Probability A B

0.1 (7%) (32%)

0.2 5 0

0.4 10   21

0.2 21 29

0.1 31 38

Stocks A and B have the following probability distributions of expected future returns

A. Calculate the expected rate of return, , for Stock B ( = 11.60%.) Do not round intermediate calculations. Round your answer to two decimal places.

B.Calculate the standard deviation of expected returns, σ_A, for Stock A (σ_B = 19.30%.) Do not round intermediate calculations. Round your answer to two decimal places.

C.Now calculate the coefficient of variation for Stock B. Do not round intermediate calculations. Round your answer to two decimal places.

Investment companies and performance evaluation

1) Consider two different hedge funds with the following data related to performance:

Hedge fund Alpha Beta

Fund A   5% 1.6

Fund B   3% 0.8

Assuming that beta is consistent with the type of investing we expected in both cases, which fund performed better.
A. Fund A, because it had the higher return
B. Fund A, because it had the higher alpha
C. Fund B, because its alpha is more impressive than Fund A when we consider how much less risk the fund took.
D. Fund B, because the beta is closer to 1.

2) When we analyze the performance of an actively managed mutual fund we find that the fund generated a beta of 1 and an alpha of zero.

A. this result shows that the manager took no risk when investing

B. this result shows that the manager did not add any value to performance with his/her decision-making

C. both (A) and (B) are true

D. none of the above

3) Consider two different hedge funds with the following data related to performance:

Hedge fund Alpha Beta

Fund A   1% 0.8

Fund B   3% -0.3
Assuming that beta is consistent with the type of investing we expected in both cases, which fund performed better?

A. Fund A, because Fund B should have negative alpha to match its negative beta
B. Fund A, because it had a higher beta than Fund B
C. Fund B, because its alpha is higher than Fund A.
D. Fund A, because the beta is closer to 1.

4) A positive alpha for a mutual fund means:

A. the fund invested in high-risk strategies

B. the fund manager’s performance was bad

C. both (A) and (B)

D. none of the above

A study is done to test the claim that Company A retains its workers longer than Company B. Company A samples 16 workers, and their average time with the company is 5.2 years with a standard deviation of 1.1. Company B samples 21 workers, and their average time with the company is 4.6 years with a standard deviation of 0.9. The populations are normally distributed.

0.2 point for writing the hypothesis in symbolic form.

0.2 point for determining the value of the test statistic.

0.2 point for finding the critical value OR the p-value.

0.2 point for determining if you should reject the null hypothesis or fail to reject the null hypothesis.

0.2 point for writing a conclusion addressing the original claim.

Compare the Greek arts to the Roman arts. When the Romans came to power, their art was heavily influenced by the Greeks, but with some changes. In what ways did the Romans change the Classics of the Greek artistic legacy? Include examples of how the Romans transformed Greek philosophy, architecture, theater, and sculpture and reinterpreted it into their own unique Roman style.   

Q1)According to economists, the biggest “cost” of unemployment is

            a.         increased “welfare” expenditures.                           c.         the value of foregone output.

            b.         lost tax revenue.                                                       d.         none of these.

Q2)

Which of the following statements is LEAST correct?

            a.         Inflation is a period of time during which the value of money is rising.

            b.         Affluent people – with assets other than money – can and often do benefit from inflation.

            c.         Both World War II (during the early 1940s) and the Vietnam War (during the late 1960s)

generated what’s known as demand-pull inflation.

            d.         “The Energy Crisis” of the 1970s generated what’s known as cost-push inflation.

Q3) The type of unemployment that economists find most concerning is

            a.         frictional unemployment.                                           c.         structural unemployment.

            b.         cyclical unemployment.                                              d.         voluntary unemployment.

A hotel wanted to develop a new system for delivering room service breakfasts. In the current system, an order form is left on the bed in each room. If the customer wishes to receive a room service breakfast, he or she places the order form on the doorknob before 11p.m. The current system requires customers to select a 15-minute interval for desired delivery time (6:30~6:45a.m., 6:45~7:00a.m., etc.). The new system is designed to allow the customer to request a specific delivery time. The hotel wants to measure the difference (in min.) between the actual delivery time and the requested delivery time of room service orders for breakfast (negative time means that the order was delivered before the requested time, whereas the positive time means that the order was delivered after the requested time). The factor included were the menu choice (American and Continental) and the desired time period in which the order was to be delivered (Early Time Period [6:30~8:00a.m.] or Late Time Period[8:00~9:30a.m.]). Ten orders for each combination of menu choice and desired time period were studied on a particular day, and the data were stored (BreakFast.xlsx)

(a) At the 0.05 level of significance, is there an interaction between type of breakfast and desired time?

(b) Draw the plot of means.
(c) At the 0.05 level of significance, is there an effect due to type of breakfast? (d) At the 0.05 level of significance, is there an effect due to desired time?

