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. (a) Compute Ex, Σx2, Σy, Σγ2. Ex 87 Ey 106 x 8.70 x: 20 0 11 23 38 22 21 -19 -14 -15 y: 24 -10 8 24 25 20 27 -1 -4 -7 s² (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 four decimal places.) X y S ✔ Ex² 5059 ✔ Ey² Lower Limit Upper Limit ✓ 10.60 X (c) Compute a 75% Chebyshev interval around the mean for x values and also for y values. (Round your answers to two decimal places.) y X Use the intervals to compare the two funds. O 75% of the returns for the balanced fund fall within a narrower range than those of the stock fund. O 75% of the returns for the stock fund fall within a narrower range than those of the balanced fund. O25% of the returns for the balanced fund fall within a narrower range than those of the stock fund. O 25% of the returns for the stock fund fall within a wider range than those of the balanced fund.
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. (a) Compute Ex, Σx2, Σy, Σγ2. Ex 87 Ey 106 x 8.70 x: 20 0 11 23 38 22 21 -19 -14 -15 y: 24 -10 8 24 25 20 27 -1 -4 -7 s² (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 four decimal places.) X y S ✔ Ex² 5059 ✔ Ey² Lower Limit Upper Limit ✓ 10.60 X (c) Compute a 75% Chebyshev interval around the mean for x values and also for y values. (Round your answers to two decimal places.) y X Use the intervals to compare the two funds. O 75% of the returns for the balanced fund fall within a narrower range than those of the stock fund. O 75% of the returns for the stock fund fall within a narrower range than those of the balanced fund. O25% of the returns for the balanced fund fall within a narrower range than those of the stock fund. O 25% of the returns for the stock fund fall within a wider range than those of the balanced fund.
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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.
y: 24 -10 8
(a) Compute Ex, Σx2, Σy, Σy2.
Ex 87
2y 106
IX N
T
Lower Limit
Upper Limit
23 38 22 21 -19 -14 -15
24 25 20 27 -1
-4
-4
-7
Σχ2 5059
Σy2
X
(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 four decimal places.)
y
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10.60
X
(c) Compute a 75% Chebyshev interval around the mean for x values and also for y values. (Round your answers to two decimal places.)
Y
Use the intervals to compare the two funds.
O 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.
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