Question

Do bonds reduce the overall risk of an investment portfolio? Let x be a random variable representing annual percent return for the Vanguard Total Stock Index (all Stocks). Let y be a random variable representing annual return for the Vanguard Balanced Index (60% stock and 40% bond). For the past several years, assume the following data. 15 0 38 21 31 23 24 -15 -15 -21 6 -4 28 18 22 17 18 -4 -5 -6 ​ The sample means for x and y are 10.10 and 9.00, respectively. Compute a 75% Chebyshev interval around the mean for x-values and also for y-values. Round your answers to the nearest hundredth. for x-values: –32.32 to 23.11 and for y-values: –4.01 to –15.92 for x-values: –17.02 to 35.02 and for y-values: –32.32 to 52.52 for x-values: –32.32 to 23.11 and for y-values: –17.02 to 22.01 for x-values: –11.11 to 52.52 and for y-values: –4.01 to 35.02 for x-values: –32.32 to 52.52 and for y-values: –17.02 to 35.02

Answer 1

At least -1/k^2 values fall between (mean - k * sd) and (mean + k * sd)

1-1/2^2 = 1-1/4 = 3/5 = 0.75

mean - 2 * sd = 10.10 - 2 * 21.205 = –32.32

mean + 2sd = 10.10 + 2 * 21.205 = 52.52

75% Chebyshev interval around the mean of the x values lies in between –32.32 to 52.52

mean - 2 * sd = 9 - 2 * 13.013 = –17.02

mean + 2sd = 10.10 + 2 * 13.013 = 35.02

75% Chebyshev interval around the mean of the y values lies in between –17.02 to 35.02

For x-values: –32.32 to 52.52 and for y-values: –17.02 to 35.02