instruction stringlengths 15 26.1k |
|---|
A lot has been written on the Fama-French and Carhart factors -- including that SMB may help proxy for the market index being too narrowly-defined. Here you may also be facing that problem. Why else might your coefficient estimates have changed so much? Perhaps HML, SMB, or MOM is multicollinear with your benchmark ind... |
I'm working on a problem where an asset owner (e.g., owner of a factory, power plant, etc.) can take a number of possible decisions (say 10). Each of those 10 decisions entails certain actions, but the profitability of those decisions is not known in advance (because of uncertainty in a number of the underlying variabl... |
Good ways to select best decision among N decisions, each with a profit/loss distribution? |
Let me specific. Suppose that you have the following process:
\begin{align}
z_t &= \sigma_t \epsilon_t \\
\sigma_t &= \sigma \exp \left( \frac{v_t}{2} \right)
\end{align}
where $v_t$ is the latent volatility component. This component could obey an AR(1) model, but I leave it open. My primary interest is... |
Can you approximate stochastic volatility processes using GARCH processes? |
I'm taking a Calculus 2 course this Fall, and for my honors project, I will be using the IRR function. My professor is requesting that I figure out a way to use an integral with the IRR.
The cash flow scenario being modeled has first period/outgoing/negative cash flow (NPV variable), and one final terminal positive ... |
Using Integrals With Internal Rate of Return? |
I think your question can be split into two parts: (i) how to value a swap mathematically and (ii) how swaps actually work as a traded product.
**Part (i)**:
As noob2 pointed out, "theoretically", a swap is valued with the help of two curves: one "forward" curve and one "discounting" curve. Say you want to "value... |
From my understanding, we have to integrate $N(d1(S_x-D,B,t))$ on both asset-price and time-space to derive the Early Exercise Premium $EEP(B,t)$ on each $t$ before the ex-date to get current early exercise premium $EEP(S,0)$. Where
$$S_x = S \exp((r-\sigma^2/2) t + x \sigma \sqrt{t})$$ Is this correct?
When... |
This is maybe a silly question, but I want to understand. As far as I understand an AR(1) model, it is basically a linear regression model with the same but lagged variable, right?
However I am wondering how the different results can be explained when we apply an OLS on the lagged price time series vs. on the return... |
We can get bond live prices from various venues, for example, BBG's CBBT prices. Usually you would get bid/ask prices. Are these prices actually where the bonds are/can be traded ? If not, what drives the actual trading prices for a bond.
If you want to come up with a sensible fair price for a bond ETF that is con... |
We can get bond live prices from various venues, for example, BBG's CBBT prices. Usually you would get bid/ask prices.
- Are these prices prices that people called bonds' marked prices ?
- are they actually where the bonds are/can be traded ? If not, what drives the actual trading prices for a bond.
- If you... |
I have a mathematical / theoretical question regarding the PV of an Overnight Index Swap (Floating Side) at the time of fixing.
Starting from this question:
https://quant.stackexchange.com/questions/34675/how-to-compute-overnight-index-swap-ois-fixed-rate
--> At each Fixing Date of the Floating Cash Flows will... |
This is maybe a silly question, but I want to understand. As far as I understand an AR(1) model, it is basically a linear regression model with the same but lagged variable, right?
However I am wondering how the different results can be explained when we apply an OLS on the lagged price time series vs. on the return... |
I was looking at some old post : https://quant.stackexchange.com/questions/30730/variance-of-time-integral-of-squared-brownian-motion?rq=1
I failed to grasp 2 derivations -
1) $\text{Cov}\left(\int_{0}^{t}W^3_tdW_s\,,\,\int_{0}^{t}W^2_tds\right)$. I know this can eventually be written as $E \left[ \left( \int_{0}... |
Earnings are down 42% while the market is flat over march. Why are people assuming total economic collapse is great? Are they assuming iPhones will enter a massive growth spurt just because people are staying home? |
Why has the market gone up while earnings got pummeled? |
The research paper ["The Allegory of the Hawk and Serpent"][1] describes an asset allocation referred to as the "Dragon" Portfolio, which allocates 18% to "active long volatility". The backtesting methodology to implement this strategy is described as:
> We modeled the strategy as buying Equity volatility (via opti... |
How to implement the “Active Long Volatility” portion of the Dragon Portfolio? |
Meaning, 'as a measure of intrinsic value, cant you use P/S to predict, loosely, future stock price movements'?
