data/cfa_knowledge_base.json

{
  "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"
    ]
  }
}