# There are three assets, A, B and C, where A is the market portfolio and C is

## Question:

There are three assets, A, B and C, where A is the market portfolio and C is the risk-free asset.

The return on the market has a mean of 12% and a standard deviation of 20%. The risk-free asset yields a return of 4%. Asset B is a risky asset whose return has a standard deviation of 40% and a market beta of 1. Assume that the CAPM holds.

(a) Compute the expected return of asset B and its covariances with asset A (the market portfolio) and asset C (the risk-free asset), respectively.

(b) Consider a portfolio of the two risky assets, A and B, with weight w in asset A (the market portfolio) and 1−w in asset B. Compute the expected return and return standard deviation of the portfolio with w being 0, 1/2, and 1, respectively, and enter them into the following table: Portfolio weight w 0 1/2 1 Expected return Standard deviation

(c) Can you rank the three portfolios in the question above? Explain. (d) Consider a portfolio with equal weights in asset B and C (the riskfree asset). Denote this portfolio as asset D. Compute the return standard deviation and expected return of asset D. (e) Consider a portfolio of asset A (the market portfolio) and C. Find the portfolio weight such that its return standard deviation is the same as that of asset D in Question.

(d). What is the expected return of this portfolio? (f) What can you say about the mean-variance efficiency of asset A, B and C (i.e., are they efficient portfolios)? Explain. (g) Construct an efficient portfolio from the assets A, B and C with an expected return of 10%.

The model as presented consists of only four equations, (1), (2), (3), and (4), while there are five endogenous variables. One may "close" the

model by adding adaptive expectations or rational expectations or some other "reasonable" expectations formation hypothesis. We leave the model "open" in this regard.

a) Consider the short run, that is, a fixed Taking expected and actual inflation as given, construct an IS-MP diagram in the plane.

b) Indicate in the diagram whether and how the IS curve and the MP curve, respectively, shift if expected inflation shifts upward. Indicate

also in the diagram whether and how the IS curve and the MP curve, respectively, shift if actual inflation shifts upward. Comment.

c) Presupposing that the zero lower bound is not binding.Short-run equilibrium value of can be written as a linear (affine)

function of the expected inflation rate. Draw the graph of this function, i.e., the "AD curve", in a diagram in the plane.

d) Give a brief account of conclusions concerning the dynamics and dynamic responses to shocks implied by the model, if one assumes perfect foresight.

e) In what sense may the dynamics be radically different depending on the size of the shock? What is the background for the difference?

Tescac's assets are worth $300 (market value). it has $180 of zero-coupon debt outstanding that is due to be repaid at the end of three years. The risk-free interest rate is 5%, and the standard deviation of the returns on Tescac's assets is 50% per year.

a. what is the value of the put option owned by shareholders?

b. what is the value of the company's debt?

c. what is the value of the company's equity?

d. what is the value of the company's debt and equity, separately, if the standard deviation of the return on asset is 60% instead?

Subject: General Finance

A stock sells for $100 today. Over each of the next two years the stock will either increase in value by 10% or decrease in value by 5% with probabilities of 70% and 30% respectively. This means, for example, that in one year the stock will sell for 100 ×1.10 = 110 with 70% probability or for 100 × 0.95 = 95 with 30% probability. (Please note that these probabilities are "physical" probabilities, NOT the risk-neutral ones!)

The stock then increases or decreases in price from these points over the following year. The one-period risk-free rate in each period is 2%.

(a) Consider a European call option on the stock where the option has two-years to maturity and is currently at the money (exercise price of $100). What should be the price of this option? (b) Suppose that the option in 5a is selling for $8. Could you take advantage of this price? If so, how?

The economic explanation for the obesity epidemic suggests the major causes are

(a) changes in GDP and income distribution over time.

(b) long-run decreases in the real interest rate and maternal employment.

(c) decreases in the price of food and increases in the costs of physical activity.

(d) improvements in medical care technology.

In Grossman's model, the aging process is represented by (a) eventually increasing rates of depreciation of health stock. (b) decreases in the efficiency of health investment. (c) MEI schedules which are monotonically decreasing in age. (d) decreases in "effective education" levels as memory fades. 8. Which of the following is NOT a valid criticism of the rational addiction model? (a) The model assumes people know all future prices, but future prices are actually uncertain. (b) The model assumes people fully understand they will become addicted, but people may not know whether or not they are prone to addiction. (c) There is only addictive good in the model, but in reality multiple addictive behaviors may interact. (d) The model predicts that addicts will regret their past decisions, but not all addicts display regret. 9. The U.S. health care system is best characterized as (a) free market provision of health care and insurance. (b) mixed public and private provision of care and insurance. (c) free market provision of insurance but socialized care. (d) free market provision of care but socialized insurance. 10. A public good is a (a) good or service provided by a local or national government. (b) good which involuntarily imposes costs or benefits on third parties. (c) good which is non-rivalrous and non-excludable. (d) good which which people display as a signal of wealth, such that demand for these goods may increase with price.

11. It is an empirical regularity that people with high school educations are on average more healthy than people who do not graduate from high school. We should infer that (a) a randomly selected person with a high school education is likely to be healthier than a randomly selected person without a high school diploma. (b) policies which increase high school graduation rates will improve public health. (c) either the high school curriculum or social interactions among high school students lead to health-promoting behaviors. (d) the government should consider diverting resources from health care to public education. 12. The external costs of cigarette smoking are (a) very large and attributable largely to health care. (b) quite small and largely attributable to factors other than health care. (c) irrelevant because cigarettes are a rationally addictive good. (d) very large because smokers seriously damage their own health through their addiction. 13. You have utility function for wealth U(W) = W3 . You are offered actuarially fair insurance against some risk. You (a) fully insure. (b) buy no insurance. (c) buy some insurance, but you do not fully insure. (d) there is not enough information to decide if (a), (b), or (c) is correct. 14. QALYs are a metric which allows analysts to (a) disentangle correlation and causation in epidemiological studies. (b) accurately assess life expectancy. (c) make tradeoffs between quantity and quality of life. (d) monetize health outcomes for cost-benefit analyses.

You are an advisor for a large pension fund. Real pension funds have liabilities (pensions) due at many dates in the future. For simplicity suppose that the pension fund you are advising has liabilities of $15 million coming due in 5 years and $25 million coming due in 15 years. Suppose that the yield curve is flat and all bonds have yields to maturity of 5% annually.

(a) What is the modified duration of the liabilities of the fund?

(b) Design an investment in a single zero coupon bond that shields the pension fund from small parallel shifts in the yield curve. Invest so that the pension fund is fully funded. (You are allowed to use a zero coupon bond that has a maturity that is not a whole number.)

(c) Consider the asset position you constructed in part 1b. What are the Macaulay and modified durations of this position? What risk exposure is measured by the quantity "duration"? Does the fund face any of this risk? Why?

(d) Suppose that the pension fund is instead "underfunded." This means that the fund's assets do not cover the discounted value of the liabilities. In response, the managers of the pension fund would like to do some active management to increase returns. In particular they have no view on the direction of change in the Treasury yield curve but feel that corporate bonds are underpriced. In words only how might you design an active bond strategy to take advantage of the opportunities reflected in this view?

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