Ch 6.Risk, Return and the CAPM. Goals:. To understand return and risk To understand portfolio To understand diversifiable risks and market (systematic) risks To understand CAPM. 1.Investment returns. Dollar return = amount received –amount invested Problems: Scale effect
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(Stand-alone risk: the risk an investor would face if he or she only held one asset)
Ex) Historical return and risk
Ex) return is high enough to compensate the investor for the perceived risk
State Probability (P) S B
Strong 0.25 0.3 0.2
Normal 0.5 0.15 0.30
Weak 0.25 0.00 -0.10
2) Expected Rates of Returns and Risks: Stand-alone
How to calculate? return is high enough to compensate the investor for the perceived risk
3) Portfolios: Return and Risks the risk per unit of return. It provides a more meaningful basis for comparison
Portfolios: combination of assets or securities to minimize total risks and to improve returns
(1) Portfolio Returns:
Simply the weighted average of the expected returns on individual assets in the portfolio
Ex) using the previous example with an assumption that weights for S and B are 40% and 60%.
Expected returns = 0.4(0.15)+0.6(0.175)=0.165
(4) If the correlation is -1, then the variance will reduce to the minimum value. Diversification effects
(5) In reality, securities’ correlations are between 0 and 1.
4) Diversifiable Risk and Market Risk
Systematic risk Unsystematic risk
Total Risk = Market risk + Firm specific risk
Undiversifiable risk Diversifiable risk
[the comovement of an asset i's return (price) to the market portfolio's return (price)]
5) CAPM (Capital Asset Pricing Model)
Based on the beta estimate, we are able to come up with CAPM that will estimate a required rate of return in individual stock.
CAPM: composed of market returns and individual stock returns
Here market risk premium (RPM) is the extra rate of return that investors require to invest in the stock market rather than purchase risk-free securities. It is determined by the degree of risk aversion that investors have on average.
SML (security market line): F503 stocks’ beta is 0.7. Required rate of return = 0.03+0.7(0.05-0.03)
r F503 stocks’ beta is 0.7. Required rate of return = 0.03+0.7(0.05-0.03)i (%)
rM = 15
rRF = 8
-1 0 1 2
10) Empirical tests: joint test of the EMH and an asset pricing model. Whether a certain strategy can beat the market.