Investing: Stocks and Bonds Do bonds reduce the overall risk of an investment portfolio? Let x be a random variable representing the annual percent return for Vanguard Total Stock Index (all stocks). Let y be a random variable representing annual return for Vanguard Balanced Index (60% stock NS 40% BOND. For the past several years, we have the following data: x: 11 0 36 21 31 23 24 -11 -11 -21 y: 10 -2 29 14 22 18 14 -2 -3 -10 (a) Compute ∑?,∑?2, ∑?, ???∑?2. (b) Use the results of part (a) to compute the sample mean, variance, and standard deviation for both x and y. (c) Compute a 75% Chebyshev interval around the mean for values and also for y values. Use the intervals to compare the two funds. (d) Interpretation: Compute the coefficient of variation for each fund. Use the coefficient of variation to compare the two funds. Why is a smaller CV better?
#16. Investing: Stocks and Bonds Do bonds reduce the overall risk of an investment portfolio? Let x be a random variable representing the annual percent return for Vanguard Total Stock Index (all stocks). Let y be a random variable representing annual return for Vanguard Balanced Index (60% stock NS 40% BOND. For the past several years, we have the following data:
x: 11 0 36 21 31 23 24 -11 -11 -21
y: 10 -2 29 14 22 18 14 -2 -3 -10
(a) Compute ∑?,∑?2, ∑?, ???∑?2.
(b) Use the results of part (a) to compute the sample mean, variance, and standard deviation for both x and y.
(c) Compute a 75% Chebyshev interval around the mean for values and also for y values. Use the intervals to compare the two funds.
(d) Interpretation: Compute the coefficient of variation for each fund. Use the coefficient of variation to compare the two funds. Why is a smaller CV better?
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