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: 16 0 13 17 11 23 20 −8 −11 −24 y: 11 −5 26 15 19 28 27 −11 −6 −7 (a) Compute Σx, Σx2, Σy, Σy2. Σx 57 Correct: Your answer is correct. Σx2 Incorrect: Your answer is incorrect. Σy 97 Correct: Your answer is correct. Σy2 Incorrect: Your answer is incorrect. (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

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: 16 0 13 17 11 23 20 −8 −11 −24

y: 11 −5 26 15 19 28 27 −11 −6 −7

Compute Σx, Σx2, Σy, Σy2.

	x:	y:	x*x	y*y
	16	11	256	121
	0	-5	0	25
	13	26	169	676
	17	15	289	225
	11	19	121	361
	23	28	529	784
	20	27	400	729
	-8	-11	64	121
	-11	-6	121	36
	-24	-7	576	49
Total	57	97	2525	3127

Σx 57 Correct: Your answer is correct

Σx2 = 2525

Σy 97 Correct: Your answer is correct.

Σy2 =3127

(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.)

Descriptive statistics
	x:	y:
count	10	10
mean	5.70	9.70
sample variance	244.46	242.90
sample standard deviation	15.64	15.59

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
mean - 1s- Lower Limit	-9.94	-5.89
mean + 1s- Upper Limit	21.34	25.29

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.