Question
Consider the following two probability distributions of expected future returns for stocks A and B: Probability Return Stock A Stock B (%) (%) 0.1 -1%
Consider the following two probability distributions of expected future returns for stocks A and B:
Probability | Return | |
---|---|---|
Stock A | Stock B | |
(%) | (%) | |
0.1 | -1% | -3.5% |
0.2 | 0.2 | 0 |
0.4 | 1.2 | 2 |
0.2 | 2 | 2.5 |
0.1 | 3.8 | 4.5 |
Suppose you know that the expected rate of return for stock A is 1.2% and would like to calculate the expected return for stock B.
For each row in the table, indicate the approximate value of product of the rate of return for stock B multiplied by the probability of that return.
Probability | Return | piripiri |
---|---|---|
Stock B | (%) | |
(%) | ||
0.1 | -3.5% | (options: -0.7,-3.5,-0.35,0.1) % |
0.2 | 0 | (options:0,0.2) |
0.4 | 2 | (options 0.8, 0.4,2) |
0.2 | 2.5 | (options 0.25, 0.5, 0.2,2.5) |
0.1 | 4.5 | (options 0.1, 0.9, 4.5,0.45) |
Using your answers from the previous part of the question, the expected rate of return for stock B is approximately (5.5,1.4,1,0.85) %.
Suppose you know that the standard deviation of expected returns for stock B is 2.0347% and would like to calculate the standard deviation of expected returns for stock A.
Hint: Recall that the expected rate of return for stock A is 1.2%.
For each row in the table, indicate the approximate value of the product of the probability multiplied by the squared difference between the rate of return and the expected rate of return for stock A.
Probability | Return | pi(rir)2pirir2 |
---|---|---|
Stock A | ||
(%) | ||
0.1 | -1% | (option: 0.004, 0.484,4.84,-0.22) |
0.2 | 0.2 | (option 0.196,0.2,1,-0.1) |
0.4 | 1.2 | (option: 0.576,0) |
0.2 | 2 | (option: 0.128,0.64,0.08,1.024) |
0.1 | 3.8 | (options:6.76,0.26,2.5,0.676) |
Using your answers from the previous part of the question, the variance of the expected returns for stock A is approximately (0.02,13.24,1.488,4.3) while the standard deviation of expected returns for stock A is approximately (0.1414,3.6387,1.2198,2.0736) %.
Let represent the standard deviation of a stocks returns and rr represent the expected returns of that stock.
The formula for calculating the coefficient of variation for a stocks return is options: r , /r , +r
Using this formula, along with your calculations in the previous parts of the problem, the coefficient of variation of stock B is approximately 1.4534, 3.434, 2.8486, 0.634699
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