Question 1

Suppose that Ms.Lynch in Workouts can make up her portfolio using a risk-free asset that offers a surefire rate of return of 10% and a risky asset with an expected rate of return of 25%, with standard deviation 5.If she chooses a portfolio with an expected rate of return of 25%, then the standard deviation of her return on this portfolio will be

Accepted Answer

If Ms. Lynch chooses a portfolio with an expected rate of return of 25%, which is the same as the expected rate of return of the risky asset alone, it means her portfolio is entirely composed of the risky asset. Therefore, the standard deviation of her portfolio's return will be the same as the standard deviation of the risky asset, which is 5%.

Question 2

If the mean is plotted on the horizontal axis, and the variance on the vertical, then indifference curves for a risk averter must slope upward and to the right.

Accepted Answer

Indifference curves for risk averters must slope upward and to the right because as the mean return increases, they become willing to accept higher levels of risk (variance) in order to achieve the higher return. This is consistent with the notion of diminishing marginal utility of wealth, where the additional utility gained from a higher return decreases as wealth increases, but the disutility (or loss aversion) from a lower return increases.

Question 3

Suppose that Ms.Lynch in Workouts can make up her portfolio using a risk-free asset that offers a surefire rate of return of 5% and a risky asset with an expected rate of return of 10%, with standard deviation 5.If she chooses a portfolio with an expected rate of return of 6.25%, then the standard deviation of her return on this portfolio will be

Accepted Answer

The standard deviation of a portfolio that combines a risk-free asset and a risky asset depends only on the portion of the portfolio invested in the risky asset. The expected return of 6.25% indicates that 25% of the portfolio is invested in the risky asset (since 5% is the risk-free rate and 10% is the risky asset's expected return, and 6.25% is exactly halfway between 5% and 7.5%, which would be the expected return if 25% were invested in the risky asset). The standard deviation of the portfolio will be 25% of the risky asset's standard deviation, which is 25% of 5%, or 1.25%.

Question 4

A risk-free asset is available at 5% interest.Another asset is available with a mean rate of return of 15% but with a standard deviation of 5%.An investor is considering an investment portfolio consisting of some of each stock.On a graph with standard deviation on the horizontal axis and mean on the vertical axis, the budget line that expresses the alternative combinations of mean return and standard deviation possible with portfolios of these assets is a straight line with

Accepted Answer

The slope of the budget line on a graph with standard deviation on the horizontal axis and mean return on the vertical axis, when combining a risk-free asset and a risky asset, is determined by the risk premium (the difference between the mean return of the risky asset and the risk-free rate) divided by the standard deviation of the risky asset. In this case, the risk premium is 15% - 5% = 10%, and the standard deviation of the risky asset is 5%. Therefore, the slope is 10%/5% = 2.

Question 5

Marvin is an expected utility maximizer.He chooses his portfolio so as to maximize the expected value of 2,000,000x - x².If m is the mean of Marvin's income and s is the standard deviation, Marvin's income as a function of the mean and standard deviation is

Accepted Answer

The expected income of Marvin is given by E(2,000,000xF1F1F1S1-F1F1F10x²), which can be simplified to 2,000,000xF1F1F1S1m - 2,000,000xF1F1F10s. Since Marvin is an expected utility maximizer, his utility function must be linear in income. Therefore his income as a function of the mean and standard deviation is given by U(2,000,000xF1F1F1S1-F1F1F10x²) = F1F1F1S1(2,000,000m - 2,000,000xF1F1F10s) = 2,000,000xF1F1F1S1m - 2,000,000xF1F1F10s. Thus the answer is A.

Question 6

If you invest half your money in a risk-free asset and half your money in a risky asset such that the standard deviation of the return on the risky asset is s, then the standard deviation of the return on your investment portfolio is s/2.

