Do bonds reduce the overall risk of an investment portfolio? Letx be a random variable representing annual percent return forVanguard Total Stock Index (all stocks). Let y be a random variablerepresenting annual return for Vanguard Balanced Index (60% stockand 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 xvalues and also for y values. Use the intervals to compare the twofunds.
(d) Compute the coefficient of variation for each fund. Use thecoefficients of variation to compare the two funds. If s representsrisks and image from custom entry tool represents expected return,then image from custom entry tool can be thought of as a measure ofrisk per unit of expected return. In this case, why is a smaller CVbetter? Explain.