Not even close at the index level, and certainly not at the stock level. Not sure how you've set up your regression to get an R2 of .25 with P/S as your only independent variable, but I'd almost guarantee... |
1. Let's use the following expression (derived in Quantuple's answer [in your link][1]), which will help us tidy up the product using [Ito's Isometry][2]
\begin{align}
\int^t_0 W^2_s ds = 2 \int^t_0 (t-s)W_s dW_s + {\frac {t^2} 2}
\end{align}
Now looking at the expectation
\begin{align}
{\mathbb E}\Bigl[ \in... |
I was looking at some old post : https://quant.stackexchange.com/questions/30730/variance-of-time-integral-of-squared-brownian-motion?rq=1
I failed to grasp 2 derivations -
1) $\text{Cov}\left(\int_{0}^{t}W^3_sdW_s\,,\,\int_{0}^{t}W^2_sds\right)$. I know this can eventually be written as $\mathbb{E} \left[ \left(... |
1. Let's use the following expression (derived in Quantuple's answer [in your link][1]), which will help us tidy up the product using [Ito's Isometry][2]
\begin{align}
\int^t_0 W^2_s ds = 2 \int^t_0 (t-s)W_s dW_s + {\frac {t^2} 2}
\end{align}
Now looking at the expectation
\begin{align}
{\mathbb E}\Bigl[ \in... |
1. Let's use the following expression (derived in Quantuple's answer [in your link][1]), which will help us tidy up the product using [Ito's Isometry][2]
\begin{align}
\int^t_0 W^2_s ds = 2 \int^t_0 (t-s)W_s dW_s + {\frac {t^2} 2}
\end{align}
Now looking at the expectation
\begin{align}
{\mathbb E}\Bigl[ \in... |
I have a mathematical / theoretical question regarding the PV of an Overnight Index Swap (Floating Side) at the time of fixing.
Starting from this question:
https://quant.stackexchange.com/questions/34675/how-to-compute-overnight-index-swap-ois-fixed-rate
--> At each Fixing Date of the Floating Cash Flows will... |
**Other Way**
By application of Ito's lemma , we have
$$W^4_t=4\int_{0}^{t}W^3_sdW_s+6\int_{0}^{t}W^2_sds\tag 1$$
We [know][1]
> $$\left\{ \begin{align} &\mathbb{E}\left[ {{W}^{2n+1}}(t)
\right]=0\,\,\,\,\,\,\,\,\,\,\,\,\,\, \\ & \quad \mathbb{E}\left[
{{W}^{2n}}(t) \right]=\frac{(2n)!}{{{2}^{n}}n\,!}\,{{... |
I've priced an exotic option with Monte Carlo method under the Heston model. Then I want to estimate Wrong way risk.
In a paper I've found this method to calculate WWR: WWR can be modeled by means of joint simulation of underlying risk factors and credit factors; the dependence structure is modeled by the correlation ... |
I understand Markowitz and targeting returns to minimize our variance. I know this optimization problem well and its constraints. However when the reverse scenario is to be considered I get very confused. How do I mathematically show optimal portfolio weights when I want to **target my variance** to maximize my return?... |
I am looking for some good textbook to understand xVA and related calculations. Can you please suggest few?
Your pointer will be highly appreciated.
Many thanks, |
If i have a vector of expected returns $A$, a covariance matrix $C$ and a vector of the corresponding weights $W$ for each investment, is it possible to generate the efficient frontier with vector algebra? I am sure I have seen the efficient frontier in matrix form somewhere but I cant remember it, something like $W^TA... |
Can I build an efficient frontier using matrix algebra? |
I hope you can help me with this rather basic question that I asked myself. A random vector $(X_1,...,X_n)$ is said to be exchangeable if it has the same distribution as the permuted random vector $(X_{\pi(1)},...,X_{\pi(d)})$, for any permutation $(\pi{(1)},...\pi{(d)})$.
Can you say that this is the case if and on... |
someone knows, maybe websites / blogs where I can find tips (preferably ready codes) to simulate the trajectory of processes? So far I only need the Poisson process and the compound Poisson process but I would like to learn to simulate more advanced processes as well so I will be grateful for every source |
In Natenberg (1994) Chapter 11 he outlines the Put-Call parity relationships.