Accepted Answer

When you diversify your investments between a risk-free asset and a risky asset, the overall risk of the portfolio is averaged out. Since the risk-free asset has a standard deviation of zero, investing half in it and half in a risky asset with standard deviation s, effectively spreads the risk over the entire investment, resulting in a portfolio standard deviation of s/2. This is because the risk (volatility) of the risk-free asset does not contribute to the portfolio's volatility, thus the portfolio's standard deviation is only coming from the risky asset, but diluted by the 50% investment in the risk-free asset.

Question 7

If the returns on two assets are negatively correlated, then a portfolio that contains some of each will have less variance in its return per dollar invested than either asset has by itself.

Accepted Answer

This statement is true. When two assets have negative correlation, they tend to move in opposite directions. Therefore, combining them in a portfolio can help reduce the overall variance of the portfolio's return. This is because when one asset is doing poorly, the other may be doing well, which helps balance out the overall return of the portfolio.

Question 8

Suppose that Fenner Smith of Workouts must divide his portfolio between two assets, one of which gives him an expected rate of return of 15% with zero standard deviation and one of which gives him an expected rate of return of 55% and has a standard deviation of 10%.He can alter the expected rate of return and the variance of his portfolio by changing the proportions in which he holds the two assets.If we draw a "budget line" with expected return on the vertical axis and standard deviation on the horizontal axis, depicting the combinations that Smith can obtain, the slope of this budget line is

Accepted Answer

The slope of the budget line is calculated by taking the difference in the expected returns of the two assets and dividing it by the difference in their standard deviations. Since the first asset has a 0% standard deviation and the second asset has a 10% standard deviation, the difference in standard deviations is 10%. The expected returns are 55% and 15%, so the difference is 40%. The slope is 40% / 10% = 4.

Question 9

Firm A sells lemonade and firm B sells hot chocolate.If you invest $100 if firm A, in one year you will get back $(30 + T)where T is the average temperature (Fahrenheit)during the summer.If you invest $100 in firm B, in one year you will get back $(150 - T), where T is the average temperature during the summer.The expected value of T is 70 and the standard deviation of T is 10.If you invest $50 in firm A and $50 in firm B, what is the standard deviation of your return on your investment?

Accepted Answer

The standard deviation of the return on investment when investing in both firms is 0 because the returns from Firm A and Firm B are perfectly negatively correlated with respect to temperature. Any variation in temperature that increases the return from one firm decreases the return from the other by the same amount, resulting in no variability in the total return.

Question 10

If you invest $100 now in firm A, in one year you will get back $(30 - T), where T is the average temperature during the next summer.If you invest $100 now in firm B, in one year you will get back $(180 - T).The expected value of T is 70 and the standard deviation of T is 10.
a.Draw a graph showing the combinations of expected return and standard deviation that you can have by dividing $100 between stock in A and stock in B.(Hint: Expected value has the property that E(ax + b)= aE(x)+ b and standard deviation has the property that SD(ax + b)= [(absolute value of a)times SD(x)] +
b.What is the expected value and standard deviation of the safest investment strategy you can make by this means? 
c.What is the highest expected value you can achieve?

Accepted Answer

The answer of If you invest $100 now in firm...

Question 11

Suppose that Fenner Smith of Workouts  must divide his portfolio between two assets, one of which gives him an expected rate of return of 10% with zero standard deviation and one of which gives him an expected rate of return of 25% and has a standard deviation of 5%.He can alter the expected rate of return and the variance of his portfolio by changing the proportions in which he holds the two assets.If we draw a "budget line" with expected return on the vertical axis and standard deviation on the horizontal axis, depicting the combinations that Smith can obtain, the slope of this budget line is

Accepted Answer

The slope of the budget line can be calculated as follows:

Slope = (Expected return of asset with 25% return - Expected return of asset with 10% return) / (Standard deviation of asset with 25% return - Standard deviation of asset with 10% return)
Slope = (25% - 10%) / (5% - 0%)
Slope = 3

Therefore, the slope of the budget line is 3. The best choice for Fenner Smith would be to choose the portfolio with the highest expected return while staying within his acceptable level of risk. This would be a portfolio that would lie on the budget line with the highest possible expected return, given his risk tolerance.

Question 12

Suppose that Ms.Lynch in Workouts can make up her portfolio using a risk-free asset that offers a surefire rate of return of 10% and a risky asset with an expected rate of return of 15%, with standard deviation 5.If she chooses a portfolio with an expected rate of return of 12.50%, then the standard deviation of her return on this portfolio will be

Accepted Answer

The standard deviation of a portfolio that combines a risk-free asset and a risky asset depends only on the portion of the portfolio invested in the risky asset. Since the risk-free asset has a 0% standard deviation, any standard deviation in the portfolio comes from the risky asset. The expected return of 12.50% is exactly halfway between the risk-free return of 10% and the risky asset's return of 15%, implying that the portfolio is composed of equal parts risk-free and risky assets. Therefore, the portfolio's standard deviation would be half of the risky asset's standard deviation, which is 2.50%.

Question 13

Bill owns an export business.The expected profit from his business is $100,000 a year.For every 1% increase in the value of the Japanese yen relative to the dollar, its profits increase by $20,000.Bill plans to buy one of two firms.One is an import business which returns an expected profit of $70,000.For every 1% increase in the value of the Japanese yen relative to the dollar, the profits of this firm shrink by $5,000.The second is a safe domestic firm which is certain to yield him $70,000 a year.The two firms cost the same.If Bill is risk averse,

Accepted Answer

The answer of Bill owns an export business.The expected profit...

Question 14

If two assets have the same expected rate of return but different variances, a risk-averse investor should always choose the one with the smaller variance, no matter what other assets she holds.

Accepted Answer

The answer of If two assets have the same expected...

Question 15

You have been hired as a portfolio manager for a stock brokerage.Your first job is to invest $100,000 in a portfolio of two assets.The first asset is a safe asset with a sure return of 4% interest.The second asset is a risky asset with a 26% expected rate of return, but the standard deviation of this return is 10%.Your client wants a portfolio with as high a rate of return as possible consistent with a standard deviation no larger than 4%.How much of her money do you invest in the safe asset?

Accepted Answer

The answer of You have been hired as a portfolio...

Question 16

Suppose that Fenner Smith of Workouts must divide his portfolio between two assets, one of which gives him an expected rate of return of 15% with zero standard deviation and one of which gives him an expected rate of return of 30% and has a standard deviation of 5%.He can alter the expected rate of return and the variance of his portfolio by changing the proportions in which he holds the two assets.If we draw a "budget line" with expected return on the vertical axis and standard deviation on the horizontal axis, depicting the combinations that Smith can obtain, the slope of this budget line is

Accepted Answer

The slope of the budget line is calculated as the change in expected return divided by the change in standard deviation. Here, the difference in expected return between the two assets is 15% (30% - 15%), and the difference in standard deviation is 5%. Thus, the slope is 15% / 5% = 3.

Quiz 12: Risky Assets-Part A

If the mean is plotted on the horizontal axis, and the variance on the vertical, then indifference curves for a risk averter must slope upward and to the right.

Marvin is an expected utility maximizer.He chooses his portfolio so as to maximize the expected value of 2,000,000x - x2.If m is the mean of Marvin's income and s is the standard deviation, Marvin's income as a function of the mean and standard deviation is

If you invest half your money in a risk-free asset and half your money in a risky asset such that the standard deviation of the return on the risky asset is s, then the standard deviation of the return on your investment portfolio is s/2.

If the returns on two assets are negatively correlated, then a portfolio that contains some of each will have less variance in its return per dollar invested than either asset has by itself.

If two assets have the same expected rate of return but different variances, a risk-averse investor should always choose the one with the smaller variance, no matter what other assets she holds.

Marvin is an expected utility maximizer.He chooses his portfolio so as to maximize the expected value of 2,000,000x - x².If m is the mean of Marvin's income and s is the standard deviation, Marvin's income as a function of the mean and standard deviation is