Chapter 11 1 Aggressive Investors Will Invest More The Tangent

Exam

Name___________________________________

MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.

1)

Which of the following statements is false?

1)

A)

The variance of a portfolio is equal to the weighted average covariances of each stock within

the portfolio.

B)

The volatility declines as the number of stocks in a portfolio grows.

C)

The variance of a portfolio is equal to the weighted average correlation of each stock within

the portfolio.

D)

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.

Use the table for the question(s) below.

Consider the following returns:

Year End

Lowes

Realized

Return

Home Depot

Realized

Return

IBM

Realized

Return

2000 20.1% –14.6% 0.2%

2001 72.7% 4.3% –3.2%

2002 –25.7% –58.1% –27.0%

2003 56.9% 71.1% 27.9%

2004 6.7% 17.3% –5.1%

2005 17.9% 0.9% –11.3%

2)

The covariance between Lowes’ and Home Depot’s returns is closest to:

2)

A)

0.29

B)

0.69

C)

0.10

D)

0.12

Use the information for the question(s) below.

You are presently invested in the Luther Fund, a broad based mutual fund that invest in stocks and other securities. The

Luther Fund has an expected return of 14% and a volatility of 20%. Risk–free Treasury bills are currently offering returns of

4%. You are considering adding a precious metals fund to your current portfolio. The metals fund has an expected return of

10% , a volatility of 30%, and a correlation of –.20 with the Luther Fund.

3)

The expected return on the precious metals fund is closest to:

3)

A)

10%

B)

1%

C)

4%

D)

–3%

Use the information for the question(s) below.

Suppose you have $10,000 in cash and you decide to borrow another $10,000 at a 6% interest rate to invest in the stock

market. You invest the entire $20,000 in an exchange traded fund (ETF) with a 12% expected return and a 20% volatility.

4)

The volatility of your of your investment is closest to:

4)

A)

24%

B)

20%

C)

40%

D)

30%

Use the information for the question(s) below.

You are presently invested in the Luther Fund, a broad based mutual fund that invest in stocks and other securities. The

Luther Fund has an expected return of 14% and a volatility of 20%. Risk–free Treasury bills are currently offering returns of

4%. You are considering adding a precious metals fund to your current portfolio. The metals fund has an expected return of

10% , a volatility of 30%, and a correlation of –.20 with the Luther Fund.

5)

The beta of the precious metals fund with the Luther Fund Luther

Metals is closest to:

5)

A)

0.6

B)

–0.6

C)

0.3

D)

–0.3

6)

Which of the following statements is false?

6)

A)

The volatility of the portfolio will differ, depending on the correlation between the securities

in the portfolio.

B)

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.

C)

We can rule out inefficient portfolios because they represent inferior investment choices.

D)

Correlation has no effect on the expected return on a portfolio.

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

7)

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:

7)

A)

.051

B)

.050

C)

–0.020

D)

.045

Use the information for the question(s) below.

Suppose you have $10,000 in cash and you decide to borrow another $10,000 at a 6% interest rate to invest in the stock

market. You invest the entire $20,000 in an exchange traded fund (ETF) with a 12% expected return and a 20% volatility.

8)

Assume that the EFT you invested in returns –10%, then the realized return on your investment is

closest to:

8)

A)

–26%

B)

–24%

C)

–20%

D)

–10%

Use the information for the question(s) below.

Suppose that you currently have $250,000 invested in a portfolio with an expected return of 12% and a volatility of 10%. The

efficient (tangent) portfolio has an expected return of 17% and a volatility of 12%. The risk–free rate of interest is 5%.

9)

You want to maximize your expected return without increasing your risk. Without increasing your

volatility beyond its current 10%, the maximum expected return you could earn is closest to:

9)

A)

.12.0%

B)

13.4%

C)

15.0%

D)

12.5%

10)

Suppose you have $10,000 in cash to invest. You decide to sell short $5,000 worth of Kinston stock

and invest the proceeds from your short sale, plus your $10,000 into one–year U.S. treasury bills

earning 5%. At the end of the year, you decide to liquidate your portfolio. Kinston Industries has

the following realized returns:

P0Div1P1

Kinston $25.00 $1.00 $29.00

The return on your portfolio is closest to?

10)

A)

–0.5%

B)

–2.5%

C)

14.5%

D)

13.5%

11)

Which of the following statements is false?

11)

A)

The volatility declines as the number of stocks in a portfolio grows.

B)

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.

C)

An equally weighted portfolio is a portfolio in which the same amount is invested in each

stock.

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.

Use the table for the question(s) below.