```
Stock Price = Call Price - Put Price + Exercise Price - Carrying Costs + Dividends
Call Price = Stock Price - Exercise Price + Put Price + Carrying Costs - Dividends
Put Price = Call Price + Exercise Price - Stock Price - Carry... |
Under Put-Call Parity, why do we add the cost of carry to Call prices but subtract them from the Stock price and Put prices? |
The time between two events in a poisson distribution has an exponential distribution, so the easiest thing to do is simulate a sequence of exponentially distributed variables and use these as the times between events, [as discussed in this primer][1].
To simulate variables given a uniform RNG, we need [the reverse ... |
The time between two events in a poisson distribution has an exponential distribution, so the easiest thing to do is simulate a sequence of exponentially distributed variables and use these as the times between events, [as discussed in this primer][1].
To simulate variables given a uniform RNG, we need [the reverse ... |
You seem to ask the following many times: "Under Put-Call Parity shouldn't we add the carrying costs to only the stock price? And then subtract the carrying costs only from the call and put?"
Those three equalities are not definitions. In the first equation, you do not add carry to the stock price unless you move it... |
Do basket options have a closed form valuation formula? |
The Sharpe ratio is an example of a performance measure for *individual* mean-variance efficient portfolios, regardless if they maximize the Sharpe ratio or not. The efficient frontier, however, consists of several portfolios.
Is there some sort of performance metric that describes the *entire* frontier? So that if ... |
Is there a performance measure for the entire efficient frontier? |
How to implement an “Active Long Volatility” Strategy? |
Try and think about linear and non-correlations in terms of joint probability density functions. What does it mean for two assets to be linearly or non-linearly correlated?
Suppose we hypothesize a non-linear relationship between two (asset returns) variables as the following:
$$ Y = \pm \sqrt{4 - X^2} + \epsi... |
Try and think about linear and non-linear correlations in terms of joint probability density functions. What does it mean for two assets to be linearly or non-linearly correlated?
Suppose we hypothesize a non-linear relationship between two (asset returns) variables as the following:
$$ Y = \pm \sqrt{4 - X^2} ... |
I'm not completely certain from your question, but I'm going to assume you have a basket of $n$ stocks with prices $S_0(t)$ to $S_n(t)$, and you want to price an option with payoff at $C(\tau)$ at time $\tau$ equal to
\begin{align}
C(\tau) = \max\Bigl({\frac 1 n}\sum^n_{i=0} S_i - K, 0\Bigr)
\end{align}
where $K$... |
In addition to StackG's answer, here is a good introductory overview of several (approximate and semi-analytical) methods to price baskets in a Black-Scholes framework:
[Krekel et al - An analysis of pricing methods for basket options][1]
[1]: https://scholar.google.nl/scholar?cluster=866282096263303311&hl=nl... |
someone knows, maybe websites / blogs where I can find tips (preferably ready codes) to simulate the trajectory of processes? So far I only need the Poisson process and the compound Poisson process but I would like to learn to simulate more advanced processes as well so I will be grateful for every source
EDIT: I ed... |
FX convertability modelling: have FX markets ever closed down? |
I am currently trying to learn more about options trading and option strategies. One thing I have noticed recently is that for a lof of stocks I look up on yahoo finance often a very low open interest and volume is shown even for large cap stocks such as UPS, Coca Cola etc. For example
if I look up the price of KO h... |
I hope you can help me with this rather basic question that I asked myself. A random vector $(X_1,...,X_n)$ is said to be exchangeable if it has the same distribution as the permuted random vector $(X_{\pi(1)},...,X_{\pi(d)})$, for any permutation $(\pi{(1)},...\pi{(d)})$.
