Financial Statistics
QUESTION 1 The managing partner for Westwood One Investment Managers Inc. gave a public seminar in which she discussed a number of issues, including investment risk analysis. In that seminar, she reminded people that the coefficient of variation can often be used as a measure of risk of an investment. To demonstrate her point of view, she used two hypothetical stocks as examples. She let x equal the change in assets for a $1,000.00 investment in stock1 and y reflect the change in assets for a $1,000.00 investment in stock2. She showed the seminar participants the following probability distributions: x | P (x) | Y | P (y) | $-1,000 | 0.1 | $-1,000 | 0.2 | $0 | 0.1 | $0 | 0.4 | $500 | 0.3 | $500 | 0.3 | $1,000 | 0.3 | $1,000 | 0.05 | $2,000 | 0.2 | $2,000 | 0.05 |
a. Compute the expected values for the random variables x and y. (2 marks)
b. Compute the standard deviations for the random variables x and y. (3 marks)
c. Compute the coefficient of variation for each random variable. (2 marks)
d. Referring to part c, suppose the seminar director said that the first stock was riskier since its standard deviation was greater than the standard deviation of the second stock. How would you respond to her assertion? (3 marks)
Solution 1: In the first solution we calculate the expected value of the random variable or population of arithmetic mean of x and y:
μ = Σ x / N = 2,500/5 = 500 = 3,000/5 = 600
Solution 2:
The variance for x is 5,000,000
The variance for y is 5,050,000
Solution 3:
The Standard deviation is found by squaring the result of the variance:
SD of x = 2236, this tells us on average how far is from sample mean.
SD of y = 2247
Solution 4:
The coefficient of variation is as follows:
The coefficient of variation for x is: 0.000447.
The coefficient of variation for y is: 0.000445.
Solution 5:
On the argument that the SD of the first is greater than to the first one is not true. In
a. Compute the expected values for the random variables x and y. (2 marks)
b. Compute the standard deviations for the random variables x and y. (3 marks)
c. Compute the coefficient of variation for each random variable. (2 marks)
d. Referring to part c, suppose the seminar director said that the first stock was riskier since its standard deviation was greater than the standard deviation of the second stock. How would you respond to her assertion? (3 marks)
Solution 1: In the first solution we calculate the expected value of the random variable or population of arithmetic mean of x and y:
μ = Σ x / N = 2,500/5 = 500 = 3,000/5 = 600
Solution 2:
The variance for x is 5,000,000
The variance for y is 5,050,000
Solution 3:
The Standard deviation is found by squaring the result of the variance:
SD of x = 2236, this tells us on average how far is from sample mean.
SD of y = 2247
Solution 4:
The coefficient of variation is as follows:
The coefficient of variation for x is: 0.000447.
The coefficient of variation for y is: 0.000445.
Solution 5:
On the argument that the SD of the first is greater than to the first one is not true. In