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:	29	0	18	35	32	18	24	−23	−16	−9
y:	18	−4	20	17	22	11	28	−2	−8	−6

(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 x values and also for y values. (Round your answers to two decimal places.)

	x	y
Lower Limit
Upper Limit

Use the intervals to compare the two funds.

75% of the returns for the balanced fund fall within a narrower range than those of the stock fund.75% of the returns for the stock fund fall within a narrower range than those of the balanced fund.    25% of the returns for the balanced fund fall within a narrower range than those of the stock fund.25% of the returns for the stock fund fall within a wider range than those of the balanced fund.

Answer 1

(a)

	108		5180
	96		2522

(b)

	10.8	9.6
	445.96	177.82
	21.12	13.33

(c)

Lower limit
Upper limit

Use the intervals to compare the two funds.

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