Can you say that this is the case if and on... |
I am trying to use QuantLib to model short rate and looks like QL has some material here
http://gouthamanbalaraman.com/blog/hull-white-simulation-quantlib-python.html
I have been able to simulate using the actual term structure, although in the attached link for simplicity GB has assumed flat forwards. Which is wha... |
Quantlib: How do I price a ZC bond using the Hull White model? |
I'm not completely certain from your question, but I'm going to assume you have a basket of $n$ stocks with prices $S_0(t)$ to $S_n(t)$, and you want to price an option with payoff at $C(\tau)$ at time $\tau$ equal to
\begin{align}
C(\tau) = \max\Bigl({\frac 1 n}\sum^n_{i=1} S_i - K, 0\Bigr)
\end{align}
where $K$... |
If I have a portfolio consisting of weights -12,11,3,-2,5,-5, I know that negative weights correspond to shorting but what do these large weights represent? I thought the weights are the proportion of your portfolio invested into each stock. Is it to do with leverage? Can I convert these weights to percentage weights c... |
What do large weights above 1 in a portfolio represent? |
I have a dataset with monthly returns (In decimals)
**Jan-2008, Feb-2008 .... Dec-2008, Jan-2009 .... Dec-2017**
This is what I have done,
```
# Formula (((1+r1/100) * (1+r2/100) .. ) ^ 1/n ) - 1
df["Rate of Return"] = df["Rate of Return"].apply(lambda x: 1+(x/100))
ann_return = pow(df["Rate of Return"].pr... |
Calculate annualized returns and annualized volatility from monthly returns? |
I assume you found these weights by Markowitz Optimization? It is quite common that MVO will deliver *extreme weights* with some weights well above 100 percent (implying leverage, i.e. buying the stock on borrowed money) and others massively negative meaning a leveraged short position. These weights are not usable in a... |
I assume you found these weights by Markowitz Optimization? It is quite common that MVO will deliver *extreme weights* with some weights well above 100 percent (implying leverage, i.e. buying the stock on borrowed money) and others massively negative meaning a leveraged short position. These weights are not usable in a... |
I assume you found these weights by Markowitz Optimization? It is quite common that MVO will deliver *extreme weights* with some weights well above 100 percent (implying leverage, i.e. buying the stock on borrowed money) and others massively negative meaning a leveraged short position. These weights are not usable in a... |
I've priced an exotic option with Monte Carlo method under the Heston model. Then I want to estimate Wrong way risk.
In a paper I've found this method to calculate WWR: WWR can be modeled by means of joint simulation of underlying risk factors and credit factors; the dependence structure is modeled by the correlation ... |
I'm not completely certain from your question, but I'm going to assume you have a basket of $n$ stocks with prices $S_0(t)$ to $S_n(t)$, and you want to price an option with payoff at $C(\tau)$ at time $\tau$ equal to
\begin{align}
C(\tau) = \max\Bigl({\frac 1 n}\sum^n_{i=1} S_i - K, 0\Bigr)
\end{align}
where $K$... |
in this paper ["The Volatility Smile and Its Implied Tree" - Derman and Kani 1994][1] i understand the derivation of all equations up to 7.
But eq 8 i cannot figure out how to derive! i have asked a quant at work who looked for 10mins and also couldnt figure it out, therefore i hope you guys can help? Note that i su... |
Do quants need to know Accounting?
In my school's undergrad Quant program, we had Financial Accounting and Managerial Accounting, which were listed as prerequisites for our undergrad Finance subjects.
I am taking grad Quant now in the same school, and I have not seen Accounting ever turn up again except in Financ... |
I would just like to confirm my understanding of how the FED controls interest rates. In my view there's no such thing as changing an interest rate. Because rate/yield is just an effect of price action.
So when the FED 'cuts rates', it starts buying more bonds.
When the FED does a rate hike, it sells bonds.
It's j... |
I would just like to confirm my understanding of how the FED controls interest rates. In my view there's no such thing as changing an interest rate. Because rate/yield is just an effect of price action.
So when the FED 'cuts rates', it starts buying more bonds.
When the FED does a rate hike, it sells bonds.
It's j... |
First of all, when you try nonlinear modelling, you should start with a linear model. Did you tried one? what was the result?
It seems that your non linear model for day $d$ (blue curve) is close to the value the day before (red curve). You model may be close to
$$\hat Y(d)=Y(d-1)+f(Y(d-1),Y(d-2),\ldots;X(d-1),X(d... |
This does not imply overestimation bias. We expect a negative autocorrelation in high- and ultra-high-frequency (every trade) data due to *bid-ask bounce*. Bounce occurs when buy and sell orders trading at the offer and bid are interspersed; that yields what seems to be returns even when the bid, ask, and midpoint do n... |
Isn't this model just a bunch of classical Heston volatility processes, driven by the same Brownian motion? In this case, you can use some common schemes like Milstein. At least as a starter to toy with the model. If speed/accuracy is an issue, there probably exist some clever solutions as well. |
I am interested in the ways how those leveraged ETFs, e.g. TQQQ, achieve their leveraged investment objective.
Questions are around,
- Do they use stock options of the underlying asset primarily to gain the leverage?
- If I want to achieve 3X performance for an individual stock, what kind of methodologies tha... |
How do leveraged ETFs achieve their investment objectives? |
How does one show that:
$$ \mathbb{E}\left[ \int f(W_s)dWs \right] = 0 $$
For all $f()$ that are powers of $W(s)$?? I assume that one would have to go via the definition of Ito integral and express the integral as a sum over martingale differences?
