Question 1

The standard deviation of a portfolio of assets
A) increases as the number of assets in the portfolio increases.
B) increases as the weight in any particular asset increases.
C) increases as the standard deviations of the assets change through time.
D) increases as the assets' expected returns increase.
E) increases as the assets' covariances increase.

Accepted Answer

The standard deviation of a portfolio of assets is affected by the covariances between the assets. Covariance is a measure of how two assets move together, and a higher covariance between assets will increase the volatility and risk of the portfolio. Therefore, the standard deviation of a portfolio increases as the assets' covariances increase.

Question 2

The standard deviation of a portfolio that has 40% of its value invested in a risk-free asset and 60% of its value invested in a risky asset with a standard deviation of 30% is
A) 18%.
B) 14%.
C) 21%.
D) 24%.
E) 20%.

Accepted Answer

The formula for the standard deviation of a portfolio that has a percentage w of its value invested in asset A with a standard deviation σA and a percentage (1 − w) of its value invested in asset B with a standard deviation σB is:

σportfolio = sqrt(w^2 * σA^2 + (1 − w)^2 * σB^2 + 2w(1 − w)ρABσAσB)

where ρAB is the correlation coefficient between the two assets (which we assume to be zero in this case since the risk-free asset has a standard deviation of zero).

Thus, the standard deviation of the portfolio is:

σportfolio = sqrt(0.4^2 * 0^2 + 0.6^2 * 0.3^2) = 0.18 or 18%

Therefore, the best choice is A) 18%.

Question 3

The utility score an investor assigns to a particular portfolio,other things equal,
A) will decrease as the rate of return increases.
B) will decrease as the standard deviation increases.
C) will decrease as the variance increases.
D) will increase as the variance increases.
E) will increase as the rate of return increases.

Accepted Answer

The utility score represents the investor's satisfaction or happiness with the portfolio. Generally, investors prefer higher returns and therefore, as the rate of return increases, the utility score assigned by the investor will increase. Therefore, choice E is the correct answer. Choices A, B, and C are incorrect as they suggest that the utility score will decrease with increasing returns, standard deviation or variance, which is not necessarily true. Choice D is also incorrect as the utility score is typically negatively affected by higher variance, as investors generally dislike risk and unpredictability.

Question 4

Which of the following statements regarding the Capital Allocation Line (CAL)is false?
A) The CAL shows risk-return combinations.
B) The slope of the CAL equals the increase in the expected return of a risky portfolio per unit of additional standard deviation.
C) The slope of the CAL is also called the reward-to-variability ratio.
D) The CAL is also called the efficient frontier of risky assets in the absence of a risk-free asset.
E) both a and d are true.

Accepted Answer

The CAL is not the efficient frontier of risky assets; it represents combinations of a risk-free asset and a risky portfolio, not just risky assets.

Question 5

Adding a home insurance policy to your portfolio of assets is an example of
A) speculating
B) asset dominance
C) hedging
D) neurosis
E) risk neutrality

Accepted Answer

Adding a home insurance policy is a form of hedging because it is a risk management strategy that protects against potential losses or damages to the asset (the home).

Question 6

You are a risk-averse investor.Portfolio A has E(r)= 12% and σ= 18%.Portfolio B has σ = 21%,and has end-of-year cash flows of either $84,000 or $144,000 with equal probability.At what price for portfolio B would you be indifferent between A and B?
A) $100,000
B) $101,786
C) $84,000
D) $121,000
E) None of these

Accepted Answer

The answer of You are a risk-averse investor.Portfolio A has...

Question 7

A fair game
A) Will not be undertaken by a risk-averse investor.
B) Is a risky investment with a zero risk premium.
C) Is a riskless investment.
D) Both a and b are true.
E) Both a and c are true.

Accepted Answer

A fair game is a risky investment with a zero risk premium, and a risk-averse investor typically avoids such investments.

Question 8

An investor invests 30 percent of his wealth in a risky asset with an expected rate of return of 0.13 and a variance of 0.03 and 70 percent in a T-bill that pays 6 percent.His portfolio's expected return and standard deviation are __________ and __________,respectively.
A) 0.114;0.128
B) 0.087;0.063
C) 0.295;0.125
D) 0.081;0.052
E) 0.795;0.14

Accepted Answer

The expected return is calculated as 0.3 * 0.13 + 0.7 * 0.06 = 0.081. The standard deviation is calculated as 0.3 * sqrt(0.03) = 0.052.

Question 9

You invest $100 in a risky asset with an expected rate of return of 0.12 and a standard deviation of 0.15 and a T-bill with a rate of return of 0.05.A portfolio that has an expected outcome of $115 is formed by
A) investing $100 in the risky asset.
B) investing $80 in the risky asset and $20 in the risk-free asset.
C) borrowing $43 at the risk-free rate and investing the total amount ($143)in the risky asset.
D) investing $43 in the risky asset and $57 in the riskless asset.
E) Such a portfolio cannot be formed.

