Ch 13. Return, Risk and Security Market Line (SML)

1. Expected Returns and Variance Until now, we mainly concerned historical returns and risks. However, in this chapter, we will cover returns and variance in future. Without estimating returns and variance in future, we can not make decisions. 1) Expected return

Ex) E(R L ) = 0.6×(-0.2)+0.4×0.7 = 0.16 E(Ru) = 0.6×(0.3)+0.4×0.1 = 0.22 If a risk free rate is 8%, then risk premium is 0.08 and 0.14, respectively.

2) (Expected) Variance Ex) in the previous example, Var(L) = 0.6*( )^2+0.4*( )^2 = and STDEV(L) = Var(U) = 0.6*( )^2+0.4*( )^2 = and STDEV(U) = Which one do you want to buy?

3) Portfolios: group of stocks, bonds or investments. Portfolio Weight: percentage of total capital for individual investment or security. Sum of all portfolio weights should be 1. (1) Portfolio Expected Returns

Ex) Assuming weights for L and U are 50%

(2) Portfolio Variance

4) Total return =Expected Return + Unexpected Return = E(R) + U Total return (actual return) differs from the expected return, because of surprises that occur during the year. Surprise usually relates to the unexpected return portion and generate the risk of investment.

2. Diversification and Portfolio risk As Table 13-7 and Figure 13-1 show, the more assets in your portfolio, the lower the risk (standard deviation). It means that by including more assets, you can reduce the risk –the principle of diversification. Also it shows that after a certain point, we can not reduce the risk furthermore.

1) Total Risk = unsystematic (diversifiable) risk + systematic (nondiversifiable) risk. Systematic risk: risk that has marketwise effects or influences, called market risk. Ex) inflation or interest rate Unsystematic risk: risk that affects a single asset or a small group of assets. Ex) strike of union. Unsystematic risk is essentially eliminated by diversification, so a portfolio with many assets has almost no unsystematic risk.

Risk decomposition implies that R=E(R)+systematic portion + unsystematic portion =E(R) + m +

2) Systematic risk. As discussed, systematic risk would not be eliminated. The rewards (or risk premium) to taking risks would directly relate to the amount of systematic risk in individual asset or portfolio. The systematic risk is measured by beta coefficient. It measures relative movements of an asset or a portfolio to the market or systematic risk relative to that in an average risk asset.

Portfolio beta is a weighted average of systematic risks of assets in a portfolio. 3. Security Market Line (SML) A line showing the relationship between systematic risks and expected returns. The slop of the SML means a reward-to-risk ratio.

If the market is in equilibrium, assets should be on SML. Any asset on SML should have the same reward to risk ratios (slope). Ex) Security A has an expected return of 10% and a beta of 0.7. Security B has an expected return of 8%. Risk free return is 3%. If the market is in equilibrium, what would be the beta of security B?

4. Capital Asset Pricing Model (CAPM): A model estimating an expected return of an asset basing on the systematic risk. Assuming two assets. One is Security i and the other one is a market portfolio supposedly composed of all securities available in the world. The systematic risk of the market portfolio is always 1.

The ratios should be the same. This is called CAPM. If we know the estimate of an security, market return and risk free return, we can estimate the expected return of a security. Practically, the market index is used as a proxy for the market portfolio. T-Bill or Bond is used as a proxy for the risk free security.

Ex) 3 years T-bond generates a return of 3%. S&P 500 produce a return of 10%. What is an expected return of a security A if it has a beta of 0.8?