Consider the following expected returns, volatilities, and correlations:

Stock

Expected

Return

Standard

Deviation

Correlation with

Duke Energy

Correlation with

Microsoft

Correlation with

Wal–Mart

Duke Energy 14% 6% 1.0 –1.0 0.0

Microsoft 44% 24% –1.0 1.0 0.7

Wal–Mart 23% 14% 0.0 0.7 1.0

12)

Consider a portfolio consisting of only Duke Energy and Microsoft. The percentage of your

investment (portfolio weight) that you would place in Duke Energy stock to achieve a risk–free

investment would be closest to:

12)

A)

23%

B)

15%

C)

10%

D)

4%

13)

Which of the following statements is false?

13)

A)

The efficient portfolio is the tangent portfolio, the portfolio with the highest Sharpe ratio in

the economy.

B)

The optimal portfolio of risky investments depends on how conservative or aggressive the

investor is.

C)

The tangent portfolio is efficient and that, once we include the risk–free investment, all

efficient portfolios are combinations of the risk–free investment and the tangent portfolio.

D)

By combining the efficient portfolio with the risk–free investment, an investor will earn the

highest possible expected return for any level of volatility her or she is willing to bear.

Use the table for the question(s) below.

Consider the following returns:

Year End

Lowes

Realized

Return

Home Depot

Realized

Return

IBM

Realized

Return

2000 20.1% –14.6% 0.2%

2001 72.7% 4.3% –3.2%

2002 –25.7% –58.1% –27.0%

2003 56.9% 71.1% 27.9%

2004 6.7% 17.3% –5.1%

2005 17.9% 0.9% –11.3%

14)

The Volatility on Lowes’ returns is closest to:

14)

A)

10%

B)

42%

C)

13%

D)

35%

15)

Which of the following statements is false?

15)

A)

Increasing the investment in investment I will increase the Sharpe ratio of portfolio P if its

expected return E[Ri] exceeds the required return ri, which is given by ri=rf+p

i× (E[Rp] –

rf).

B)

A portfolio is efficient if it has the highest possible Sharpe ratio; that is it is efficient if it

provides the largest increase in expected return possible for a given increase in volatility.

C)

The required return for an investment is equal to a risk premium that is equal to the risk

premium of the investor’s current portfolio scaled by p

i.

D)

If a security i‘s expected return is less than the required return ri, we should reduce our

holding of security i.

16)

Which of the following statements is false?

16)

A)

The Sharpe ratio if the portfolio tells us how much our expected return will increase for a

given increase in volatility.

B)

We should continue to trade securities until the expected return of each security equals its

required return.

C)

If security i’s required return exceeds its expected return, then adding more of it will improve

the performance of the portfolio.

D)

The required return is the expected return that is necessary to compensate for the risk that an

investment will contribute to the portfolio.

17)

Which of the following statements is false?

17)

A)

Efficient portfolios can be easily ranked, because investors will choose from among them

those with the highest expected returns.

B)

When stocks are perfectly positively correlated, the set of portfolios is identified graphically

by a straight line between them.

C)

When the correlation between securities is less than 1, the volatility of the portfolio is reduced

due to diversification.

D)

An investor seeking high returns and low volatility should only invest in an efficient

portfolio.

18)

Which of the following equations is incorrect?

18)

A)

Corr(Ri,Rj) =

Cov(Ri,Rj)

Var(Ri)Var(Rj)

B)

Cov(Ri,Rj) = E[(Ri–E[Ri])(Rj–E[Rj])]

C)

Cov(Ri,Rj) =1

T– 1 (Ri–Ri)(Rj–Rj)

D)

Var(Rp) =x12Var(R1) +x22Var(R2) + 2X1X2Cov(R1,R2)

Use the information for the question(s) below.

Suppose you invest $20,000 by purchasing 200 shares of Abbott Labs (ABT) at $50 per share, 200 shares of Lowes (LOW) at

$30 per share, and 100 shares of Ball Corporation (BLL) at $40 per share.

19)

The weight on Ball Corporation in your portfolio is:

19)

A)

30%

B)

50%

C)

20%

D)

40%

20)

Which of the following statements is false?

20)

A)

An investor’s preferences will determine only how much to invest in the tangent or efficient

portfolio versus the risk–free investment.

B)

Only aggressive investors will choose to hold the portfolio of risky assets, the tangent or

efficient portfolio.

C)

Conservative investors will invest a small amount in the tangent or efficient portfolio,

choosing a portfolio on the line near the risk–free investment

D)

Aggressive investors will invest more in the tangent portfolio choosing a portfolio that is near

the tangent portfolio or even beyond it by buying stocks on margin.

Corr(Ri,Rj) =

Use the information for the question(s) below.