Accepted Answer

The expected outcome of $115 from an initial investment of $100 implies a 15% return. By borrowing $43 at the risk-free rate and investing a total of $143 in the risky asset with an expected rate of return of 0.12, the portfolio's expected value aligns with achieving the desired outcome.

Question 10

An investor invests 30 percent of his wealth in a risky asset with an expected rate of return of 0.15 and a variance of 0.04 and 70 percent in a T-bill that pays 6 percent.His portfolio's expected return and standard deviation are _________ and __________,respectively.
A) 0.114;0.12
B) 0.087;0.06
C) 0.295;0.12
D) 0.087;0.12
E) none of these

Accepted Answer

The expected return is calculated as (0.3 * 0.15) + (0.7 * 0.06) = 0.087. The standard deviation is 0.3 * sqrt(0.04) = 0.06.

Question 11

An investor can choose to invest in T-bills paying 5% or a risky portfolio with end-of-year cash flow of $132,000.If the investor requires a risk premium of 5%,what would she be willing to pay for the risky portfolio?
A) $100,000
B) $108,000
C) $120,000
D) $145,000
E) $147,000

Accepted Answer

The answer of An investor can choose to invest in...

Question 12

You invest $100 in a risky asset with an expected rate of return of 0.12 and a standard deviation of 0.15 and a T-bill with a rate of return of 0.05.What percentages of your money must be invested in the risky asset and the risk-free asset,respectively,to form a portfolio with an expected return of 0.09?
A) 85% and 15%
B) 75% and 25%
C) 67% and 33%
D) 57% and 43%
E) cannot be determined

Accepted Answer

The answer of You invest $100 in a risky asset...

Question 13

The Capital Allocation Line can be described as the
A) investment opportunity set formed with a risky asset and a risk-free asset.
B) investment opportunity set formed with two risky assets.
C) line on which lie all portfolios that offer the same utility to a particular investor.
D) line on which lie all portfolios with the same expected rate of return and different standard deviations.
E) none of these.

Accepted Answer

The Capital Allocation Line is formed by combining a risk-free asset and a risky asset. It represents all the possible portfolios formed by combining the risk-free asset and the risky asset in different proportions, depending on the investor's risk preference. Therefore, choice A is the correct answer.

Question 14

An investor invests 60 percent of his wealth in a risky asset with an expected rate of return of 0.14 and a variance of 0.32 and 40 percent in a T-bill that pays 3 percent.His portfolio's expected return and standard deviation are __________ and __________,respectively.
A) 0.096;0.339
B) 0.087;0.267
C) 0.295;0.123
D) 0.087;0.182
E) none of these

Accepted Answer

The expected return is 0.6*0.14 + 0.4*0.03 = 0.096. The variance is 0.6^2*0.32 + 0.4^2*0 = 0.1152. The standard deviation is the square root of the variance, which is 0.339.

Question 15

Steve is more risk-averse than Edie.On a graph that shows Steve's and Edie's indifference curves,which of the following is true? Assume that the graph shows expected return on the vertical axis and standard deviation on the horizontal axis.
I.Steve and Edie's indifference curves might intersect.
II.Steve's indifference curves will have flatter slopes than Edie's.
III.Steve's indifference curves will have steeper slopes than Edie's.
IV.Steve and Edie's indifference curves will not intersect.
V.Steve's indifference curves will be downward sloping and Edie's will be upward sloping.
A) I and V
B) I and III
C) III and IV
D) I and II
E) II and IV

Accepted Answer

Since Steve is more risk-averse than Edie, his indifference curves must be flatter than Edie's because he requires a higher expected return for any given level of risk. Therefore, option II is correct. Option III is incorrect since Steve's indifference curves will have flatter slopes, not steeper. Option V is also incorrect since both Steve's and Edie's indifference curves will be downward sloping. Option I is possible; their indifference curves could intersect, but it is not necessarily true. Option IV is incorrect since the statement contradicts option I.

Question 16

Given the capital allocation line,an investor's optimal portfolio is the portfolio that
A) maximizes her expected profit.
B) maximizes her risk.
C) minimizes both her risk and return.
D) maximizes her expected utility.
E) none of these.

Accepted Answer

The optimal portfolio for an investor is the portfolio that maximizes their expected utility. The capital allocation line represents a combination of risk-free and risky assets. The point where the investor's indifference curve is tangent to the capital allocation line represents the optimal portfolio for the investor. This point maximizes the investor's expected utility, which takes into account the trade-off between risk and expected return. Therefore, the correct answer is D) maximizes her expected utility.

Question 17

The presence of risk means that
A) Investors will lose money.
B) More than one outcome is possible.
C) the standard deviation of the payoff is larger than its expected value.
D) Final wealth will be greater than initial wealth.
E) Terminal wealth will be less than initial wealth.

