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| { | |
| "metadata": { | |
| "version": "1.0.0", | |
| "last_updated": "2024-01-21", | |
| "description": "CFA Level I Knowledge Base - Free Version for Hugging Face Spaces", | |
| "total_concepts": 50, | |
| "total_formulas": 25 | |
| }, | |
| "topics": { | |
| "Time Value of Money": { | |
| "description": "Core finance concept dealing with value of money over time. Fundamental to investment analysis and capital budgeting.", | |
| "key_concepts": [ | |
| { | |
| "name": "Present Value", | |
| "definition": "Current worth of future cash flows given a specified rate of return.", | |
| "formula": "PV = FV / (1 + r)^n", | |
| "example": "PV of $110 received in 1 year at 10% discount rate is $100." | |
| }, | |
| { | |
| "name": "Future Value", | |
| "definition": "Value of current investment at future date based on assumed growth rate.", | |
| "formula": "FV = PV × (1 + r)^n", | |
| "example": "$100 at 10% interest for 1 year grows to $110." | |
| }, | |
| { | |
| "name": "Net Present Value", | |
| "definition": "Difference between present value of cash inflows and outflows.", | |
| "formula": "NPV = Σ [CF_t / (1 + r)^t]", | |
| "example": "Used to evaluate investment projects." | |
| }, | |
| { | |
| "name": "Internal Rate of Return", | |
| "definition": "Discount rate that makes NPV of all cash flows equal to zero.", | |
| "formula": "0 = Σ [CF_t / (1 + IRR)^t]", | |
| "example": "IRR helps compare different investment opportunities." | |
| } | |
| ], | |
| "common_applications": [ | |
| "Valuing bonds and stocks", | |
| "Capital budgeting decisions", | |
| "Retirement planning", | |
| "Loan amortization" | |
| ], | |
| "cfa_level": "I", | |
| "weight": "8-12%", | |
| "difficulty": "Medium" | |
| }, | |
| "Statistics": { | |
| "description": "Collection, analysis, interpretation, and presentation of data for financial decision making.", | |
| "key_concepts": [ | |
| { | |
| "name": "Mean", | |
| "definition": "Average of a dataset.", | |
| "formula": "μ = Σ x_i / n", | |
| "example": "Mean of [2,4,6,8] is 5." | |
| }, | |
| { | |
| "name": "Standard Deviation", | |
| "definition": "Measure of data dispersion around the mean.", | |
| "formula": "σ = √[Σ(x_i - μ)² / (n-1)]", | |
| "example": "Higher std dev indicates greater volatility." | |
| }, | |
| { | |
| "name": "Correlation", | |
| "definition": "Statistical relationship between two variables.", | |
| "formula": "ρ = Cov(X,Y) / (σ_X × σ_Y)", | |
| "example": "Correlation ranges from -1 to +1." | |
| }, | |
| { | |
| "name": "Normal Distribution", | |
| "definition": "Bell-shaped probability distribution.", | |
| "formula": "68% within ±1σ, 95% within ±2σ, 99.7% within ±3σ", | |
| "example": "Many financial returns approximate normal distribution." | |
| } | |
| ], | |
| "common_applications": [ | |
| "Portfolio risk analysis", | |
| "Performance measurement", | |
| "Hypothesis testing", | |
| "Quality control" | |
| ], | |
| "cfa_level": "I", | |
| "weight": "5-8%", | |
| "difficulty": "Medium" | |
| }, | |
| "Portfolio Management": { | |
| "description": "Art and science of making decisions about investment mix and policy.", | |
| "key_concepts": [ | |
| { | |
| "name": "Diversification", | |
| "definition": "Reducing risk by holding different assets.", | |
| "formula": "", | |
| "example": "Don't put all your eggs in one basket." | |
| }, | |
| { | |
| "name": "Capital Asset Pricing Model", | |
| "definition": "Model describing relationship between risk and expected return.", | |
| "formula": "E(R) = Rf + β(Rm - Rf)", | |
| "example": "CAPM is used to price risky securities." | |
| }, | |
| { | |
| "name": "Beta", | |
| "definition": "Measure of systematic risk relative to market.", | |
| "formula": "β = Cov(asset, market) / Var(market)", | |
