Question $1)$

What is the beta of a portfolio with E$($rP$)=18\%,$ if rf$=6\%$ and E$($rM$)=14\%?$

Question $2$

The market price of a security is $50$$$.$ Its expected rate of return is $14\%.$ The risk$-$free rate is $6\%$ and

the market risk premium is $8\mathrm{.}5\%.$ What will be the market price of the security if its covariance with

the market portfolio doubles $($and all other variables remain unchanged$)?$ Assume that the stock is

expected to pay a constant dividend in perpetuity. Hint: Recall that in the case of perpetual dividends

price of the stock is equal to D$/$r

Question $3)$

Are the following true or false?

a$.$ Stocks with a beta of zero offer an expected rate of return of zero.

b$.$ The CAPM implies that investors require a higher return to hold highly volatile securities$.$

Question $4$

A share of stock sells for $$50$ today. It will pay a dividend of $$6$ per share at the end of the year. Its

beta is $1\mathrm{.}2.$ Rf$=6\%.$ RM$=16\%.$ What do investors expect the stock to sell for at the end of the year?

Question $5$

In $1997$ the rate of return on short$-$term government securities $($perceived to be risk$-$free$)$ was about

$5\%.$ Suppose the expected rate of return required by the market for a portfolio with a beta of $1$ is $12\%.$

According to the CAPM $($security market line$)$:

a$.$What is the expected rate of return on the market portfolio?

b$)$ What would be the expected rate of return on a stock with beta$=0?$

c$.$Suppose you consider buying a share of stock at $$40.$ The stock is expected to

pay $$3$ dividends next year and you expect it to sell then for $$41.$ The stock risk has been

evaluated by beta$=-0\mathrm{.}5.$ Is the stock overpriced or underpriced?