime: sideways

Compute portfolio weights (w_USMV, w_HAUZ) that minimize portfolio variance while satisfying the minimum return constraint. Constraints: all weights >= 0, weights sum to 1. Report as: w_USMV=X.XXXX, w_HAUZ=X.XXXX

Answer: w_USMV=0.9586, w_HAUZ=0.0414

Explanation:
Analytic min-variance formula:
  w1* = (σ2² - σ12) / (σ1² + σ2² - 2σ12)
  = (0.000105 - 0.000024) / (0.000027 + 0.000105 - 0.000047)
  Unconstrained: w_USMV=0.9555
  After long-only clamp: w_USMV=0.9555, w_HAUZ=0.0445.