Expected returns Stocks X and Y have the following probability distributions of
ID: 2708982 • Letter: E
Question
Expected returns
Stocks X and Y have the following probability distributions of expected future returns:
1. Calculate the expected rate of return, rY, for Stock Y (rX = 9.60%.) Round your answer to two decimal places.
%
2. Calculate the standard deviation of expected returns, X, for Stock X (Y = 21.45%.) Round your answer to two decimal places.
%
3. Now calculate the coefficient of variation for Stock Y. Round your answer to two decimal places.
4. Is it possible that most investors might regard Stock Y as being less risky than Stock X? CHOOSE ONE.
If Stock Y is more highly correlated with the market than X, then it might have the same beta as Stock X, and hence be just as risky in a portfolio sense.
If Stock Y is less highly correlated with the market than X, then it might have a lower beta than Stock X, and hence be less risky in a portfolio sense.
If Stock Y is less highly correlated with the market than X, then it might have a higher beta than Stock X, and hence be more risky in a portfolio sense.
If Stock Y is more highly correlated with the market than X, then it might have a higher beta than Stock X, and hence be less risky in a portfolio sense.
If Stock Y is more highly correlated with the market than X, then it might have a lower beta than Stock X, and hence be less risky in a portfolio sense.
ANSWER FULLY
Probability X Y 0.2 -12% -23% 0.2 5 0 0.3 10 22 0.2 23 25 0.1 34 47Explanation / Answer
Probability
X
rX (Prob * X)
Y
rY
0.2
-0.12
-0.02
-0.23
-0.05
0.2
0.05
0.01
0
0
0.3
0.1
0.03
0.22
0.07
0.2
0.23
0.05
0.25
0.05
0.1
0.34
0.03
0.47
0.05
0.0960
0.1170
(‘a) Expected rate of return for stock Y
rY = 11.70 %
(‘2) Standard Deviation of x ( X )
Probability
X
rX
Deviation
(D = x-0.096)
D2
D2 x Probability
0.2
-0.12
-0.02
-0.2160
0.0467
0.0093
0.2
0.05
0.01
-0.0460
0.0021
0.0004
0.3
0.1
0.03
0.0040
0.00002
0.000005
0.2
0.23
0.05
0.1340
0.0180
0.0036
0.1
0.34
0.03
0.2440
0.0595
0.0060
0.0960
0.0193
X = (D2 x Probability)1/2
X = 13.89 %
(‘3) Coefficient of Variation of stock Y
Coefficient of variation = Standard Deviation / Expected Return
Coefficient of variation = 21.45/11.70
Coefficient of variation = 1.83
(‘4)
Correlation coefficient and beta can be same only in the case when the standard deviation of two stocks is same.
Beta shows how strongly a stock responds to market volatility. A beta of 1 means stocks move with market. Beta of less than 1 means stock is less responsive to market volatility. Beta of more than 1 means stock is high responsive to market.
= a,b a / b
Where = a,b is the correlation between two returns. is the respective volatility.
It shows if correlation is high beta will be high , and high beta shows high risk.
Hence the following option is correct.
If stock Y is less highly correlated with market than X, then it might have a lower beta than stock X, and hence be less risky in a portfolio sense.
Probability
X
rX (Prob * X)
Y
rY
0.2
-0.12
-0.02
-0.23
-0.05
0.2
0.05
0.01
0
0
0.3
0.1
0.03
0.22
0.07
0.2
0.23
0.05
0.25
0.05
0.1
0.34
0.03
0.47
0.05
0.0960
0.1170
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