Stocks A and B have the following probability distributions of expected future returns: $$ \begin{matrix} \text{Probability} & \text{A} & \text{B}\\ \text{0.1} & \text{(10\\%)} & \text{(35\\%)}\\ \text{0.2} & \text{2} & \text{0}\\ \text{0.4} & \text{12} & \text{20}\\ \text{0.2} & \text{20} & \text{25}\\ \text{0.1} & \text{38} & \text{45}\\ \end{matrix} $$ a. Calculate the expected rate of return,$\hat{\mathrm{r}}_{\mathrm{B}}$, for Stock B $\left(\hat{\mathrm{r}}_{\mathrm{A}}=12 \%\right)$. b. Calculate the standard deviation of expected returns, $\sigma_{\mathrm{A}}$, for Stock A$\left(\sigma_{\mathrm{B}}=20.35 \%\right)$. Now calculate the coefficient of variation for Stock B. Is it possible that most investors will regard Stock B as being less risky than Stock A? Explain.

A stock’s returns have the following distribution: $$ \begin{matrix} \text{Demand for the Company's Products} & \text{Probability of This Demand Occurring} & \text{Rate of Return if This Demand Occurs}\\ \text{Weak} & \text{0.1} & \text{(30\\%)}\\ \text{Below average} & \text{0.1} & \text{(14)}\\ \text{Average} & \text{0.3} & \text{11}\\ \text{Above average} & \text{0.3} & \text{20}\\ \text{Strong} & \text{0.2} & \text{45}\\ \text{ } & \text{1.0}\\ \end{matrix} $$ Calculate the stock’s expected return, standard deviation, and coefficient of variation.

Assume that the risk-free rate is 3.5% and the market risk premium is 4%. What is the required return for the overall stock market? What is the required rate of return on a stock with a beta of 0.8?

Stocks X and Y have the following probability distributions of expected future returns:

$$\begin{array}{ccc} \text { Probability } & \mathbf{X} & \mathbf{Y} \\ \hline 0.1 & (10 \%) & (35 \%) \\ 0.2 & 2 & 0 \\ 0.4 & 12 & 20 \\ 0.2 & 20 & 25 \\ 0.1 & 38 & 45 \end{array}$$

a. Calculate the expected rate of return, $\hat{r}_Y$, for Stock $Y\left(\hat{\mathbf{r}}_X=12 \%\right)$.

b. Calculate the standard deviation of expected returns, $\sigma_X$, for Stock X $\left(\sigma_Y=20.35 \%\right)$. Now calculate the coefficient of variation for Stock Y. Is it possible that most investors will regard Stock Y as being less risky than Stock X? Explain.

Suppose you are the money manager of a $4.82 million investment fund. The fund consists of four stocks with the following investments and betas:$

$$\begin{matrix} \text{Stock} & \text{Investment} & \text{Beta}\\ \text{A} & \text{\$ 460.000} & \text{1.50}\\ \text{B} & \text{500.000} & \text{(0.50)}\\ \text{C} & \text{1.260.000} & \text{1.25}\\ \text{D} & \text{2.600.000} & \text{0.75}\\ \end{matrix}$$

$ If the market’s required rate of return is 8% and the risk-free rate is 4%, what is the fund’s required rate of return?

Assume that the risk-free rate is 5.5% and the required return on the market is 12%. What is the required rate of return on a stock with a beta of 2?

An individual has $20,000 invested in a stock with a beta of 0.6 and another$75,000 invested in a stock with a beta of 2.5. If these are the only two investments in her portfolio, what is her portfolio’s beta?

