$2.$ CAPM, Portfolio Risk, and Return $($Formula Approach$)$

Step $1$: Quick Take: CAPM, Portfolio Risk, and Return

CAPM, portfolio risk and return are fundamental concepts in finance.

Read the following text and answer the question that follows.

The capital asset pricing model $($CAPM$)$ is a model that assumes that the required rate of return on a stock is equal to the risk$-$free rate plus a risk premium. This risk premium is determined by the risk remaining after diversification. The implications of such a model lead to important intuitions about risk in the context of a portfolio $($multiple stocks or assets held together$).$

Consider a portfolio of multiple stocks. The expected return of the portfolio is simply the weighted average of the expected returns of each stock in the portfolio. However, the risk $($as measured by the standard deviation of expected returns$)$ of the portfolio is not equal to the weighted average of the risk of the individual stocks. The risk of the portfolio as a whole is usually smaller than the weighted average of the risk of the stocks $($unless the stocks are perfectly positively correlated$),$ because of diversification. However, not all risk can be eliminated with diversification.

Market risk is the risk that remains after all diversifiable risk has been eliminated. Thus, when a stock is held in a diversified portfolio, the riskiness of a stock is measured by the degree to which the stock contributes to the portfolio$$s market risk. In other words, the risk of a stock in a well diversified portfolio is measured by how that stock moves $($up or down$)$ with the broader market. This is measured by a stock$$s beta coefficient. The beta for a portfolio as a whole is simply the weighted average beta of the securities therein. In theory, the beta of a stock is the most relevant measure of risk for that stock.

True or False: The risk of a portfolio is generally not equal to the weighted average standard deviation of expected returns of each stock in the portfolio.

True

False

Step $2$: Learn It: CAPM, Portfolio Risk, and Return

Watch the following video for an example, then answer the questions that follow.

Consider the following information for Stocks A$,$ B$,$ and C$.$ The returns on the three stocks, while positively correlated, are not perfectly correlated.

The risk$-$free rate is $5\mathrm{.}50\%.$

Stock

Expected Return

Standard Deviation

Beta

A $7\mathrm{.}00\%20\%0\mathrm{.}6$

B $8\mathrm{.}50\%20\%1\mathrm{.}2$

C $10\mathrm{.}00\%20\%1\mathrm{.}8$

Let ri

be the expected return of stock i

$,$ rRF

represent the risk$-$free rate, b

represent the Beta of a stock, and rM

represent the market return.

Assume that the market is in equilibrium, with the required rate of returns equal to expected returns.

According to the video, which equation most closely describes the relationship between required returns, beta, and the market risk premium?

ri$=$rRF$+$b$\backslash$times $($rM$$rRF$)$

ri$=$rRF$+$brM$$rRF

ri$=$rRF$+$b$\backslash$times $($rM$+$rRF$)$

ri$=$rRF$$b$\backslash$times $($rM$$rRF$)$

Hint: Recall that because the market is in equilibrium, the required rate of return is equal to the expected rate of return for each stock.

Using the equation you just identified, you can solve for the market risk premium which, in this case, equals approximately $.$

Consider Fund P$,$ which has one third of its funds invested in each of stock A$,$ B$,$ and C$.$

True or False: The beta for a fund is equal to the weighted average of the betas of the individual stocks in the fund.

True

False

Using your answer to the previous question, the beta for Fund P is approximately $.$

You have the market risk premium, the beta for Fund P$,$ and the risk$-$free rate.

Hint: Recall that because the market is in equilibrium, the required rate of return is equal to the expected rate of return for each stock.

This information implies that the required rate of return for Fund P is approximately $.$

True or False: The standard deviation for Fund P is less than $20\%.$

True

False