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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. (a) Compute Σx, Σx2, Σy, Σy2. Ex 97 ✓ Ex² Ey 100 ✔ Ey² x: 28 0 15 31 26 18 26 -12 -11 -24 y: 12 -3 28 8 24 28 23 -1 -9 -10 (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 x 9.7 s² S ✓ Lower Limit Upper Limit x X y (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 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. O 25% of the returns for the balanced fund fall within a narrower range than those of the stock fund. O25% of the returns for the stock fund fall within a wider range than those of the balanced fund. 8:21 PM

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 Σx, Σx2, Σy, Σy2. Ex 97 ✓ Ex² Ey 100 ✔ Ey² x: 28 0 15 31 26 18 26 -12 -11 -24 y: 12 -3 28 8 24 28 23 -1 -9 -10 (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 x 9.7 s² S ✓ Lower Limit Upper Limit x X y (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 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. O 25% of the returns for the balanced fund fall within a narrower range than those of the stock fund. O25% of the returns for the stock fund fall within a wider range than those of the balanced fund. 8:21 PM

MATLAB: An Introduction with Applications
MATLAB: An Introduction with Applications
6th Edition
ISBN:9781119256830
Author:Amos Gilat
Publisher:Amos Gilat
Chapter1: Starting With Matlab
Section: Chapter Questions
Problem 1P
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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. x: 28 0 15 31 26 18 26 -12 -11 -24 y: 12 -3 28 8 24 28 23 -1 59 -10 (a) Compute Σx, Σx2, Σy, Σy2. x 97 ΣΧ2 ✓ Ey² ΣΥ 100 (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 x 9.7 $2 6 y (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 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. AHORAR CON 86 8:21 PM 9/17/2023
Transcribed Image Text: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 15 31 26 18 26 -12 -11 -24 y: 12 -3 28 8 24 28 23 -1 59 -10 (a) Compute Σx, Σx2, Σy, Σy2. x 97 ΣΧ2 ✓ Ey² ΣΥ 100 (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 x 9.7 $2 6 y (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 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. AHORAR CON 86 8:21 PM 9/17/2023
(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 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.) 19/6 Use the coefficients of variation to compare the two funds. For each unit of return, the stock fund has lower risk. For each unit of return, the balanced fund has lower risk. For each unit of return, the funds have equal risk. If s represents risks and represents expected return, then s/x can be thought of as a measure of risk per unit of expected return. In this case, why is a smaller CV better? Explain. A smaller CV is better because it indicates a higher risk per unit of expected return. A smaller CV is better because it indicates a lower risk per unit of expected return. Fascing 海口 1761 8:22 PI
Transcribed Image Text:(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 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.) 19/6 Use the coefficients of variation to compare the two funds. For each unit of return, the stock fund has lower risk. For each unit of return, the balanced fund has lower risk. For each unit of return, the funds have equal risk. If s represents risks and represents expected return, then s/x can be thought of as a measure of risk per unit of expected return. In this case, why is a smaller CV better? Explain. A smaller CV is better because it indicates a higher risk per unit of expected return. A smaller CV is better because it indicates a lower risk per unit of expected return. Fascing 海口 1761 8:22 PI
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