Question

Do bonds reduce the overall risk of an investment portfolio? Let x be a random variable representing 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 and 40% bond).

For the past several years, we have the following data

x: 17,0,20,35,37,33,26,−15,−24,−22

y: 20,−10,8,18,19,11,18,−8,−5,−4

(a) Compute ∑x, ∑x2, ∑y, ∑y2

(b) Use the results of part (a) to compute the sample mean, variance, and standard deviation for x and for y.

(c) Compute a 75% Chebyshev interval around the mean for x values and also for y values. Use the intervals to compare the two funds.

(d) Compute the coefficient of variation for each fund. Use the coefficients of variation to compare the two funds. If s represents risks and image from custom entry tool represents expected return, then image from custom entry tool can be thought of as a measure of risk per unit of expected return. In this case, why is a smaller CV better? Explain.

Answer 1