8A-1 BETA COEFFICIENTS AND RATES OF RETURN You are given the following set of data: Historical Rates of Return () Stock Y(F,) NYSE (F.) Year 1 3.0% 4.0% 18.2 14.3 3 9.1 19.0 4 (6.0) (14.7) 5 (15.3) (26.5) 33.1 37.2 6.1 23.8 8. 3.2 (7.2) 9. 14.8 6.6 10 24.1 20.5 11 18.0 30.6 Mean 9.8% 9.8% 13.8 19.6 d. Suppose the regression line had been downward sloping and the beta coefficient had been negative. What would this imply about (1) Stock Y's relative riskiness and (2) its probable risk premium? e. Construct an illustrative probability distribution graph of returns (see Figure 8.3) for portfolios consisting of (1) only Stock Y, (2) 1% each of 100 stocks with beta coefficients similar to that of Stock Y, and (3) all stocks (i.e., the distribution of returns on the market). Use as the expected rate of return the arithmetic mean as given previously for both Stock Y and the market, and assume that the distributions are normal. Are the expected returns "reasonable"; that is, is it reasonable that fy = fM = 9.8%? %3D %3D f. Now, suppose that in the next year, Year 12, the market return was 27%, but Firm Y increased its use of debt, which raised its perceived risk to investors. Do you think that the return on Stock Y in Year 12 could be approximated by this historical characteristic line?

Essentials Of Investments
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Chapter1: Investments: Background And Issues
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BETA COEFFICIENTS AND RATES OF RETURN You are given the following
set of data:
8A-1
Historical Rates of Return (r)
Stock Y(F,)
NYSE (F.)
Year
1
3.0%
4.0%
18.2
14.3
9.1
19.0
(6.0)
(14.7)
(15.3)
(26.5)
33.1
37.2
7
6.1
23.8
3.2
(7.2)
9.
14.8
6.6
10
24.1
20.5
11
18.0
30.6
Mean
9.8%
9.8%
13.8
19.6
d. Suppose the regression line had been downward sloping and the beta
coefficient had been negative. What would this imply about (1) Stock
Y's relative riskiness and (2) its probable risk premium?
e. Construct an illustrative probability distribution graph of returns (see
Figure 8.3) for portfolios consisting of (1) only Stock Y, (2) 1% each
of 100 stocks with beta coefficients similar to that of Stock Y, and (3)
all stocks (i.e., the distribution of returns on the market). Use as the
expected rate of return the arithmetic mean as given previously for
both Stock Y and the market, and assume that the distributions are
normal. Are the expected returns "reasonable"; that is, is it reasonable
that î, = fM = 9.8%?
%3D
%3D
f. Now, suppose that in the next year, Year 12, the market return was
27%, but Firm Y increased its use of debt, which raised its perceived
risk to investors. Do you think that the return on Stock Y in Year 12
could be approximated by this historical characteristic line?
f, = 3.8% + 0.62(r.) = 3.8% + 0.62(27%) = 20.5%
%3D
%3D
Transcribed Image Text:Problems BETA COEFFICIENTS AND RATES OF RETURN You are given the following set of data: 8A-1 Historical Rates of Return (r) Stock Y(F,) NYSE (F.) Year 1 3.0% 4.0% 18.2 14.3 9.1 19.0 (6.0) (14.7) (15.3) (26.5) 33.1 37.2 7 6.1 23.8 3.2 (7.2) 9. 14.8 6.6 10 24.1 20.5 11 18.0 30.6 Mean 9.8% 9.8% 13.8 19.6 d. Suppose the regression line had been downward sloping and the beta coefficient had been negative. What would this imply about (1) Stock Y's relative riskiness and (2) its probable risk premium? e. Construct an illustrative probability distribution graph of returns (see Figure 8.3) for portfolios consisting of (1) only Stock Y, (2) 1% each of 100 stocks with beta coefficients similar to that of Stock Y, and (3) all stocks (i.e., the distribution of returns on the market). Use as the expected rate of return the arithmetic mean as given previously for both Stock Y and the market, and assume that the distributions are normal. Are the expected returns "reasonable"; that is, is it reasonable that î, = fM = 9.8%? %3D %3D f. Now, suppose that in the next year, Year 12, the market return was 27%, but Firm Y increased its use of debt, which raised its perceived risk to investors. Do you think that the return on Stock Y in Year 12 could be approximated by this historical characteristic line? f, = 3.8% + 0.62(r.) = 3.8% + 0.62(27%) = 20.5% %3D %3D
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