Suppose you invest $20,000 by purchasing 200 shares of Abbott Labs (ABT) at $50 per share, 200 shares of Lowes (LOW) at

$30 per share, and 100 shares of Ball Corporation (BLL) at $40 per share.

21)

The weight on Lowes in your portfolio is:

21)

A)

30%

B)

40%

C)

50%

D)

20%

Use the information for the question(s) below.

Suppose that you currently have $250,000 invested in a portfolio with an expected return of 12% and a volatility of 10%. The

efficient (tangent) portfolio has an expected return of 17% and a volatility of 12%. The risk–free rate of interest is 5%.

22)

The Sharpe ratio for your portfolio is closest to:

22)

A)

0.7

B)

1.0

C)

1.2

D)

0.6

23)

Which of the following statements is false?

23)

A)

We say a portfolio is long those stocks that have negative portfolio weights.

B)

The lower the correlation of the securities in a portfolio the lower the volatility we can obtain.

C)

The efficient portfolios are those portfolios offering the highest possible expected return for a

given level of volatility.

D)

When two stocks are perfectly negatively correlated, it becomes possible to hold a portfolio

that bears absolutely no risk.

Use the table for the question(s) below.

Consider the following returns:

Year End

Lowes

Realized

Return

Home Depot

Realized

Return

IBM

Realized

Return

2000 20.1% –14.6% 0.2%

2001 72.7% 4.3% –3.2%

2002 –25.7% –58.1% –27.0%

2003 56.9% 71.1% 27.9%

2004 6.7% 17.3% –5.1%

2005 17.9% 0.9% –11.3%

24)

The Correlation between Lowes’ and Home Depot’s returns is closest to:

24)

A)

0.69

B)

0.29

C)

0.58

D)

0.10

25)

Which of the following statements is false?

25)

A)

Correlation is the expected product of the deviations of two returns.

B)

The amount of risk that is eliminated in a portfolio depends on the degree to which the stocks

face common risks and their prices move together.

C)

Because the prices of the stocks do not move identically, some of the risk is averaged out in a

portfolio.

D)

The covariance and correlation allow us to measure the co–movement of returns.

Use the table for the question(s) below.

Consider the following returns:

Year End

Lowes

Realized

Return

Home Depot

Realized

Return

IBM

Realized

Return

2000 20.1% –14.6% 0.2%

2001 72.7% 4.3% –3.2%

2002 –25.7% –58.1% –27.0%

2003 56.9% 71.1% 27.9%

2004 6.7% 17.3% –5.1%

2005 17.9% 0.9% –11.3%

26)

The Correlation between Lowes’ and IBM’s returns is closest to:

26)

A)

0.60

B)

0.05

C)

0.71

D)

0.62

Use the information for the question(s) below.

Sisyphean industries is seeking to raise capital from a large group of investors to fund a new project. Suppose that the

efficient portfolio has an expected return of 14% and a volatility of 20%. Sisyphean’s new project is expected to have a

volatility of 40% and a 70% correlation with the efficient portfolio. The risk–free rate is 4%.

27)

The beta for Sisyphean’s new project is closest to:

27)

A)

1.25

B)

1.75

C)

1.40

D)

0.70

28)

Which of the following statements is false?

28)

A)

A portfolio weight is the fraction of the total investment in the portfolio held in an individual

investment in the portfolio.

B)

Portfolio weights add up to 1 so that they represent the way we have divided our money

between the different individual investments in the portfolio.

C)

Without trading, the portfolio weights will decrease for the stocks in the portfolio whose

returns are above the overall portfolio return.

D)

The expected return of a portfolio is simply the weighted average of the expected returns of

the investments within the portfolio.

29)

Which of the following statements is false?

29)

A)

A positive investment in a security can be referred to as a long position in the security.

B)

It is possible to invest a negative amount in a stock or security call a short position.

C)

The efficient portfolios are those portfolios offering the lowest possible level of volatility for a

given level of expected return.

D)

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.

Use the information for the question(s) below.

Suppose that you currently have $250,000 invested in a portfolio with an expected return of 12% and a volatility of 10%. The

efficient (tangent) portfolio has an expected return of 17% and a volatility of 12%. The risk–free rate of interest is 5%.

30)

The Sharpe ratio for the efficient portfolio is closest to:

30)

A)

1.0

B)

1.2

C)

1.4

D)

0.7

31)

Which of the following statements is false?

31)

A)

To earn the highest possible expected return for any level of volatility we must find the

portfolio that generates the steepest possible line when combined with the risk–free

investment.

B)

Every investor should invest in the tangent portfolio independent of his or her taste for risk.

