Deck 4: Portfolio Tools

Question 1

Which of the following is true of the standard deviation?

A)The standard deviation is a measure of relative changes of two random variables.
B)The standard deviation is the square root of variance.
C)The standard deviation is the expected value of the squared demeaned return.
D)The value of standard deviation ranges between -1 and 1.

Answer 1

B

Question 2

Marginal variance is:

A)the portfolio of risky investments with the lowest variance.
B)the change in the variance of a portfolio for a small increase in the portfolio weight on the asset.
C)the change in the variance of a portfolio for a small increase in the standard deviation of the asset.
D)the change in the standard deviation of a portfolio for a small increase in the variance of the asset.

Answer 2

B

Question 3

Explain a short position and long position.How do they affect portfolio weights?

Answer 3

In many markets investors can sell short certain securities,which means that they can sell investments that they do not currently own.To sell short shares or bonds,the investor must borrow the securities from someone who owns them.This is known as taking a short position in a security.To close out the short position,the investor buys the investment back and returns it to the original owner.In contrast,a long position,achieved by buying an investment,has a positive portfolio weight.To compute portfolio weights when some investments are sold short,sum the amount invested in each asset of the portfolio,treating shorted (or borrowed)investments as negative numbers.

Question 4

Selling short an investment with a low expected return and using the proceeds to increase a position in an investment with a higher expected return results in a larger expected return than can be achieved by investing only in the investment with the high expected return.This is known as:

A)passive trading.
B)scalping.
C)diversifying an investment.
D)leveraging an investment.

Question 5

Determine the covariance between the returns of equities A and B,given the following joint distribution.

A)-0.0023
B)0.0023
C)0.007125
D)0.00475

Question 6

Which of the following can be an example of a short position?

A)An investor buying a preferred stock
B)A corporation that issues a bond
C)A borrower repaying a bank loan
D)A risk-averse investor investing in Treasury bills

Question 7

Which of the following is true of the mean-standard deviation diagram?

A)It plots means on the X-axis and standard deviations on the Y-axis of all feasible portfolios.
B)When investors employ risk-free borrowing to increase their holdings in a risky investment,the risk of the portfolio increases.
C)If the risky investment has a positive weight,and the graph has a mean return for the risky investment that is larger than the return of the risk-free asset,the slope of this line is negative.
D)The graph of portfolios of two perfectly positively correlated,but risky investments,has the same shape as the graph for a portfolio of a riskless and a risky investment.

Question 8

If a portfolio consists of two investments which have perfectly correlated returns,the portfolio standard deviation is:

A)the sum of the products of the squared portfolio weights and the variances of the investment returns.
B)the absolute value of the portfolio-weighted average of the standard deviations of the two investments.
C)is the difference between the portfolio-weighted average of the standard deviations of the two investments.
D)twice the product of the two portfolio weights and the covariance between the investment returns.

Question 9

Based on the mean-variance analysis,the risk of a portfolio is defined as:

A)the standard deviation of the risks of the individual portfolio.
B)the variance of its return.
C)the sum of the risks of the individual stocks.
D)the portfolio-weighted average of the risks of the individual stocks.

Question 10

The correlation between two returns:

A)is the covariance between the two returns divided by the product of their standard deviations.
B)is the standard deviations of the two returns divided by the covariance between them.
C)is the standard deviations of the two returns multiplied by the covariance between them.
D)is the covariance between the two returns divided by the product of their variances.

Question 11

Explain the concept of standard deviation as a portfolio tool.

Question 12

A portfolio consists of £23 million in Stock A,£46 million in Stock B and £115 million in Stock

A)Stock A has 12.5%,stock B has 25% and stock C has 62.5%
B)Stock A has 12.5%,stock B has 37.5% and stock C has 50%
C)Stock A has 10%,stock B has 20% and stock C has 50%
C)What are the portfolio weights of the three equities?
D)Stock A has 10%,stock B has 30% and stock C has 60%

Question 13

Explain how return variances are calculated.

Question 14

Explain the ratio method and the portfolio-weighted average method.

Question 15

A £50,000 portfolio consists of £30,000 of Stock A and £20,000 of Stock

A)9.48%
B)13.8%
B)Find the return on the portfolio if Stock A has a return of 15% and Stock B has a return of 12%.
C)10.48%
D)11.32%

Question 16

Which of the following is the correct mathematical expression for variance?

A)
B)
C)
D)

Question 17

Which of the following explains the computation of return variance in the correct chronological order?

A)Compute demeaned returns,take the probability-weighted average of the demeaned returns and square the resulting number
B)Compute demeaned returns,square the demeaned returns and take the probability-weighted average of these squared numbers
C)Compute demeaned returns and take the probability-weighted average of these squared numbers
D)Compute demeaned returns,square the demeaned returns,take the probability-weighted average of these squared numbers and take square root of the resulting number

Question 18

The range of correlation values between the returns of two investments is from:

A)-1 to +1
B)0 to 1.
C)- $\infty$ to + $\infty$ .
D)-1 to 0.

Question 19

Which of the following is true of the properties of expected returns?

A)The expected value of a constant times a return will be less than the constant times the expected return.
B)The expected value of a constant times a return will be greater than the constant times the expected return.
C)The expected value of the sum or difference of two returns need not be the sum or difference between the expected returns themselves.
D)The expected return of a portfolio is the portfolio-weighted average of the expected returns.