Do bonds reduce the overall risk of an investment portfolio
Last updated: 1/19/2024
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 120 35 35 20 30 24 23 12 12 22 y 10 a Compute Ex Ex 98 LAUSE SALT Compute Ex Ex 4546 Compute y Sy 86 Compute Ey Sy2 2260 s 2 30 12 21 17 15 2 s 358 56 x S 18 9357 x 152 04 1 4 b Use the results of part a to compute the sample mean variance and standard deviation for x Round your answers to four decimal places X 9 8 Use the results of part a to compute the sample mean variance and standard deviation for y Round your answers to four decimal places y 8 6 x S 12 3304 x 3 12 c Compute a 75 Chebyshev interval around the mean for x values Enter your answer in the form lower limit to upper limit Include the word to Round your numerical values to two decimal places x Use the intervals to compare the two funds Compute a 75 Chebyshev interval around the mean for y values Enter your answer in the form lower limit to upper limit Include the word to Round your numerical values to two decimal places k 2 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 25 of the returns for the stock fund fall within a wider range than those of the balanced fund x d Compute the coefficient of variation in percent for fund x Round your answer to the nearest whole number X 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 Compute the coefficient of variation in percent for fund y Round your answer to the nearest whole number 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