EXPECTED RETURNS

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

1. Calculate the expected rate of return, r_B, for Stock B (r_A = 12.80%.) Do not round intermediate calculations. Round your answer to two decimal places.
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2. Calculate the standard deviation of expected returns, σ_A, for Stock A (σ_B = 18.87%.) Do not round intermediate calculations. Round your answer to two decimal places.
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3. Now calculate the coefficient of variation for Stock B. Round your answer to two decimal places.

4. Is it possible that most investors might regard Stock B as being less risky than Stock A?  

   1. If Stock B is more highly correlated with the market than A, then it might have a lower beta than Stock A, and hence be less risky in a portfolio sense.
   2. If Stock B is more highly correlated with the market than A, then it might have the same beta as Stock A, and hence be just as risky in a portfolio sense.
   3. If Stock B is less highly correlated with the market than A, then it might have a lower beta than Stock A, and hence be less risky in a portfolio sense.
   4. If Stock B is less highly correlated with the market than A, then it might have a higher beta than Stock A, and hence be more risky in a portfolio sense.
   5. If Stock B is more highly correlated with the market than A, then it might have a higher beta than Stock A, and hence be less risky in a portfolio sense.

Select one:

(1) American ladybugs have an average adult length of 1 cm with a known standard deviation of 0.2 cm. The population of American ladybugs in Raleigh was around 1914000 last spring. Assume a normal distribution for the lengths of adult American ladybugs.

Your niece asks you what's the probability of a random ladybug in Raleigh being bigger than 1.5 cm. Is it appropriate to calculate this probability?

Select one: a. Yes.

b. No, because the population distribution is skewed.

c. No, because the sample size is less than 30.

d. No, because the empirical rule is violated.

(2)Regardless of your answer to the previous question, calculate this probability using a normal distribution. Report your answer to four decimal places.

(3)

Although it would be difficult in practice, assume we are able to randomly sample 20 American ladybugs. What's the sampling distribution of the sample mean of these ladybugs?

Select one:

a. A t-distribution with 19 degrees of freedom

b. The sampling distribution is unknown because relevant assumptions are violated.

c. A normal distribution with mean 1 and standard deviation 0.2.

d. A normal distribution with mean 1 and standard deviation 0.045.

(4) Calculate the probability of observing an average American ladybug length between 0.95 cm and 1.05 cm for a random sample of 20 ladybugs. Give your answer accurate to four decimal places. If you found assumptions to be violated in the previous question, answer this question as if the assumptions had not been violated.

We are interested in how long on average it takes Deadpool to grow back a leg. A simple random sample of 25 occasions results in an average of 63 minutes before Deadpool's leg grows back. Assume that the standard deviation of all grow-back-times is 10 minutes.

A. The 80% confidence interval for Deadpool's average time to grow back a leg is ( ,  ). (Answers to two places after the decimal.)

B. Unless our sample is among the most unusual 5% of samples, Deadpool's average time to grow back a leg is between ( ) and ( ) . (Answers to two places after the decimal.)

C. Vanessa claims that average, it takes Deadpool 65 minutes to grow back a leg. Do we have evidence that she's exaggerating the truth at each of the following levels?
The associated p-value for this hypothesis test is ( ) (Answers to four places after the decimal.)

At the 15% level:

At the 13% level:

At the 10% level:

At the 7% level:

At the 5% level:

At the 3% level:

At the 2% level:

At the 1% level:

At the 0.2% level:

At the 0.1% level:

D. Colossus claims that average, it takes Deadpool 65 minutes to grow back a leg. Do we have evidence that he's mistaken at each of the following levels?
The associated p-value for this hypothesis test is ( ) (Answers to four places after the decimal.)
- At the 20% level:

- At the 15% level:

- At the 13% level:

- At the 10% level:

- At the 7% level:

- At the 5% level:

- At the 3% level:

- At the 2% level:

- At the 1% level:

- At the 0.2% level:

- At the 0.1% level:

An object of irregular shape has a characteristic length of L = 1 m and is maintained at a uniform surface temperature of T_s = 325 K. It is suspended in an airstream that is at atmospheric pressure (p = 1 atm) and has a velocity of V = 100 m/s and a temperature of T_? = 275 K. The average heat flux from the surface to the air is 12,000 W/m². Referring to the foregoing situation as case 1, consider the following cases and determine whether conditions are analogous to those of case 1. Each case involves an object of the same shape, which is suspended in an airstream in the same manner. Where analogous behavior does exist, determine the corresponding value of the average heat or mass transfer convection coefficient, as appropriate.

(a) The values of T_s, T_?, and p remain the same, but L = 2 m and V = 50 m/s.

(b) The values of T_s and T_? remain the same, but L = 2 m, V = 50 m/s, and p = 0.2 atm.

(c) The surface is coated with a liquid film that evaporates into the air. The entire system is at 300 K, and the diffusion coefficient for the air–vapor mixture is D_AB = 1.12 × 10^?4 m²/s. Also, L = 2 m, V = 50 m/s, and p = 1 atm.

