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:	20	0	16	15	30	38	23	−15	−10	−23
y:	15	−7	22	26	27	21	10	−1	−5	−8

(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.

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

	x	y
CV	%	%

Answer 1

a) From the given data

S.NO.	X	Y	X^2	Y^2
1	20	15	400	225
2	0	-7	0	49
3	16	22	256	484
4	15	26	225	676
5	30	27	900	729
6	38	21	1444	441
7	23	10	529	100
8	-15	-1	225	1
9	-10	-5	100	25
10	-23	-8	529	64
Total:	94	100	4608	2794

Σx = 94 Σx^{2 =} 4608 Σy = 100 Σy².= 2794

b) Mean and Variance of X :

Sample SD(X) = sqrt(413.822) = 20.3426

Mean and Variance of Y:

SD(Y) = Sqrt(199.333) = 14.1185

c)

d)