REALIZED RATES OF RETURN Stocks A and B have the following historical returns:

Questions

a$.$ What is the holding company$$s beta?

b$.$ If the risk$-$free rate is $4\%$ and the market risk premium is $5\%,$ what is the holding

company$$s required rate of return?

c$.$ ECRIisconsideringachangeinitsstrategicfocus;itwillreduceitsrelianceonthe

electric utility subsidiary, so the percentage of its capital in this subsidiary will be reduced to $50\%.$ At the same time, it will increase its reliance on the international$/$ special projects division, so the percentage of its capital in that subsidiary will rise to $15\%.$ What will the company$$s required rate of return be after these changes?

$8-1$ Suppose you owned a portfolio consisting of $$250,000$ of long$-$term U$.$S$.$ government bonds.

a$.$ Would your portfolio be riskless? Explain.

b$.$ Now suppose the portfolio consists of $$250,000$ of $30-$day Treasury bills. Every $30$ days

your bills mature, and you will reinvest the principal $($$$250,000)$ in a new batch of bills. You plan to live on the investment income from your portfolio, and you want to maintain a constant standard of living. Is the T$-$bill portfolio truly riskless? Explain.

c$.$ What is the least risky security you can think of$?$ Explain.

Year

$2013$

$2014$

$2015$

$2016$

$2017$

Stock A$$s Returns, rA

$(24\mathrm{.}25\%)18\mathrm{.}5038\mathrm{.}6714\mathrm{.}3339\mathrm{.}13$

Stock B$$s Returns, rB

$5\mathrm{.}50\%26\mathrm{.}7348\mathrm{.}25$

$(4\mathrm{.}50)43\mathrm{.}86$a$.$ Calculate the average rate of return for each stock during the period $2013$ through $2017.$ Assume that someone held a portfolio consisting of $50\%$ of Stock A and $50\%$ of Stock B$.$ What would the realized rate of return on the portfolio have been in each year from $2013$ through $2017?$ What would the average return on the portfolio have been during that period?

b$.$ Calculate the standard deviation of returns for each stock and for the portfolio. Use Equation $8\mathrm{.}2$a$.$

c$.$ Assume the risk$-$free rate during this time was $3\mathrm{.}5\%.$ What are the Sharpe ratios for Stocks A and B and the portfolio over this time period using their average returns?

d$.$ Looking at the annual returns on the two stocks, would you guess that the correlation coefficient between the two stocks is closer to $10\mathrm{.}8$ or to $20\mathrm{.}8?$

e$.$ If more randomly selected stocks had been included in the portfolio, which of the fol$-$ lowing is the most accurate statement of what would have happened to sp$?$

$1.$ sp would have remained constant.

$2.$ sp would have been in the vicinity of $20\%.$

$3.$ sp would have declined to zero if enough stocks had been included.