| "example": "Beta of 1 means moves with market." | |
| }, | |
| { | |
| "name": "Sharpe Ratio", | |
| "definition": "Measure of risk-adjusted return.", | |
| "formula": "Sharpe = (Rp - Rf) / σ_p", | |
| "example": "Higher Sharpe ratio indicates better risk-adjusted performance." | |
| } | |
| ], | |
| "common_applications": [ | |
| "Asset allocation", | |
| "Risk management", | |
| "Performance evaluation", | |
| "Investment strategy" | |
| ], | |
| "cfa_level": "I", | |
| "weight": "5-10%", | |
| "difficulty": "Medium" | |
| }, | |
| "Economics": { | |
| "description": "Study of how individuals, businesses, and governments allocate resources.", | |
| "key_concepts": [ | |
| { | |
| "name": "Supply and Demand", | |
| "definition": "Economic model of price determination in a market.", | |
| "formula": "Equilibrium where Qd = Qs", | |
| "example": "Price increases when demand exceeds supply." | |
| }, | |
| { | |
| "name": "Elasticity", | |
| "definition": "Responsiveness of quantity demanded to price changes.", | |
| "formula": "E = (%ΔQ) / (%ΔP)", | |
| "example": "Elastic demand means quantity changes significantly with price." | |
| } | |
| ], | |
| "common_applications": [ | |
| "Market analysis", | |
| "Pricing strategies", | |
| "Policy evaluation", | |
| "Business planning" | |
| ], | |
| "cfa_level": "I", | |
| "weight": "8-12%", | |
| "difficulty": "Medium" | |
| } | |
| }, | |
| "formulas": { | |
| "TVM Formulas": [ | |
| { | |
| "name": "Future Value", | |
| "formula": "FV = PV(1+r)^n", | |
| "description": "Future value of single cash flow" | |
| }, | |
| { | |
| "name": "Present Value", | |
| "formula": "PV = FV/(1+r)^n", | |
| "description": "Present value of single cash flow" | |
| }, | |
| { | |
| "name": "Annuity PV", | |
| "formula": "PV = PMT[1 - (1+r)^-n]/r", | |
| "description": "Present value of ordinary annuity" | |
| }, | |
| { | |
| "name": "Annuity FV", | |
| "formula": "FV = PMT[(1+r)^n - 1]/r", | |
| "description": "Future value of ordinary annuity" | |
| }, | |
| { | |
| "name": "Perpetuity PV", | |
| "formula": "PV = PMT/r", | |
| "description": "Present value of perpetuity" | |
| } | |
| ], | |
| "Statistics Formulas": [ | |
| { | |
| "name": "Mean", | |
| "formula": "x̄ = Σx/n", | |
| "description": "Sample mean" | |
| }, | |
| { | |
| "name": "Variance", | |
| "formula": "s² = Σ(x - x̄)²/(n-1)", | |
| "description": "Sample variance" | |
| }, | |
| { | |
| "name": "Standard Deviation", | |
| "formula": "s = √Variance", | |
| "description": "Sample standard deviation" | |
| }, | |
| { | |
| "name": "Correlation", | |
| "formula": "r = Σ[(x-x̄)(y-ȳ)]/√[Σ(x-x̄)²Σ(y-ȳ)²]", | |
| "description": "Pearson correlation coefficient" | |
| } | |
| ], | |
| "Portfolio Formulas": [ | |
| { | |
| "name": "CAPM", | |
| "formula": "E(R) = Rf + β(Rm - Rf)", | |
| "description": "Capital Asset Pricing Model" | |
| }, | |
| { | |
| "name": "Portfolio Variance", | |
| "formula": "σ²_p = w₁²σ₁² + w₂²σ₂² + 2w₁w₂σ₁σ₂ρ₁₂", | |
| "description": "Two-asset portfolio variance" | |
| }, | |
| { | |
| "name": "Sharpe Ratio", | |
| "formula": "Sharpe = (Rp - Rf)/σ_p", | |
| "description": "Risk-adjusted return measure" | |
| }, | |
| { | |
| "name": "Beta", | |
| "formula": "β = Cov(r_a, r_m)/Var(r_m)", | |
| "description": "Systematic risk measure" | |
| } | |
| ] | |
| }, | |
| "glossary": { | |
| "NPV": "Net Present Value - Difference between present value of cash inflows and outflows. Used to evaluate investment profitability.", | |
| "IRR": "Internal Rate of Return - Discount rate that makes NPV zero. Used to compare different investments.", | |
| "Beta": "Measure of a stock's volatility relative to the overall market. Beta of 1 indicates market-like volatility.", | |
| "Alpha": "Measure of performance on a risk-adjusted basis. Positive alpha indicates outperformance.", | |
