80.2K

Verified Solution

Link Copied!

Do bonds reduce the overall risk of an investment portfolio? Letx be a random variable representing annual percent returnfor Vanguard Total Stock Index (all stocks). Let y be arandom variable representing annual return for Vanguard BalancedIndex (60% stock and 40% bond). For the past several years, we havethe following data.

x:	19	0	34	15	13	20	37	−23	−17	−17
y:	17	−4	25	18	12	23	12	−5	−8	−10

(a) Compute Σx, Σx², Σy,Σy².

Σx		Σx2
Σy		Σy2

(b) Use the results of part (a) to compute the sample mean,variance, and standard deviation for x and for y.(Round your answers to two decimal places.)

	x	y
x
s2
s

(c) Compute a 75% Chebyshev interval around the mean for xvalues and also for y values. (Round your answers to twodecimal places.)

	x	y
Lower Limit
Upper Limit

Use the intervals to compare the two funds.

a. 75% of the returns for the balanced fund fall within anarrower range than those of the stock fund.

b. 75% of the returns for the stock fund fall within a narrowerrange than those of the balanced fund.    

c. 25% of the returns for the balanced fund fall within anarrower range than those of the stock fund.

d. 25% of the returns for the stock fund fall within a widerrange than those of the balanced fund.

(d) Compute the coefficient of variation for each fund. (Round youranswers to the nearest whole number.)

	x	y
CV	%	%

Use the coefficients of variation to compare the two funds.

a. For each unit of return, the stock fund has lower risk.

b. For each unit of return, the balanced fund has lowerrisk.    

c. For each unit of return, the funds have equal risk.

If s represents risks and x represents expectedreturn, then s/x can be thought of as a measureof risk per unit of expected return. In this case, why is a smallerCV better? Explain.

a. A smaller CV is better because it indicates a higherrisk per unit of expected return.

b. A smaller CV is better because it indicates a lowerrisk per unit of expected return.