I tried doing that, but it didn't work for me: Taking $f(W(s)... |
I am working with the rugarch package which includes a solver.control argument. I am using the solnp solver. I can pass values for tol and delta. In the rsolnp the authors suggest that the control parameters need to be **specified accordingly to the user's problem**. However, I do not understand what tol and delta exac... |
I know that the Heston volatility model should be the best approach for computing fair volatility on capped variance swap but is there a way to estimate it from replication portfolio?
What I call capped variance swap is a VS with a cap on the realized volatility in order to bound the maximum payoff for the buyer.
R... |
Should we adjust greeks on stock splits? Let's just ask about splits instead of reverse splits. I'm also interested how answers change if we change models/assumptions.
I have some contradicting thoughts:
1) We should not adjust, because market conditions are the same i.e. market cap stays the same, and we assume tr... |
Suppose we have a portfolio with many assets.
Since this portfolio receives monthly contributions and withdrawals, what is the best method to evaluate its global rate of return and avoid computing these contributions as a "profit" and withdrawals as "losses"?
I've already seen some people using abstract entities ... |
Assuming no dividends, the put-call parity equation says:
$c + \mathrm{Ke}^\mathrm{-rT} = p + S$
where $c$ is the price of the call, $p$ is the price of the put, $S$ is the current stock price, $K$ is the option strike price, $r$ is the risk-free rate, $T$ is the time to expiry.
In *You Can Be a Stock Market G... |
Assuming no dividends, the put-call parity equation says:
$c + \mathrm{Ke}^\mathrm{-rT} = p + S$
where $c$ is the price of the European call, $p$ is the price of the European put, $S$ is the current stock price, $K$ is the option strike price, $r$ is the risk-free rate, $T$ is the time to expiry.
In *You Can B... |
I have been struggling with the problem below for quite some time now. I really don't know how to approach it. All I could think of is to use the Black-Scholes formula with $T \rightarrow \infty$, but that would only leave the stock price, $S_t$, on the right-hand side, if I am not mistaken. This seems a bit too sim... |
Basic question , but if I do a daily regression and get an alpha of 0.00004. Should the yearly alpha be : 0.00004 *100 *252 = 1.008% OR 0.00004 * 100 *365 = 1.46%. What is considered the yearly alpha if one wants to know the outperformance of a manager annually? Should one use 252 trading days or 365 days in a year?
... |
When the market talks about 5Y5Y expectation, is it referring to `FWISUS55 Index`, or `G0169 5Y5Y BLC2 Curncy` on Bloomberg? I suspect it's the first one (e.g. comparing to [FRED][1]), but can't explain why, or what's the difference between the two.
[1]: https://fred.stlouisfed.org/series/T5YIFR |
Which is the "correct" 5Y5Y Inflation Expectation on Bloomberg, and what are the differences? |
Assuming no dividends, the put-call parity equation says:
$c + \mathrm{Ke}^\mathrm{-rT} = p + S$
where $c$ is the price of the European call, $p$ is the price of the European put, $S$ is the current stock price, $K$ is the option strike price, $r$ is the risk-free rate, $T$ is the time to expiry.
In *You Can B... |
As mentioned in the title, I am trying to calculate MC VaR for a portfolio consisting entirely of bonds.
I already modeled the zero curve using Vasicek and Cox,Ingersoll & Ross models.
Next steps are:
- Valuate the portfolio at date 0.
- Simulate N zero curves.
- Revaluate the portfolio N times.
- Calcula... |
Assuming no dividends, the put-call parity equation says:
$c + \mathrm{Ke}^\mathrm{-rT} = p + S$
where $c$ is the price of the European call, $p$ is the price of the European put, $S$ is the current stock price, $K$ is the option strike price, $r$ is the risk-free rate, $T$ is the time to expiry.
In *You Can B... |
i am not very good at finance ,but i have been trying to calculate the example from this link. https://www.dropbox.com/s/egfx0ktolojfsek/3.PRIIPs%20Workshop%20-%20Risk%20Reward%20Methodology.pdf?dl=0
According to the regulation we have to calculate M1, M2, M3 and M4.
For example M2=(ri-M1)^2/Mo ,M30(ri-M1^3/Mo
... |
Assuming no dividends, the put-call parity equation says:
$c + \mathrm{Ke}^\mathrm{-rT} = p + S$
where $c$ is the price of the European call, $p$ is the price of the European put, $S$ is the current stock price, $K$ is the option strike price, $r$ is the risk-free rate, $T$ is the time to expiry.
