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:	30	0	17	38	38	34	25	−16	−22	−22
y:	10	−4	16	14	20	20	20	−8	−1	−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

Answer 1

from above:

a)

Σx=	122.00	Σx2=	7082.0000
Σy=	81.00	Σy2=	1869.0000

b)

	x	y
x̅ =	12.20	8.10
s2	621.51	134.77
s	24.93	11.61

c)

		x	y
lower limit		-37.66	-15.12
upper limit		62.06	31.32