现代投资组合理论与投资分析 第七章 答案

Elton, Gruber, Brown, and Goetzmann

Modern Portfolio Theory and Investment Analysis , 7th Edition

Solutions to Text Problems: Chapter 7

Chapter 7: Problem 1

We will illustrate the answers for stock A and the market portfolio (S&P 500); the answers for stocks B and C are found in an identical manner.

The sample mean monthly return on stock A is:

%

946.212

94

.048.775.1207.118.197.879.216.357.112.427.1505.1212

12

1

=-+++---++-+=

=

∑=t At

A R

R

The sample mean monthly return on the market portfolio (the answer to part 1.E) is:

%

005.312

15

.147.216.646.311.277.643.441.448.441.299.528.1212

12

1

=-+++--+++++=

=

∑=t m t

m R

R

Using data given in the problem and the above two sample mean monthly returns, we have the following: Month t

A

At R R - ()2

A

At

R R

-

m

m t R R - ()

2

m

mt

R R

-

()()m

m t A At

R R R R

--

1 9.104 82.883 9.275 86.026 84.44

2 12.324 151.881 2.985 8.910 36.79

3 -7.066 49.928 -0.595 0.35

4 4.2 4 -1.376 1.893 1.47

5 2.17

6 -2.03 5 0.214 0.046 1.405 1.974 0.3 6 -5.736 32.902 1.425 2.031 -8.1

7 7 -11.916 141.991 -9.775 95.551 116.4

8 8 -4.126 17.024 -5.115 26.163 21.1

9 -1.876 3.519 0.455 0.207 -0.85 10 9.804 96.118 3.155 9.954 30.93 11 4.534 20.557 -0.535 0.286 -2.43 12

-3.886 15.101 -4.155 17.264 16.15

Sum

0.00

613.84

0.00

250.90

296.91

The sample variance and standard deviation of the stock A’s monthly return are:

()

15.5112

84.61312

12

1

2

2==

-=

∑=t A

At

A

R R

σ

%15.715.51==A σ

The sample variance (the answer to part 1.F) and standard deviation of the market portfolio’s monthly return are:

()

91.2012

90.25012

12

1

2

2==

-=

∑=t m

m t

m

R R

σ

%57.491.20==m σ

The sample covariance of the returns on stock A and the market portfolio is:

()()[]

74.2412

91.29612

12

1

==

--=

∑=t m

m t A At

Am R R R R

σ

The sample correlation coefficient of the returns on stock A and the market portfolio (the answer to part 1.D) is:

757

.057

.415.774.24=⨯=

=

m

A Am Am σσσρ

The sample beta of stock A (the answer to part 1.B) is:

183.191

.2074.242==

=

m

Am A σ

σβ

The sample alpha of stock A (the answer to part 1.A) is:

%609.0%005.3183.1%946.2-=⨯-=-=m A A A R R βα

Each month’s sample residual is security A’s actual return that month minus the return that month predicted by the regression. The regression’s predic ted monthly return is: mt A A edict ed t A R R βα-=Pr ,,