Accepted Answer

The presence of risk means that there is uncertainty about the outcome or potential consequences of an investment or decision. More than one outcome is possible, which creates risk. It does not necessarily mean that investors will lose money, as there is also the possibility of gain. The standard deviation of the payoff may or may not be larger than its expected value, depending on the specific investment or decision. The final and terminal wealth may be greater or less than the initial wealth, depending on the outcome of the risk.

Question 18

You invest $100 in a risky asset with an expected rate of return of 0.12 and a standard deviation of 0.15 and a T-bill with a rate of return of 0.05.What percentages of your money must be invested in the risk-free asset and the risky asset,respectively,to form a portfolio with a standard deviation of 0.06?
A) 30% and 70%
B) 50% and 50%
C) 60% and 40%
D) 40% and 60%
E) cannot be determined

Accepted Answer

Let X be the portion invested in the risky asset, and (1-X) be the portion invested in the risk-free asset.

The formula for the standard deviation of a portfolio is:

σP = XσR + (1-X)σF

where σR is the standard deviation of the risky asset, σF is the standard deviation of the risk-free asset (which is 0), and σP is the desired standard deviation of the portfolio.

Plugging in the values:

0.06 = X(0.15) + (1-X)(0)

Simplifying:

0.06 = 0.15X 
X = 0.4

So you should invest 40% in the risky asset and 60% in the risk-free asset.

Question 19

The certainty equivalent rate of a portfolio is
A) the rate that a risk-free investment would need to offer with certainty to be considered equally attractive as the risky portfolio.
B) the rate that the investor must earn for certain to give up the use of his money.
C) the minimum rate guaranteed by institutions such as banks.
D) the rate that equates "A" in the utility function with the average risk aversion coefficient for all risk-averse investors.
E) represented by the scaling factor "-.005" in the utility function.

Accepted Answer

The definition of the certainty equivalent rate of a portfolio is the rate that a risk-free investment would need to offer with certainty to be considered equally attractive as the risky portfolio. Choice B is describing the risk-free rate, not the certainty equivalent rate. Choice C is describing the guaranteed minimum rate offered by institutions, which may or may not be related to the certainty equivalent rate. Choice D is describing the average risk aversion coefficient, which is not directly related to the certainty equivalent rate. Choice E is describing a specific scaling factor in a utility function and is not a general definition of the certainty equivalent rate.

Question 20

Which of the following sayings illustrates the concept of diversification?
A) Don't throw the baby out with the bathwater.
B) A stitch in time saves nine.
C) Neither a borrower nor a lender be.
D) Don't put all your eggs in one basket.
E) Out of sight,out of mind.

Accepted Answer

The saying "Don't put all your eggs in one basket" illustrates diversification. It means spreading out investments or resources to avoid risk or loss in case one investment or resource fails.

Quiz 5: Risk and Return: Past and Prologue

The standard deviation of a portfolio of assets

The standard deviation of a portfolio that has 40% of its value invested in a risk-free asset and 60% of its value invested in a risky asset with a standard deviation of 30% is

The utility score an investor assigns to a particular portfolio,other things equal,

Which of the following statements regarding the Capital Allocation Line (CAL) is false?

Adding a home insurance policy to your portfolio of assets is an example of

You are a risk-averse investor.Portfolio A has E(r) = 12% and σ= 18%.Portfolio B has σ = 21%,and has end-of-year cash flows of either $84,000 or $144,000 with equal probability.At what price for portfolio B would you be indifferent between A and B?

A fair game

An investor invests 30 percent of his wealth in a risky asset with an expected rate of return of 0.13 and a variance of 0.03 and 70 percent in a T-bill that pays 6 percent.His portfolio's expected return and standard deviation are and ,respectively.

You invest $100 in a risky asset with an expected rate of return of 0.12 and a standard deviation of 0.15 and a T-bill with a rate of return of 0.05.A portfolio that has an expected outcome of $115 is formed by

An investor invests 30 percent of his wealth in a risky asset with an expected rate of return of 0.15 and a variance of 0.04 and 70 percent in a T-bill that pays 6 percent.His portfolio's expected return and standard deviation are _ and __,respectively.

An investor can choose to invest in T-bills paying 5% or a risky portfolio with end-of-year cash flow of $132,000.If the investor requires a risk premium of 5%,what would she be willing to pay for the risky portfolio?

The Capital Allocation Line can be described as the

An investor invests 60 percent of his wealth in a risky asset with an expected rate of return of 0.14 and a variance of 0.32 and 40 percent in a T-bill that pays 3 percent.His portfolio's expected return and standard deviation are and ,respectively.

Given the capital allocation line,an investor's optimal portfolio is the portfolio that

The presence of risk means that

The certainty equivalent rate of a portfolio is

Which of the following sayings illustrates the concept of diversification?