In *You Can B... |
You have made a few typos. The basic idea is for asset returns $r_i$ where $i$ denotes the observation (often, $i$ indexes days), you have:
$$
\begin{align}
M0 &= \sum_i 1_{r_i} = \text{# of returns} \\
M1 &= \sum_i r_i/M0 = \text{mean return} \\
M2 &= \sum_i (r_i-M1)^2/M0 = \text{variance of returns}^* \\
M3 &= ... |
We have two different products that follow the same price $S(t)$ for all time $t$. The payout for product one is given by $w_1(\frac{100}{S(t)} - \frac{100}{S(t + \Delta t)})$ and the payout for product two is $w_2(S(t + \Delta t) - S(t))$. Where $w_1$ and $w_2$ are the quantities to buy or sell of product one and two ... |
**Discretized Time?**
If we take $t=0$ and $t+\delta t=\tau$, you have payouts of:
$$
\begin{align}
\text{Payoff 1} &= \omega_1 \left(K_1 - \frac{100}{S_\tau}\right) \quad \text{and} \\
\text{Payoff 2} &= \omega_2 (S_\tau - K_2).
\end{align}
$$
Payoff 1 clearly increases with $S_\tau$ as does Payoff 2. (Ima... |
Up to now, I have been unable to find a clear explanation on the calculation of the forward delivery date for 1M. I understand that when the spot delivery date is e.g. 14-Jan, then the 1M delivery date equals 14-Feb, given that it is a working day and not a holiday, otherwise move forward.
But what is the result fo... |
I am trying to build up a factor model for gold. To be able to identify the correct factors, I did a correlation analysis between a few factors vs gold and I integrated this analysis with what I saw in literature. I ended up with a set of factors as: VIX Index, EURUSD currency, H15X10YR Index (which is the US 10YR real... |
Can someone please explain how to read the heatmap(Exhibit #3 on Page 3) in the research paper *[A Data Science Solution to the Multiple-Testing Crisis in Financial Research][1]* ?
Interpretation of the information is color scheme is straightforward. But I am not getting how the Index vs Strategy correlation data p... |
Can someone please explain the heatmap of Corr from backtests in this research paper *[A Data Science Solution to the Multiple-Testing Crisis in Financial Research][1]* (Exhibit #3 on Page 3)?
It is not clear how the Index vs Strategy correlation data points from 6,385 trials are represented/ordered in the Heat map... |
Can someone please explain the heatmap of Corr from backtests in this research paper ?
*[A Data Science Solution to the Multiple-Testing Crisis in Financial Research - Lopez De Prado (2019)][1]* - (Exhibit #3 on Page 3)
It is not clear how the Index vs Strategy correlation data points from 6,385 trials are... |
You have a portfolio of credit-risk-free bonds all in the sam currency, so just one yield curve.
You are tasked with setting up a Monte Carlo simulation that would create many different scenarios of changes in your yield curves that "look consistent" with the last several years of history.
I suggest you use princ... |
I am building a portfolio simulator and finding ways to make it more 'realistic'. For example, giving the option to reinvest dividends, include capital gain taxes, commission/fees (fixed for now) etc. Regarding slippage/latency, however, I'd like to make a more dynamic model. Have you ever had experience for modeling s... |
Need some expert advice and suggestions:
I am trying out pairs trading or statistical arbitrage (as traders say). But even if two price series are co-integrated (ADF test, Hurst exponent, Ornstein–Uhlenbeck tests etc) and correlated, I see that the normalized prices of a pair always end up diverging in the end and n... |
When I regress the excess performance of a portfolio on the MKT Factor using daily data. I get a Beta of 0.95 and an alpha of 0.00011 that I annualize *252 = 2.77%
I know that the annualized return of the MKT Factor is 8.5% for the period and the annualized performance of the excess return of the portfolio is 11%. W... |
I want to maximize the return of a $n$-asset portfolio under known risk:
$$\max_{\{w \in \mathbb{R}^{n}|w_{1}+...+w_{n}=1\}} \; \mathbb{E}\left[\sum_{i=1}^{n}w_{i}R_{i}\right]$$
under the constraint
$$ES\left(\sum_{i=1}^{n}w_{i}R_{i}\right) \le r$$
where $ES$ is the expected shortfall, also known as conditional val... |
Subsets and Splits
No community queries yet
The top public SQL queries from the community will appear here once available.