Question

a. Given the​ holding-period returns shown in the popup​ window,

MONTH   ZEMIN CORP.   MARKET
1   5%   4%
2   4%   2%
3   0%   2%
4   -3%   -3%
5   4%   1%
6   1%   3%

compute the average returns and the standard deviations for the Zemin Corporation and for the market. b. If​ Zemin's beta is 1.79 and the​ risk-free rate is 8 ​percent, what would be an appropriate required return for an investor owning​ Zemin? ​(​Note: Because the returns of Zemin Corporation are based on monthly​ data, you will need to annualize the returns to make them compatible 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 to be a fair​ return, given the​ firm's systematic​ risk?

Answer 1

Calculating the Average Return and Standard Deviation:-

Month	Zemin Return (Z) (%)	Market Return (M) (%)	[(Z) - E(Z)]	[(Z) - E(Z)]^2	[(M)-E(M)]	[(M) - E(M)]^2
1	5.00	4.00	3.17	10.0278	2.5000	6.2500
2	4.00	2.00	2.17	4.6944	0.5000	0.2500
3	0.00	2.00	-1.83	3.3611	0.5000	0.2500
4	-3.00	-3.00	-4.83	23.3611	-4.5000	20.2500
5	4.00	1.00	2.17	4.6944	-0.5000	0.2500
6	1.00	3.00	-0.83	0.6944	1.5000	2.2500
	11.00	9.00		46.8333		29.5000

a). - Average Return of Zemin Corp, [E(Z)] =

= 1.833%

- Average Return of Market, [E(M)] =

= 1.5%

- Standard Deviation of Zemin Corp =

= 2.79%

- Standard Deviation of Market =

= 2.22

b). Beta of Stock = 1.79

Risk-free rate = 8%

Average Monthly Market Return = 1.5%

Annual Market Return = 1.5%*12= 18%

Rf = Risk free Return = 8%

Rm = Market return = 18

Expected Return = 8% + 1.79(18% - 8%)

= 25.9%

c). Average Monthly Return of Zemin Corp = 1.833%

Annual Return of Zemin Corp = 1.833%*12

= 22%

Expected Return of Zemin Corp as per CAPM = 25.9%

As the Expected return as per systematic risk is higher than the historical period return. Thus, the stock is overvalued.

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