Question

Based on current dividend yields and expected capital gains, the expected rates of return on portfolios A and B are 11% and 14%, respectively. The beta of A is .8 while that of B is 1.5. The T-bill rate is currently 6%, while the expected rate of return of the S&P 500 Index is 12%. The standard deviation of portfolio A is 10% annually, while that of B is 31%, and that of the index is 20%.

a. If you currently hold a market-index portfolio, would you choose to add either of these portfolios to your holdings? Explain.

b. If instead you could invest only in bills and one of these portfolios, which would you choose?

Short answer

The correct answer would be:

a. Portfolio A

b. Portfolio A

Step-by-step solution

Given Information

	Expected Return	Beta	Deviation
Portfolio A	11%	0.8	10%
Portfolio B	14%	1.5	31%
S & P 500	12%	1	20%
T - Bills	5%	0	0%

Solution for ‘a’

So, using the SML, the fair rate of return for a portfolio P E ( r_P ) =r_f + β_i[E(r_M) - r_f]

Substituting the values for Portfolio A and B:

E ( r_A ) =6% + (0.8) (12%- 6%) = 10.08%

E ( r_B ) =6% + (1.5) (12%- 6%) = 15%

From the above scenario, Portfolio A appears to be more desirable.

Solution for ‘b’

The slope of the CAL supported by a portfolio P is given by: S = E (r_P) –(r_F) /σ_P

Computing this slope for each of the three alternative portfolios

S (A) = (11 – 6) / 10 = 5/10

S (B) = (14 – 6) / 31 = 8/31

S (S&P 500) = (12- 6) / 20 = 6/20

For the above calculations, it appears tha portfolio A would be a good substitute for the S&P 500.