(d) The surface is coated with another liquid film for which D_AB = 1.12 × 10^?4 m²/s, and the system is at 300 K. In this case L = 2 m, V = 250 m/s, and p = 0.2 atm.

You plan to invest in the Kish Hedge Fund, which has total capital of $500 million invested in five stocks:

Kish's beta coefficient can be found as a weighted average of its stocks' betas. The risk-free rate is 5%, and you believe the following probability distribution for future market returns is realistic:

1. What is the equation for the Security Market Line (SML)? (Hint: First determine the expected market return.)
   1. r_i = 3.7% + (7.3%)b_i
   2. r_i = 5.0% + (6.9%)b_i
   3. r_i = 4.0% + (8.1%)b_i
   4. r_i = 4.0% + (6.9%)b_i
   5. r_i = 5.0% + (8.1%)b_i

   -Select-IIIIIIIVV

2. Calculate Kish's required rate of return. Do not round intermediate calculations. Round your answer to two decimal places.

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3. Suppose Rick Kish, the president, receives a proposal from a company seeking new capital. The amount needed to take a position in the stock is $50 million, it has an expected return of 14%, and its estimated beta is 1.5. Should Kish invest in the new company?

   The new stock -Select-should notshould be purchased.

   At what expected rate of return should Kish be indifferent to purchasing the stock? Round your answer to two decimal places.

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You plan to invest in the Kish Hedge Fund, which has total capital of $500 million invested in five stocks: Stock Investment Stock's Beta Coefficient A $160 million 0.4 B 120 million 1.6 C 80 million 1.8 D 80 million 1.0 E 60 million 1.6

Kish's beta coefficient can be found as a weighted average of its stocks' betas. The risk-free rate is 6%, and you believe the following probability distribution for future market returns is realistic: Probability Market Return 0.1 -29% 0.2 0 0.4 13 0.2 28 0.1 49

What is the equation for the Security Market Line (SML)? (Hint: First determine the expected market return.) ri = 9.7% + (6.8%)bi ri = 9.7% + (7.1%)bi ri = 6.0% + (6.8%)bi ri = 9.8% + (7.0%)bi ri = 6.0% + (7.1%)bi

Calculate Kish's required rate of return. Do not round intermediate calculations. Round your answer to two decimal places. % Suppose Rick Kish, the president, receives a proposal from a company seeking new capital. The amount needed to take a position in the stock is $50 million, it has an expected return of 14%, and its estimated beta is 1.4. Should Kish invest in the new company? The new stock be purchased.

At what expected rate of return should Kish be indifferent to purchasing the stock? Round your answer to two decimal places. %

Most developed countries have some form of a national health plan. A number of possible plans have been proposed in the U.S. recently with price tags of upwards of $200 billion per year (depending on the extent of coverage). An important question in choosing among such plans is how their adoption will affect demand (moral hazard). The empirical question is how large the increase in demand might be.

Estimates of the price elasticity of demand for medical services vary with –0.2 to –0.40 being a representative range. A figure in this range might be a starting point in predicting the effect of health insurance on medical demand. Of course, the above figures apply to all medical services and as we know some price elasticities are likely to differ (such as demand for hospital stays v. office visits to physicians). On the other hand, estimates of price elasticities for more discretionary services (dental care, ophthalmologic care, and psychiatric counseling) tend to be higher.

1. Interpret a price elasticity coefficient of –0.2.
2. Does the relatively high price elasticity of demand for some medical services imply that these services are not really "necessary?" Should health care planners use such elasticity estimates as a guide for the kinds of services people really need, or are there important drawbacks to basing such a judgment on people's responses to prices? How would you judge what medical services are really necessary for a person's wellbeing?
3. Isn't the use of demand concepts in the health care field inappropriate since physicians, not by the patient, determine a great deal of medical demand? Is there any reason for physicians to take the price of a service into account when deciding what to prescribe?

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

1. Calculate the expected rate of return, r_B, for Stock B (r_A = 12.10%.) Do not round intermediate calculations. Round your answer to two decimal places.
   %

2. Calculate the standard deviation of expected returns, σ_A, for Stock A (σ_B = 18.79%.) Do not round intermediate calculations. Round your answer to two decimal places.
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3. Now calculate the coefficient of variation for Stock B. Round your answer to two decimal places.

4. Is it possible that most investors might regard Stock B as being less risky than Stock A?  

   1. If Stock B is more highly correlated with the market than A, then it might have the same beta as Stock A, and hence be just as risky in a portfolio sense.
   2. If Stock B is less highly correlated with the market than A, then it might have a lower beta than Stock A, and hence be less risky in a portfolio sense.
   3. If Stock B is less highly correlated with the market than A, then it might have a higher beta than Stock A, and hence be more risky in a portfolio sense.
   4. If Stock B is more highly correlated with the market than A, then it might have a higher beta than Stock A, and hence be less risky in a portfolio sense.
   5. If Stock B is more highly correlated with the market than A, then it might have a lower beta than Stock A, and hence be less risky in a portfolio sense.