Summary Measures

Document Sample

```					As a financial analyst for CKC Corporation, you have provided a forecast (as demonstrated
below) of the economy and the performance of your company in the economy. Use this
information to illustrate the expected rate of return and the risk as measured by the standard
deviation of those returns.

Economic State     Probability    Return    (r - E( r ))2

Recession           15%           -2%        0.01932
Normal Growth         65%           12%        0.00000
Prosperity          20%           22%        0.01020

Expected Return 11.90%
Variance 0.00494
Standard Deviation  7.03%

Summary Measures
Formula   E(r) = S pi*ri           mean
s = S pi*(ri-E(r))
2                   2
variance
2 1/2
s = (s )                 standard deviation

Summary Measures
You have decided to create a portfolio that includes only two assets, Mars, Inc. common
stock and JVC Common stock. Before making your investment, you would like to
determine the risk and return tradeoffs between these two stocks as you create your
portfolio. Given the following return information, determine the correlation between these
stocks and create the efficient frontier (using 10% weight increments) their combinations
would reveal.
Period        rMars        rJVC                  wMars      rportfolio sportfolio  rportfolio
1         18%         19%                      0%      16.30%        7.47%    16.30%
2         14%         12%                     10%      16.29%        6.75%    16.29%
3         13%         26%                     20%      16.28%        6.04%    16.28%
4         14%         14%                     30%      16.27%        5.33%    16.27%
5         15%          6%                     40%      16.26%        4.65%    16.26%
6         17%          8%                     50%      16.25%        3.99%    16.25%
7         19%         28%                     60%      16.24%        3.37%    16.24%
8         18%         12%                     70%      16.23%        2.81%    16.23%
9         18%         15%                     80%      16.22%        2.37%    16.22%
10         16%         23%                     90%      16.21%        2.10%    16.21%
mean         16.20%      16.30%                 100%      16.20%        2.10%    16.20%
Std. Dev.      2.10%        7.47%
Variance     0.00044 0.00558
Correlation  0.109214
Covariance 0.000171

rportfolio

68b374c6-2be8-4ff7-b26f-71abcdea699f.xls
rportfolio

16.32%

16.30%

16.28%

16.26%

16.24%

16.22%

16.20%

16.18%
0.00%   1.00%   2.00%   3.00%   4.00%        5.00%   6.00%   7.00%   8.00%

68b374c6-2be8-4ff7-b26f-71abcdea699f.xls
Suppose you are the money manager of a \$4 million investment fund. The fund
consists of 4 stocks with the following investments and betas. If the market's
required rate of return is 14%, and the risk-free rate is 6%, what is the fund's
required rate of return?
Stock        Investment     Beta       w     rM   14%             rRF      6%
A          \$400,000       1.50   10.00%
B          \$600,000      -0.50   15.00%
C         \$1,000,000      1.25   25.00%
D         \$2,000,000      0.75   50.00%
Port            \$4,000,000   0.7625

rp           12.10%

Portfolio Return
HR Industries (HRI) has a beta of 1.8, while LR Industries (LRI) beta is 0.6. The
risk-free rate is 6%, and the required rate of return on an average stock is 13%.
Now the expected rate of inflation built into rRF falls by 1.5 percentage points,
the real risk-free rate remains constant, the required return on the market falls
to 10.5%, and all betas remain constant. After all of these changes, what will
be the difference in the required returns for HRI and LRI?

b HRI       1.80        old rM     13%       rRF      6%       Dp      -1.5%
b LRI      0.60         Dr*       0%      new rM   10.5%
new rRF        4.5%
rHRI       15.3%
rLRI       8.1%
rHRI - rLRI   7.20%

CAPM
Stock X has a 10% expected return, a beta of 0.9, and a 35% standard
deviation of expected return. Stock Y has a 12.5% expected return, a
beta of 1.2, and a 25% standard deviation of expected return. The risk-
free rate is 6% and the market risk premium is 5%.
expected r       b          s         rRF      6%   rM - rRF   5%
X       10%         0.9       35%
Y      12.5%        1.2       25%
a Calculate each stock's coefficient of variation.
CVX         3.5                  CVY       2.0

b Which stock is riskier for a diversified investor?
Y, since the beta is higher than X

c Calculate each stock's required rate of return.
rX         10.500%                 rY      12.000%

On the basis of the two stocks' expected and required returns, which
d stock would be more attractive to a diversified investor?

Y since its expected return exceeds its required return.

Calculate the required return of a portfolio that has \$7,500 invested in
e Stock X and \$2,500 invested in Stock Y.
X          \$7,500        Y      \$2,500
rp         10.875%

If the market risk premium increased to 6%, which of the two stocks would
f   have the larger increase in its required return?
Y, since its beta is higher

CV
You plan to invest in the Kish Hedge Fund, which has total capital of \$500 million
invested in five stocks. Kish's beta coefficient can be found as a weighted average
of its stocks' beta. The risk-free rate is 6%, and you believe the following probability
distribution for future market returns is realistic.
Stock   Investment        Beta        w                Prob      rM       rRF       6%
A        \$160          0.50        0.32               0.1      7%
B        \$120          2.00        0.24               0.2      9%
C         \$80          4.00        0.16               0.4     11%
D         \$80          1.00        0.16               0.2     13%
E         \$60          3.00        0.12               0.1     15%
\$500           1.8                                     0.11
a           What is the equation for the SML?
ri =        6.00%       +           b* (   11.00% -6.00% )

b           Calculate Kish's required rate of return.
15.00%

c           Suppose Rick Kish, the president, receives a proposal from a company seeking
new capital. The amount needed to take a position in the stock is \$50 million, it
has an expected return of 15%, and its estimated beta is 2.0. Should Kish invest
in the new company? At what expected rate of return should Kish be indifferent to
exp. ret.      15%        b         2
required return on new stock        16.00% No, the return is below the required return.
indifferent at 16%.

SML
required return.

SML

```
DOCUMENT INFO
Shared By:
Categories:
Tags:
Stats:
 views: 17 posted: 11/27/2011 language: English pages: 9