C)

As we increase the fraction invested in the efficient portfolio, we increase our risk premium

but not our risk proportionately.

D)

If we increase the fraction invested in the efficient portfolio beyond 100%m we are short

selling the risk–free investment.

Use the information for the question(s) below.

Suppose you invest $20,000 by purchasing 200 shares of Abbott Labs (ABT) at $50 per share, 200 shares of Lowes (LOW) at

$30 per share, and 100 shares of Ball Corporation (BLL) at $40 per share.

32)

Suppose over the next year Ball has a return of 12.5%, Lowes has a return of 20%, and Abbott Labs

has a return of –10%. The weight on Lowes in your portfolio after one year is closest to:

32)

A)

34.8%

B)

20.0%

C)

30.0%

D)

36.0%

33)

Suppose over the next year Ball has a return of 12.5%, Lowes has a return of 20%, and Abbott Labs

has a return of –10%. The value of your portfolio over the year is?

33)

A)

$20,700

B)

$21,500

C)

$21,000

D)

$20,000

34)

Suppose over the next year Ball has a return of 12.5%, Lowes has a return of 20%, and Abbott Labs

has a return of –10%. The return on your portfolio over the year is:

34)

A)

5.0%

B)

3.5%

C)

0%

D)

7.5%

35)

Which of the following statements is false?

35)

A)

If a security’s expected return exceeds its required return given our current portfolio, then we

can improve the performance of our portfolio by adding more of the security.

B)

Because all other risk is diversifiable, it is an investment’s beta with respect to the efficient

portfolio that measures its sensitivity to systematic risk, and therefore determines its cost of

capital.

C)

The appropriate risk premium for an investment can be determined from its beta with the

efficient portfolio.

D)

As we buy shares of a security i, its correlation with our portfolio P will increase, ultimately

raising its required return until E[Ri] =Rp.

36)

Which of the following statements is false?

36)

A)

Because our return on the risk–free investments is fixed and does not move with (or against)

our portfolio, the correlation between the risk–free investment and the portfolio is always

equal to one.

B)

Margin investing is a risky investment strategy.

C)

Short selling the risk free investment is equivalent to borrowing money at the risk–free

interest rate through a standard loan.

D)

Margin investing can provide higher expected returns than investing in the efficient portfolio

using only the funds we have available.

37)

Which of the following statements is false?

37)

A)

Volatility is the square root of variance.

B)

Dividing the covariance by the volatilities ensures that correlation is always between –1 and

+1.

C)

The closer the correlation is to 0, the more the returns tend to move together as a result of

common risk.

D)

If two stocks move together, their returns will tend to be above or below average at the same

time, and the covariance will be positive.

38)

Which of the following statements is false?

38)

A)

The covariance allows us to gauge the strength of the relationship between stocks.

B)

If two stocks move in opposite directions, one will tend to be above average when to other is

below average, and the covariance will be negative.

C)

The correlation between two stocks has the same sign as their covariance, so it has a similar

interpretation.

D)

The covariance of a stock with itself is simply its variance.

39)

Which of the following statements is false?

39)

A)

To arrive at the best possible set of risk and return opportunities, we should keep adding

stocks until all investment opportunities are represented.

B)

We say a portfolio is short those stocks that have negative portfolio weights.

C)

Adding new investment opportunities allows for greater diversification and improves the

efficient frontier.

D)

Graphically, the efficient portfolios are those on the northeast edge of the set of possible

portfolios, an area which we call the efficient frontier.

40)

Which of the following equations is incorrect?

40)

A)

SD( Rxp) = xSD(Rp)

B)

E[Rxp] =rf+x(E[Rp] –rf)

C)

Sharpe ratio =portfolio return

portfolio volatility

D)

E[Rxp] = (1 –x)rf+xE[Rp]

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

41)

The variance on a portfolio that is made up of equal investments in Duke Energy and Microsoft

stock is closest to:

41)

A)

0.090

B)

–0.020

C)

.065

D)

.149

42)

Suppose you invest $15,000 in Merck stock and $25,000 in Home Depot stock. You receive an

actual return of –8% for Merck and 12% for Home Depot. What is the actual return on your

portfolio?

42)

A)

10.00%

B)

4.50%

C)

4.00%

D)

2.00%

43)

Which of the following statements is false?

43)

A)

A stock’s return is perfectly positively correlated with itself.

B)

When the covariance equals 0, the stocks have no tendency to move either together or in

opposition of one another.

C)

The variance of a portfolio depends only on the variance of the individual stocks.

D)

The closer the correlation is to –1, the more the returns tend to move in opposite directions.

C

B