Use the table
for the question(s) below.

Consider the
following covariances between securities:

Duke

Microsoft

Wal-Mart

Duke

0.0568

-0.0193

0.0037

Microsoft

-0.0193

0.2420

0.1277

Wal-Mart

0.0037

0.1277

0.1413

17) The variance
on a portfolio that is made up of equal investments in Duke Energy and
Microsoft stock is closest to:
A) .065
B) 0.090
C) .149
D) -0.020

18) The variance
on a portfolio that is made up of a $6000 investments in Duke Energy and a
$4000 investment in Wal-Mart stock is closest to:
A) .050
B) .045
C) .051
D) -0.020

Use the table
for the question(s) below.

Consider the
following returns:

Year End

Stock
X
Realized
Return

Stock
Y Realized Return

Stock
Z
Realized Return

2004

20.1%

-14.6%

0.2%

2005

72.7%

4.3%

-3.2%

2006

-25.7%

-58.1%

-27.0%

2007

56.9%

71.1%

27.9%

2008

6.7%

17.3%

-5.1%

2009

17.9%

0.9%

-11.3%

19) Calculate
the covariance between Stock Y’s and Stock Z’s returns.

20) Calculate
the correlation between Stock Y’s and Stock Z’s returns.

21) Calculate
the variance on a portfolio that is made up of equal investments in Stock Y and
Stock Z stock.
Answer:

Use the table
for the question(s) below.

Consider the
following covariances between securities:

Duke

Microsoft

Wal-Mart

Duke

0.0568

-0.0193

0.0037

Microsoft

-0.0193

0.2420

0.1277

Wal-Mart

0.0037

0.1277

0.1413

22) The variance
on a portfolio that is made up of a $6000
investments in Microsoft and a $4000 investment in Wal-Mart stock is closest
to:

1) Which of the
following statements is false?
A) The variance
of a portfolio is equal to the weighted average correlation of each stock
within the portfolio.
B) The variance
of a portfolio is equal to the sum of the covariances of the returns of all
pairs of stocks in the portfolio multiplied by each of their portfolio weights.
C) The variance
of a portfolio is equal to the weighted average covariances of each stock
within the portfolio.
D) The
volatility declines as the number of stocks in a portfolio grows.

2) Which of the
following statements is false?
A) The
volatility declines as the number of stocks in a portfolio grows.
B) An equally
weighted portfolio is a portfolio in which the same amount is invested in each
stock.
C) As the number
of stocks in a portfolio grows large, the variance of the portfolio is
determined primarily by the average covariance among the stocks.
D) When
combining stocks into a portfolio that puts positive weight on each stock,
unless all of the stocks are uncorrelated with the portfolio, the risk of the
portfolio will be lower than the weighted average volatility of the individual
stocks.

3) Which of the
following statements is false?
A) The expected
return of a portfolio is equal to the weighted average expected return, but the
volatility of a portfolio is less than the weighted average volatility.
B) Each security
contributes to the volatility of the portfolio according to its volatility,
scaled by its covariance with the portfolio, which adjusts for the fraction of
the total risk that is common to the portfolio.
C) Nearly half
of the volatility of individual stocks can be eliminated in a large portfolio
as a result of diversification.
D) The overall
variability of the portfolio depends on the total co-movement of the stocks
within it.

4) Which of the
following formulas is incorrect?
A) Variance of
an equally Weighted Portfolio =

(Average Variance of Individual Stocks)

(Average
covariance between the stocks)
B) Variance of a
portfolio =

C) Variance of a
portfolio =

D) Variance of a
portfolio =

5) Consider an
equally weighted portfolio that contains five stocks. If the average volatility of these stocks is
40% and the average correlation between the stocks is .5, then the volatility
of this equally weighted portfolio is closest to:
A) .17
B) .44
C) .41
D) .19

6) Consider an
equally weighted portfolio that contains 20 stocks. If the average volatility of these stocks is
35% and the average correlation between the stocks is .4, then the volatility
of this equally weighted portfolio is closest to:
A) .17
B) .41
C) .14
D) .37

7) Consider an
equally weighted portfolio that contains 100 stocks. If the average volatility of these stocks is
50% and the average correlation between the stocks is .7, then the volatility
of this equally weighted portfolio is closest to:
A) .72
B) .63
C) .40
D) .50

Use the table
for the question(s) below.

Consider the
following covariances between securities:

Duke

Microsoft

Wal-Mart

Duke

0.0568

-0.0193

0.0037

Microsoft

-0.0193

0.2420

0.1277

Wal-Mart

0.0037

0.1277

0.1413

8) What is the
variance on a portfolio that has $2000 invested in Duke Energy, $3000 invested
in Microsoft, and $5000 invested in Wal-Mart stock?

9) What is the
variance on a portfolio that has $3000 invested in Duke Energy, $4000 invested
in Microsoft, and $3000 invested in Wal-Mart stock?

11.4 Risk Versus Return: Choosing an Efficient
Portfolio

1) Which of the
following statements is false?
A) We say a
portfolio is an efficient portfolio whenever it is possible to find another
portfolio that is better in terms of both expected return and volatility.
B) We can rule
out inefficient portfolios because they represent inferior investment choices.
C) The
volatility of the portfolio will differ, depending on the correlation between
the securities in the portfolio.
D) Correlation
has no effect on the expected return on a portfolio.

2) Which of the
following statements is false?
A) When stocks
are perfectly positively correlated, the set of portfolios is identified
graphically by a straight line between them.
B) An investor
seeking high returns and low volatility should only invest in an efficient
portfolio.
C) When the
correlation between securities is less than 1, the volatility of the portfolio
is reduced due to diversification.
D) Efficient
portfolios can be easily ranked, because investors will choose from among them
those with the highest expected returns.

3) Which of the
following statements is false?
A) We say a
portfolio is long those stocks that have negative portfolio weights.
B) The efficient
portfolios are those portfolios offering the highest possible expected return
for a given level of volatility.
C) When two
stocks are perfectly negatively correlated, it becomes possible to hold a
portfolio that bears absolutely no risk.
D) The lower the
correlation of the securities in a portfolio the lower the volatility we can
obtain.

4) Which of the
following statements is false?
A) A short sale
is a transaction in which you buy a stock that you do not own and then agree to
sell that stock back in the future.
B) The efficient
portfolios are those portfolios offering the lowest possible level of
volatility for a given level of expected return.
C) A positive
investment in a security can be referred to as a long position in the security.
D) It is
possible to invest a negative amount in a stock or security call a short
position.

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