A hotel wanted to develop a new system for delivering room service breakfasts. In the current system, an order form is left on the bed in each room. If the customer wishes to receive a room service breakfast, he or she places the order form on the doorknob before 11p.m. The current system requires customers to select a 15-minute interval for desired delivery time (6:30~6:45a.m., 6:45~7:00a.m., etc.). The new system is designed to allow the customer to request a specific delivery time. The hotel wants to measure the difference (in min.) between the actual delivery time and the requested delivery time of room service orders for breakfast (negative time means that the order was delivered before the requested time, whereas the positive time means that the order was delivered after the requested time). The factor included were the menu choice (American and Continental) and the desired time period in which the order was to be delivered (Early Time Period [6:30~8:00a.m.] or Late Time Period[8:00~9:30a.m.]). Ten orders for each combination of menu choice and desired time period were studied on a particular day, and the data were stored

(a) At the 0.05 level of significance, is there an interaction between type of breakfast and desired time?

(b) Draw the plot of means.

(c) At the 0.05 level of significance, is there an effect due to type of breakfast?

(d) At the 0.05 level of significance, is there an effect due to desired time?

What is the expected return, standard deviation, and CV for each of these stocks? Which offers you the best risk/reward ratio?

1. a. Two investors, A and B, are evaluating the same investment opportunity, which has an expected value of £100. The utility functions of A and B are ln(x) and ​​​​​x​², respectively. Which investor has a certainty equivalent higher than 100? Which investor requires the higher risk premium?

b. (i) Describe suitable measures of risk for ‘loss-aversion’ and ‘risk aversion’.

(ii) Concisely define the term ‘risk neutral’ with respect to a utility function u (w), where w is the realisation of a random variable W.

(c) Suppose you are facing a lottery that has a payoff of 10b pounds with probability 0.01 and that of 0 with probability 0.99. You are an expected utility maximiser with a utility function, u(x) = −exp(−ax) where x is the payoff in money terms and a > 0 is a parameter. What is the risk premium for this lottery - describe the risk premium as a function of ‘a’ and ‘b’.

(d) How does the risk premium in (c) change as ‘b’ changes.

2.

​​​​​​​There are two distinct portfolios, A and B.

1. A portfolio D assigns weight w to portfolio A and weight (1-w) to portfolio B. What should w be so as to minimise the variance of portfolio D, if ρ_AB = -0.5? The variance of a portfolio is given by:   
2. If ρ_AB = 0.5, and A and B are frontier portfolios, what is the expected return and standard deviation of the minimum variance portfolio?
3. Given that A and B are frontier portfolios and that another frontier portfolio C, has an expected rate of return of 25% and variance of 2 %, evaluate the new ρ_AB.

3.

1. Project A has a payoff of 1 with probability 0.8 and 100 with probability 0.2. Project B has a payoff of 5 with probability 0.99 and 1585 with probability 0.01 Which project is preferred by an investor who maximises expected utility and has an utility function u(x) = ln 2x? Comment on the preferences.
2. Is it true that if an investor with utility function u (x) = x ^1/2 prefers risky project A to risky project B, another investor with utility function v(x) = 5x^1/2 + 5 also prefers A to B? Explain.
3. A risk neutral expected utility maximiser is facing a risky investment opportunity. Her utility is a function of the net payoff of the project in terms of money u(y) where £ y is the net payoff. When she makes an investment of £ x (> 0 ), the project yields a gross payoff of £ 30*x ^1/2on the investment with probability 0.4 and a gross payoff of £ 10* x^1/2with probability 0.6. The net payoff is the difference between gross payoff and the cost of the investment. How much should she invest to maximize her expected utility?
4. State the conditions needed to ensure that the choices made to maximise expected utility will coincide with the choices in a mean-variance framework.

4.

1. The cash flows of a firm that has just conducted an Initial Public Offering (IPO) are expected to be either £10 million per annum for 10 years and zero afterwards with probability ‘p’ or £5 million forever with probability (1-p). The risk-adjusted discount rate for this firm is 10% per annum. I. Express the current fundamental value of the firm in terms of ‘p’. II. If the current stock market value of the firm is £55 million, what is the value of ‘p’ implied by the market?

(b) The cash flows of a firm are expected to be £1 million per year starting next year for the first ten years and are then expected to start declining forever at the rate of 5% per year. The risk-adjusted discount rate is 10% per annum. What is the present value of the cash flows?

c) Investment analysts regularly prepare forecasts and reports for their clients on the valuation of the firms they follow as analysts. Briefly discuss the factors that should be taken into account in arriving at such valuations.

A 3-person jury has 2 members each of whom have independently a probability 0.7 of making a correct decision. The third juror just flips a coin for each decision. In this jury, the majority rules. A 1-person jury has a probability 0.7 of making a correct decision. What is the probability of the best jury of making a correct decision?