Question

CAPM and expected​ returns..

a.  Given the following​ holding-period returns, compute the average returns and the standard deviations for the Zemin Corporation and for the market.

b.  If​ Zemin's beta is 1.88 and the​ risk-free rate is 7 percent, what would be an expected return for an investor owning​ Zemin? ​

(Note: Because the preceding returns are based on monthly​ data, you will need to annualize the returns to make them comparable with the​ risk-free rate. For​ simplicity, you can convert from monthly to yearly returns by multiplying the average monthly returns by​ 12.)

c.  How does​ Zemin's historical average return compare with the return you believe you should expect based on the capital asset pricing model and the​ firm's systematic​ risk?

Month	Zemin Corp.	Market
1	8%	6%
2	4%	1%
3	0%	1%
4	-1%	-1%
5	6%	4%
6	2%	1%

Answer 1

Answer a:

Zemin Corp:

Average monthly return = 3.17%

Standard deviation = 3.4881%

Market:

Average monthly return = 2%

Standard deviation = 2.5298%

Working:

The above excel with 'show formula' is as below:

Answer b:

Average monthly return (market.) = 2%

Annualized return (market) = 2% * 12 = 24%

Zemin's beta is = 1.88 and

Risk-free rate is = 7%

Expected Return = Risk free rate + Beta * (Market rate of return - Risk free rate)

Expected return for an investor owning​ Zemin Corp. = 7% + 1.88 * (24%- 7%) = 38.96%

Expected return for an investor owning​ Zemin Corp. = 38.96%

Answer c:

Average monthly return (Zemin Corp.) = 3.1667%

Annualized return (Zemin Corp.) = 3.1667% * 12 = 38%

As such:

Zemin's historical average return = 38%

Expected return for an investor owning​ Zemin Corp. using CAPM = 38.96%

Zemin's historical return is slightly below (by 0.96%) its expected return based on CAPM.