Question

1. Expected return on two stocks for two particular market returns:

                        Market Return         Aggressive Stock         Defensive Stock

                                 5%                           0%                               6%

                               30%                          40%                             20%

1. What are the betas of the two stocks?
2. What is the expected rate of return on each stock if the market return is equally likely to be 5% or 30%?
3. If the T-bill rate is 4.5% and the market return is equally likely to be 5% or 30%, draw the SML for this economy.
4. Between aggressive and defensive stocks, which one is undervalued, which is overvalued, and why?

Please show work and formulas. Use Excel

Answer 1

Solution:

a)Calculation of beta

Beta=% cahnge in stock's return/% change in market's return

Beta of Aggressive Stock=40%-0%/30%-5%

=1.6

Beta of Defensive Stock=20%-6%/30%-5%

=14%/25%=0.56

b)Calculation of expected rate of return on each stock

Probability(a)	Return(b)	Expected Return(a*b)
	Aggressive Stock	Defensive Stock	Aggressive Stock	Defensive Stock
0.50	0%	6%	0%	3%
0.50	40%	20%	20%	10%
	20%	13%

Therefore expected rate of return on;

Aggressive Stock =20%

Defensive Stock=13%

c)Market return=.50*5%+0.50*30%

=2.5%+15%=17.5%

Required return of each stock

Aggressive Stock =20%

Defensive Stock=13%

Return as per CAPM

Return=Risk free rate+beta(market rate-risk free rate)

Aggressive Stock=4.5%+1.6*(17.5%-4.5%)

=25.30%

Defensive Stock=4.5%+0.56(17.5%-4.5%)

d)Defensive stock is undervalued because its expected return is higher than the return as per CAPM(as it appear above the SML)

Aggressive stock is overvalued because its expected return is lower than the return as per CAPM(as it appear below the SML)

=11.78%