Question

Question 1. (15 marks) Mr. Horsefield, the manager of Solomon Mutual Fund Co., expects to evaluate the return and risk of several possible portfolios through the relationships among the risk-free rate of return, market rate of return, market risk premium, and systematic risk. Then, the manager finds that the risk-free rate of return is equal to 4% annually, the average return rate of market is 13%. The manager also collects that each of the three targeting portfolio consists of the same four assets held in different proportions, and each asset has different systematic risks. All of the components of each portfolio have been shown in the following table: Portfolio weights Asset beta Portfolio A Portfolio B Portfolio C 2.0 20% 30% 40% 1.8 20% 10% 20% 20% 10% 30% Total 100% 100% 100% Asset 2 20% 3 1.2 4 0.4 40% 40% Required: (a). After collecting above information, Mr. Horsefield believes that he should start from calculating the systematic risk of Portfolio A, B and C. Set the market portfolio as benchmark, please rank the risk level of Portfolio A, B and C. (5 marks) (b). After realizing the risk level of Portfolio A, B and C, Mr. Horsefield's next task is to find the expected return rate for portfolios A, B and C. He plans to apply the risk level of portfolio, market rate of retum, and the risk-free rate of return to obtain the value. Please show his calculation. (3 marks) (C). If Mr. Horsefield found that the return rates of portfolios A, B and C are all 15.34% in market, should he know which portfolio is overvalued and which one is undervalued? Then, this result can help investors to make their purchasing or selling decision. (4 marks) (d). Finally, from the above empirical procedure, please help Mr. Horsefield explain the relationships among the risk-free rate of return, market rate of return and market risk premium, beta. (3 marks) (15 marks)

Answer 1

A) Systematic Risks of Portfolios

Portfolio A = (Weight of Asset 1 in Portfolio A * Beta of Assets 1) + (Weight of Asset 2 in Portfolio A * Beta of Assets 2) + (Weight of Asset 3 in Portfolio A * Beta of Assets 3)

= 1.16

Portfolio B = (Weight of Asset 1 in Portfolio B * Beta of Assets 1) + (Weight of Asset 2 in Portfolio B * Beta of Assets 2) + (Weight of Asset 3 in Portfolio B * Beta of Assets 3)

= 1.32

Portfolio C = (Weight of Asset 1 in Portfolio C * Beta of Assets 1) + (Weight of Asset 2 in Portfolio C * Beta of Assets 2) + (Weight of Asset 3 in Portfolio C * Beta of Assets 3)

= 1.26

Ranking	Portfolio Name
1 (Least Risky	A
2	C
3 (Most Risky)	B

B) Expected Rate of return from portfolio = (rp) = rf + (β)*(rm - rf) (CAPM Model)

rf = risk free rate of return

β = beta of portfolio

rm = market rate of return

Portfolio A = rp(A) = 4% + (1.16)*(13%-4%) = 14.44%

Portfolio B = rp(B) = 4% + (1.32)*(13%-4%) = 15.88%

Portfolio C = rp(C) = 4% + (1.26)*(13%-4%) = 15.34%

C)  If,

Expected return > Actual return = Portfolio/Security is Overvalued

Expected return < Actual return = Portfolio/Security is Undervalued

Expected return = Actual return = Portfolio or security is fairly priced

Portfolio	Beta	Actual Market return	Expected Market return	Result
A	1.16	15.34%	14.4400%	Overvalued
B	1.32	15.34%	15.8800%	Undervalued
C	1.26	15.34%	15.3400%	Fair-value

Often Undervalued stocks are recommended to Buy Undervalued as they will reach to their fair price sooner or later and SELL Overvalued for the same reason.

D) Relationship:

Risk free rate of return	Market rate of return	Market risk premium	Beta
The risk-free rate in the CAPM formula accounts for the time value of money.	It refers to the average rate of return of an equity/stock/asset trading in the market	It refers to the return an investor expect from the market above the risk-free rate in response for additional risk he/she is taking in an investment	The beta of a potential investment is a measure of how much risk the investment will add to a portfolio that looks like the market.