problems

$(255)$

Problems $1-5$

$8-1$ EXPECTED RETURN A stock's returns have the following distribution:

Assume the risk$-$free rate is $2\%.$ Calculate the stock's expected return, standard deviation,

coefficient of variation, and Sharpe ratio.

$8-2$ PORTFOLIO BETA An individual has $$20,000$ invested in a stock with a beta of $0\mathrm{.}6$ and

another $$75,000$ invested in a stock with a beta of $2\mathrm{.}5.$ If these are the only two investments

in her portfolio, what is her portfolio's beta?

$8-3$ REQUIRED RATE OF RETURN Assume that the risk$-$free rate is $5\mathrm{.}5\%$ and the required return

on the market is $12\%.$ What is the required rate of return on a stock with a beta of $2?$

$8-4$ EXPECTED AND REQUIRED RATES OF RETURN Assume that the risk$-$free rate is $3\mathrm{.}5\%$ 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 $0\mathrm{.}8?$

$8-5$ BETA AND REQUIRED RATE OF RETURN A stock has a required return of $9\%,$ the risk$-$free

rate is $4\mathrm{.}5\%,$ and the market risk premium is $3\%.$

a$.$ What is the stock's beta?

b$.$ If the market risk premium increased to $5\%,$ what would happen to the stock's

required rate of return? Assume that the risk$-$free rate and the beta remain

unchanged.

$8-6$ EXPECTED RETURNS Stocks A and $B$ have the following probability distributions of

expected future returns: