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.

x: 22 0 12 14 31 37 16 −22 −11 −18

y: 12 −4 21 20 12 19 9 −3 −11 −8

(a) Compute Σx, Σx2, Σy, Σy2. Σx Σx2 Σy Σy2 (

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 s2 s

(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 y Lower Limit: Upper Limit:

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.

(d) Compute the coefficient of variation for each fund. (Round your answers to the nearest whole number.) x y CV % %

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.

Answer #1

(a)

x | y | x² | y² |

22 | 12 | 484 | 144 |

0 | -4 | 0 | 16 |

12 | 21 | 144 | 441 |

14 | 20 | 196 | 400 |

31 | 12 | 961 | 144 |

37 | 19 | 1369 | 361 |

16 | 9 | 256 | 81 |

-22 | -3 | 484 | 9 |

-11 | -11 | 121 | 121 |

-18 | -8 | 324 | 64 |

Σx |
Σy |
Σx² |
Σy² |

81 |
67 |
4339 |
1781 |

(b)

x | y | |

xbar | 8.1 | 6.7 |

s² | 409.21 | 148.01 |

s | 20.23 | 12.17 |

(c)

x | y | |

Lower Limit | -32.36 | -17.63 |

Upper Limit | 48.56 | 31.03 |

75% of the returns for the balanced fund fall within a narrower range than those of the stock fund.

(d)

x | y | |

CV | 250% | 182% |

For each unit of return, the balanced fund has lower risk.

A smaller CV is better because it indicates a lower risk per unit of expected return.

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:
20
0
28
34
18
35
14
−21
−18
−16
y:
22
−3
25
23
14
8
16
−8
−11
−8
(a) Compute Σx,...

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: 23 0 37 35 16 22 14 −20 −11 −15 y: 21 −10 17 21 16 18 17
−3 −9 −4
(a) Compute Σx,...

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:
38
0
21
24
19
16
36
−22
−24
−8
y:
10
−2
27
25
16
15
15
−10
−7
−5
(a) Compute Σx,...

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: 32 0 36 21 38 12 33 −24 −22 −24
y: 26 −10 18 13 9 26 18 −4 −4 −9
(a) Compute Σx,...

Pax World Balanced is a highly respected, socially responsible
mutual fund of stocks and bonds. Vanguard Balanced Index is another
highly regarded fund that represents the entire U.S. stock and bond
market (an index fund). The mean and standard deviation of
annualized percent returns are shown below. The annualized mean and
standard deviation are for a recent 10-years period.
†. Pax World Balanced: x = 9.55%; s = 13.83% Vanguard Balanced
Index: x = 8.79%; s = 12.32%
(a) Compute...

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. Compute the coefficient of variation for each fund.
Round your answers to the nearest tenth. x: 15 0 37 22 35 24 25 -15...

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. Compute. x: 15 0 38 25 31 27 28 15 15 25 y: 8 2 29
18 26 16 18 2 3 8

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...

Pax World Balanced is a highly respected, socially responsible
mutual fund of stocks and bonds. Vanguard Balanced Index is another
highly regarded fund that represents the entire U.S. stock and bond
market (an index fund). The mean and standard deviation of
annualized percent returns are shown below. The annualized mean and
standard deviation are for a recent 10-years period.†. Pax World
Balanced: x = 9.43%; s = 14.28% Vanguard Balanced Index: x = 9.00%;
s = 12.80% (a) Compute the...

Do heavier cars really use more gasoline? Suppose a car is
chosen at random. Let x be the weight of the car (in hundreds of
pounds), and let y be the miles per gallon (mpg).
x
27
43
31
47
23
40
34
52
y
30
20
25
13
29
17
21
14
Complete parts (a) through (d), given Σx = 297, Σy = 169, Σx2 =
11,737, Σy2 = 3861, Σxy = 5845, and r ≈ −0.944.
(a) Verify...

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