| "Sharpe Ratio": "Measure of risk-adjusted return. Higher Sharpe indicates better risk-adjusted performance.", | |
| "Standard Deviation": "Measure of dispersion of a dataset. In finance, measures volatility or risk.", | |
| "Correlation": "Statistical measure of relationship between two variables. Ranges from -1 to +1.", | |
| "Annuity": "Series of equal payments made at regular intervals. Examples include mortgages and retirement payments.", | |
| "Perpetuity": "Infinite series of equal payments. Present value = Payment / Discount rate.", | |
| "Discount Rate": "Interest rate used to calculate present value of future cash flows.", | |
| "Compounding": "Process where investment earnings earn additional earnings over time.", | |
| "Diversification": "Risk management strategy that mixes different investments to reduce overall risk.", | |
| "CAPM": "Capital Asset Pricing Model - Theoretical model that describes relationship between risk and expected return.", | |
| "Efficient Frontier": "Set of optimal portfolios offering highest expected return for given risk level.", | |
| "Risk-Free Rate": "Theoretical rate of return with zero risk, typically based on government bonds." | |
| }, | |
| "practice_problems": { | |
| "Time Value of Money": [ | |
| { | |
| "id": "tvm_001", | |
| "question": "What is the present value of $10,000 received in 5 years at 8% annual discount rate?", | |
| "options": ["$6,810", "$6,500", "$7,000", "$6,200"], | |
| "correct": 0, | |
| "explanation": "PV = FV / (1+r)^n = 10000 / (1.08)^5 = 10000 / 1.4693 = $6,805.83 ≈ $6,810", | |
| "difficulty": "easy" | |
| }, | |
| { | |
| "id": "tvm_002", | |
| "question": "An investment of $5,000 grows to $7,500 in 4 years. What is the annual compound rate?", | |
| "options": ["8.45%", "10.67%", "9.14%", "11.18%"], | |
| "correct": 1, | |
| "explanation": "r = (FV/PV)^(1/n) - 1 = (7500/5000)^(1/4) - 1 = 1.5^0.25 - 1 = 0.1067 = 10.67%", | |
| "difficulty": "medium" | |
| } | |
| ], | |
| "Statistics": [ | |
| { | |
| "id": "stat_001", | |
| "question": "Calculate the mean and standard deviation of: [12, 15, 18, 22, 25]", | |
| "options": ["Mean: 18.4, SD: 5.0", "Mean: 18.4, SD: 4.8", "Mean: 18.0, SD: 5.2", "Mean: 18.0, SD: 5.0"], | |
| "correct": 0, | |
| "explanation": "Mean = (12+15+18+22+25)/5 = 92/5 = 18.4. Variance = [(12-18.4)^2 + ...]/4 = 100.8/4 = 25.2. SD = √25.2 = 5.02 ≈ 5.0", | |
| "difficulty": "easy" | |
| } | |
| ], | |
| "Portfolio Management": [ | |
| { | |
| "id": "pm_001", | |
| "question": "If stock A has beta of 1.2, risk-free rate is 3%, and market return is 8%, what is expected return using CAPM?", | |
| "options": ["9%", "8.6%", "9.6%", "10%"], | |
| "correct": 0, | |
| "explanation": "E(R) = Rf + β(Rm - Rf) = 3% + 1.2(8% - 3%) = 3% + 6% = 9%", | |
| "difficulty": "easy" | |
| } | |
| ] | |
| }, | |
| "exam_tips": { | |
| "general": [ | |
| "Read each question carefully - look for key words like 'most likely', 'least likely', 'best', 'worst'", | |
| "Manage your time - about 1.5 minutes per question", | |
| "Answer every question - no penalty for wrong answers", | |
| "Use process of elimination when unsure", | |
| "Trust your first instinct unless you find clear evidence to change" | |
| ], | |
| "calculations": [ | |
| "Write down known variables before starting", | |
| "Check units and ensure consistency", | |
| "Use calculator memory functions for multi-step calculations", | |
| "Estimate answers first to check reasonableness", | |
| "Practice with the calculator you'll use on exam day" | |
| ], | |
| "ethics": [ | |
| "When in doubt, choose the most ethical option", | |
| "Client interests always come first", | |
| "Disclose all conflicts of interest", | |
| "Maintain independence and objectivity", | |
| "Remember: integrity, competence, confidentiality" | |
| ] | |
| } | |
| } |