Do bonds reduce the overall risk of an investment portfolio? Let x be a random v
ID: 3237557 • 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.
34
0
34
35
12
28
14
18
8
17
25
2
28
8
11
24
27
9
4
2
(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.)
x(- this is above the 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.)
Use the intervals to compare the two funds.
(a) 75% of the returns for the balanced fund fall within a narrower range than those of the stock fund.
(b) 75% of the returns for the stock fund fall within a narrower range than those of the balanced fund.
(c)25% of the returns for the balanced fund fall within a narrower range than those of the stock fund.
(d)25% of the returns for the stock fund fall within a wider range than those of the balanced fund.
Which is the answer_______?__________
(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.
Which is the answer_______________?___________
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.
Which is the answer_______?_________
x:34
0
34
35
12
28
14
18
8
17
y:25
2
28
8
11
24
27
9
4
2
Explanation / Answer
Answer:
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:
34
0
34
35
12
28
14
18
8
17
y:
25
2
28
8
11
24
27
9
4
2
(a) Compute x, x2, y, y2.
x=114
x2
5338
y=106
y2
3004
(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.)
x
y
x(- this is above the x)_____?_______
11.40
10.60
s2_____?_______
448.71
208.93
s_____?________
21.18
14.45
(c) Compute a 75% Chebyshev interval around the mean for x values and also for y values. (Round your answers to two decimal places.)
75% Chebyshev interval around the mean is mean ±2sd
x
y
Lower Limit
x=-30.97 y=
-18.31
Upper Limit
53.77
39.51
Use the intervals to compare the two funds.
(a) 75% of the returns for the balanced fund fall within a narrower range than those of the stock fund.
Which is the answer_______?__________
(d) Compute the coefficient of variation for each fund. (Round your answers to the nearest whole number.)
x
y
CV
185.81 %
136.36 %
Use the coefficients of variation to compare the two funds.
(b) For each unit of return, the balanced fund has lower risk.
Which is the answer b
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.
(b) A smaller CV is better because it indicates a lower risk per unit of expected return.
Which is the answer b
Descriptive statistics
x:
y:
n
10
10
mean
11.40
10.60
sample standard deviation
21.18
14.45
sample variance
448.71
208.93
minimum
-18
-9
maximum
35
28
range
53
37
sum
114.00
106.00
sum of squares
5,338.00
3,004.00
deviation sum of squares (SSX)
4,038.40
1,880.40
empirical rule
mean - 1s
-9.78
-3.85
mean + 1s
32.58
25.05
percent in interval (68.26%)
50.0%
60.0%
mean - 2s
-30.97
-18.31
mean + 2s
53.77
39.51
percent in interval (95.44%)
100.0%
100.0%
mean - 3s
-52.15
-32.76
mean + 3s
74.95
53.96
percent in interval (99.73%)
100.0%
100.0%
tolerance interval 99.73% lower
-52.15
-32.76
tolerance interval 99.73% upper
74.95
53.96
half-width
63.55
43.36
skewness
-0.24
0.02
kurtosis
-1.67
-1.93
coefficient of variation (CV)
185.81%
136.36%
x:
34
0
34
35
12
28
14
18
8
17
y:
25
2
28
8
11
24
27
9
4
2
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