Consider the following information for Stocks A, B, and C. The returns on the three stocks are positively correlated, but they are not perfectly correlated. (That is, each of the correlation coefficients is between 0 and 1.) $$ \begin{matrix} \text{Stock} & \text{Expected Return} & \text{Standard Deviation} & \text{Beta}\\ \text{A} & \text{9.55\\%} & \text{15\\%} & \text{0.9}\\ \text{B} & \text{10.45} & \text{15} & \text{1.1}\\ \text{C} & \text{12.70} & \text{15} & \text{1.6}\\ \end{matrix} $$ Fund P has one-third of its funds invested in each of the three stocks. The risk-free rate is 5.5%, and the market is in equilibrium. (That is, required returns equal expected returns.) a. What is the market risk premium $\left(\mathrm{r}_{\mathrm{M}}-\mathrm{r}_{\mathrm{RF}}\right) ?$ b. What is the beta of Fund P? c. What is the required return of Fund P? d. Would you expect the standard deviation of Fund P to be less than 15%, equal to 15%, or greater than 15%? Explain.

You plan to invest in the Kish Hedge Fund, which has total capital of $500 million invested in five stocks:$ $$ \begin{matrix} \text{Stock} & \text{Investment} & \text{Stock's Beta Coefficient}\\ \text{A} & \text{\$ 160 million} & \text{0.5}\\ \text{B} & \text{120 million} & \text{1.2}\\ \text{C} & \text{80 million} & \text{1.8}\\ \text{D} & \text{80 million} & \text{1.0}\\ \text{E} & \text{60 million} & \text{1.6}\\ \end{matrix} $$ $$ Kish’s beta coefficient can be found as a weighted average of its stocks’ betas. The risk-free rate is 6%, and you believe the following probability distribution for future market returns is realistic: $$ $$ \begin{matrix} \text{Probability} & \text{Market Return}\\ \text{0.1} & \text{-28\\%}\\ \text{0.2} & \text{0}\\ \text{0.4} & \text{12}\\ \text{0.2} & \text{30}\\ \text{0.1} & \text{50}\\ \end{matrix} $$ $a. What is the equation for the security market line (SML)? (Hint: First, determine the expected market return.) b. Calculate Kish’s required rate of return. c. Suppose Rick Kish, the president, receives a proposal from a company seeking new capital. The amount needed to take a position in the stock is$50 million, it has an expected return of 15%, and its estimated beta is 1.5. Should Kish invest in the new company? At what expected rate of return should Kish be indifferent to purchasing the stock?

Stocks R and S have the following probability distributions of returns:

$$\begin{array}{ccc} \text{Probability} & \text{Stock R} & \text{Stock S} \\ \hline 0.5 & -2 \% & 20 \% \\ 0.1 & 10 & 12 \\ 0.4 & 15 & 2 \end{array}$$

Calculate the expected return for each stock.

Calculate the required rate of return for Mudd Enterprises assuming that investors expect a 3.6% rate of inflation in the future. The real risk-free rate is 1.0%, and the market risk premium is 6.0%. Mudd has a beta of 1.5, and its realized rate of return has averaged 8.5% over the past 5 years.

Stock X has a 10% expected return, a beta coefficient of 0.9, and a 35% standard deviation of expected returns. Stock Y has a 12.5% expected return, a beta coefficient of 1.2, and a 25% standard deviation. The risk-free rate is 6%, and the market risk premium is 5%. a. Calculate each stock’s coefficient of variation. b. Which stock is riskier for a diversified investor? c. Calculate each stock’s required rate of return. d. On the basis of the two stocks’ expected and required returns, which stock would be more attractive to a diversified investor? e. Calculate the required return of a portfolio that has $7,500 invested in Stock X and$2,500 invested in Stock Y. f. If the market risk premium increased to 6%, which of the two stocks would have the larger increase in its required return?

Stock R has a beta of 2.0, Stock S has a beta of 0.45, the required return on an average stock is 10%, and the risk-free rate of return is 5%. By how much does the required return on the riskier stock exceed the required return on the less risky stock?

Beale Manufacturing Company has a beta of 1.1, and Foley Industries has a beta of 0.30. The required return on an index fund that holds the entire stock market is 11%. The risk-free rate of interest is 4.5%. By how much does Beale’s required return exceed Foley’s required return?