Do bonds reduce the overall risk of an investment portfolio? Let x be a random v
ID: 3290941 • Letter: D
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.
15
0
21
21
22
19
17
23
20
16
21
6
10
15
14
9
27
11
1
9
(a) Compute x, x2, y, y2.
(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.)
(c) Compute a 75% Chebyshev interval around the mean for x values and also for y values. (Round your answers to two decimal places.)
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.)
Use the coefficients of variation to compare the two funds.
a)For each unit of return, the stock fund has lower risk.
b)For each unit of return, the balanced fund has lower risk.
c)For each unit of return, the funds have equal risk.
If s represents risks and x 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)A smaller CV is better because it indicates a higher risk per unit of expected return.
b)A smaller CV is better because it indicates a lower risk per unit of expected return.
x:15
0
21
21
22
19
17
23
20
16
y:21
6
10
15
14
9
27
11
1
9
Explanation / Answer
a)
b)
c) 75 % chebyshev is within 2 sd
hence for x
=(5.6 - 2*19.51068 , 5.6 +2*19.51068)
=(-33.42136,44.62136)
for y
(6.9 - 2 *14.94806) ,(6.9 + 2 *14.94806)
=(-22.9961,36.79612)
y is balanced and it is narrower
hence
option A)
75% of the returns for the balanced fund fall within a narrower range than those of the stock fund is correct
d) CV = s /mean
x = 19.51068/5.6 = 3.48405
y = 14.94806/6.9 = 2.166385
since y has less CV
b)For each unit of return, the balanced fund has lower risk. is correct
b)A smaller CV is better because it indicates a lower risk per unit of expected return.
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x y x^2 y^2 15 21 225 441 0 -6 0 36 21 10 441 100 21 15 441 225 22 14 484 196 19 9 361 81 17 27 289 729 -23 -11 529 121 -20 -1 400 1 -16 -9 256 81 summation 56 69 3426 2011Related Questions
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