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:	28	0	38	25	17	33	28	−18	−21	−19
y:	18	−8	28	18	8	15	12	−9	−9	−4

Compute a 75% Chebyshev interval around the mean for x values and also for y values. (Round your answers to two decimal places.)

Answer 1

We start by calculating the mean and standard deviation

i	1	2	3	4	5	6	7	8	9	10	Total	Avergae	Std dev
X:	28	0	38	25	17	33	28	-18	-21	-19	111	11.1	23.35
	285.61	123.21	723.61	193.21	34.81	479.61	285.61	846.81	1030.41	906.01	4908.9
y:	18	-8	28	18	8	15	12	-9	-8	-4	70	7	13.33
	121	225	441	121	1	64	25	256	225	121	1600

Formula

Mean =

Std Dev =

\

Chebyshev's interval

......k is the no.of std dev away from the mean.

Where

Solving for k

k = 2....................Since k is a positive integer.

Substituting in the above formulae

Variable	Mean	Std Dev	Lower limit ()	Upper Limit ()
X	11.1	23.35	-35.61	57.81
Y	7	13.33	-19.67	33.67