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Learning Objectives
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Now · 1. Measuring Risk and Return
Learning Objectives
- Measure risk and return for individual assets and portfolios
- Apply Capital Asset Pricing Model (CAPM)
- Understand diversification and the Security Market Line
1. Measuring Risk and Return
Expected Return: E(R) = sum(pi x Ri) Variance: sigma^2 = sum(pi x (Ri - E(R))^2) Standard Deviation: sigma = sqrt(variance)
2. Portfolio Theory
Portfolio Return: E(Rp) = w1E(R1) + w2E(R2) Portfolio Variance: sigma_p^2 = w1^2sigma1^2 + w2^2sigma2^2 + 2w1w2sigma1sigma2rho12
Diversification: Reducing risk by combining assets with imperfect correlation.
3. CAPM
Capital Asset Pricing Model:
Beta: Measures systematic risk. beta = Cov(Ri, Rm)/Var(Rm)
4. Security Market Line
Graph of CAPM: Expected return vs Beta. Securities above SML are undervalued.
| Concept | Formula |
|---|---|
| Portfolio Expected Return | E(Rp) = sum(wi x E(Ri)) |
| Portfolio Variance | See above |
| CAPM | E(Ri) = Rf + beta(Rm - Rf) |
| Beta | beta = Cov(i,m)/Var(m) |
Q1: Rf=3%, Rm=10%, beta=1.2. What is E(R) according to CAPM?E(R) = 3 + 1.2(10-3) = 3 + 8.4 = 11.4% Q2: A stock has beta=0.8. Market rises 15%. Expected stock return?Expected = 0.8 x 15% = 12%. Stock is less volatile than market. Q3: What is the difference between systematic and unsystematic risk?Systematic (market) risk cannot be diversified away. Unsystematic (firm-specific) risk can be eliminated through diversification. Q4: Two stocks with correlation coefficient = -1. What does this mean?Perfect negative correlation. Can construct a risk-free portfolio (zero variance) with appropriate weights. Join Discord PreviousNPV, IRR & Capital BudgetingNextCost of Capital & WACC