Question

9-4 The expected retum for the market is 12 percent, with a standard deviation of 21 percent. The expected risk-free rate is 8 percent. Information is available for five mutual funds, all assumed to be efficient: Mutual Funds SD(%) Affiliated Omega Value Line Fund New Horizons a. Calculate the slope of the CML b. Calculate the expected return for each portfolio. c. Rank the portfolios in increasing order of expected risk. d. Do any of the portfolios have the same expected return as the market? Why?

Answer 1

The solution to the part a)

The Slope of CML =( r_m - r_f ) / SD_m

where,

r_m = Return of the market

r_f = Risk-free return

SD_m = standard deviation of the market

Hence,

The Slope of CML =( 12% - 8%) / 21% = 19.05%

The solution to the part b)

Using CML equation,

The expected return of Portfolio = r_f + [ ( r_m - r_f ) / SD_m ] * SD_p

where,

r_m = Return of the market

r_f = Risk-free return

SD_m = standard deviation of the market

SD_p= standard deviation of the portfolio

Hence,

Return of Affiliated = 8% + [(12%-8%)/21%]*14% = 10.67%

Return of Omega = 8% + [(12%-8%)/21%]*16% = 11.05%

Return of Ivy = 8% + [(12%-8%)/21%]*21% = 12.00%

Return of Value Line Fund = 8% + [(12%-8%)/21%]*25% = 12.76%

Return of New Horizons = 8% + [(12%-8%)/21%]*30% = 13.71%

The solution to the part c)

Portfolio	Return	Rank
Affiliated	10.67%	5
Omega	11.05%	4
Ivy	12.00%	3
Value Line Fund	12.76%	2
New Horizons	13.71%	1

The solution to the part d)

Portfolio Ivy and return of the market is the same as 12.00% because of the standard deviation of the portfolio Ivy and Market is the same as 21%