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: 24 0 21 21 20 15 31 −19 −23 −17 y: 23 −4 8 8 28 18 27 −9 −1 −3

(a) Compute Σx, Σx2, Σy, Σy2.

Σx 73 Σx2 4223

Σy 95 Σy2 2601

(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
s2
s

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

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

	x	y
CV	%	%

Answer 1

a) Variable X:

Let x be a random variable representing annual percent return for Vanguard Total Stock Index (all stocks).

Variable Y:

b) Mean, Variance and SD of X :

Sample SD (X) = Sqrt(410.0111) = 20.2487

Mean, Variance and SD of Y :

SD(Y) = Sqrt(188.722) = 13.7376

c)

d) CV of X is:

CV of Y is:

CV of Y is