# CAPM, Futures contract, Payoff on option strategy

1. Is the following statement True, False, or Ambiguous? Provide a short justification for your answer (you are evaluated on the justification).

"In the CAPM model, since investors are compensated for holding risk, two securities with the same standard deviation should have the same expected return."

2. Suppose there are two types of risky assets in the market: high growth and low growth stocks. High growth stocks have a standard deviation of .5 and make up 35% of the market while low growth stocks have a standard deviation of .2 and make up 65% of the market. The correlation between the two stocks is .5. The coefficient of relative risk aversion for the average investor is 2.5 and the risk free rate of return is .07. What is the risk premium on high growth stocks according to the CAPM?

3. Assume the following properties for two stocks (stock 1 and stock 2) and of the market.

Expected return on market=0,10, standard deviation of stock 1= 0.20, correlation coefficient between stock 1 and market =0.4 , standard deviation of market = 0.15, standard deviation of stock 2 = 0.30, correlation coefficient between stock 2 and market =0.7. . Suppose further that the risk-free rate is 5%.

a) According to the Capital Asset Pricing Model, what should be the expected return of stock 1 and of stock 2?

b) Suppose that the correlation between the return of stock 1 and the return of stock 2 is 0.5. What is the expected return and the standard deviation of the return of a portfolio that has a 40% investment in stock 1 and a 60% investment in stock 2?

c) Assume that the Capital Asset Pricing Model is valid. How could you construct a new portfolio using the market portfolio and the risk-free asset that has the same expected return as the portfolio you considered in 2(b), but has the lowest standard deviation possible? What is the standard deviation of the return of this portfolio?

d) Suppose that the correlation between the return of stock 1 and the return of stock 2 is -0.7. What is the expected return and the standard deviation of the return of a portfolio that has a 40% investment in stock 1 and a 60% investment in stock 2?

4. a) A futures contract on a non-dividend paying stock with a current price $150 has a maturity of 1 year. If the T-bill rate is 6%, what should the futures price be?

b) What should the futures price be if the maturity of the contract is lengthened to 3 years?

5. Are the following statements True, False, or Ambiguous? Provide a short justification for your answers (you are evaluated on the justification).

a) All else equal, the futures price on a stock index with a high dividend yield should be higher than the futures price on an index with a low dividend yield.

b) All else equal, the futures price on a high-beta stock should be higher than the futures price on a low-beta shock.

c) "The current price of Digital stock is $44 a share. You are offered a forward price for Digital stock to be delivered in one year of $42. The forward price is lower than the spot price because the market anticipates a sharp decline in the price of Digital stock, and the contract offers a way to hedge this risk. There is no arbitrage opportunity."

6. Consider the following option strategy:

? Long one call with $100 strike price bought for $6

? Long one call with $90 strike price bought for $20

? Short one call with $105 strike price sold for $8

? Short one call with $95 strike price sold for $16

a) Draw a picture of the payoff of this option strategy at expiration as a function of the stock price.

b) Draw a picture of the investor's profit at expiration as a function of the stock price. (Hint: The profit includes the cost of the strategy)

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Please see the attached file.

Please provide formulae and explain all of your calculations.

© BrainMass Inc. brainmass.com October 24, 2018, 11:49 pm ad1c9bdddfhttps://brainmass.com/economics/contracts/206450

#### Solution Summary

Answers questions on Capital Asset Pricing Model (CAPM), Futures contract, Payoff on option strategy.

19 Questions on Derivatives: beta of a hedge fund, put option, CAPM, Capital Asset Pricing Model, investors, risk averse, portfolios, mean, variance, highest return portfolio, efficient frontier, abnormal returns, equity mutual funds, riskless return, options position, time to maturity, interest rates, convexity of a puttable bond, futures contracts, gold, initial margin, margin calls, volatility, Palm, 3COM, financial markets, beta calculation, value of a put option, exercise price, maturity, arbitrage opportunity, riskless return, call, 6-month forward rate, Canadian dollars, US dollars, implied volatility, historical volatility, SPX, floating to fixed swap, LIBOR, swap counterparty

For each of the following 8 statements determine if it is true, false or uncertain. You must justify your answer with a one-sentence explanation.

1. The beta of a hedge fund is usually close to one.

2. Suppose you hold a share of stock and a put option on that share. If the stock price is below the exercise price when the option expires the value of your position is the value of the stock.

3. There is a much greater outstanding volume of futures contracts as opposed to forward contracts because futures contracts are much more flexible in terms of settlement dates, amounts, etc.

4. The CAPM (Capital Asset Pricing Model) would be an accurate way to estimate the cost of equity for a company like Federal Express.

5. Assume that all investors are risk averse and select portfolios based on mean and variance. Then the highest return portfolio is always on the efficient frontier.

6. It is easier to earn "abnormal returns," i.e., returns greater than what investments of similar risk earn, by investing in financial rather than real assets.

7. If the price of a stock has gone up for ten consecutive trading days then on the eleventh day we would expect its price to decline.

Assume that we have the following monthly return data on 2 U.S. equity mutual funds. Assume the riskless return is 0.4% per month and the SPX return was 1.4% and its standard deviation was 3.0% per month over this period. You must show your computation to get any credit for your answer.

Fund A Fund B

Realized return 0.012 0.015

Standard deviation of return 0.06 0.08

Beta 1.5 2

8. Give an example of an options position that increases in value as the time to maturity decreases.

9. If interest rates rise, the convexity of a puttable bond will increase ______ an otherwise equivalent non-puttable bond.

a. more than

b. the same as

c. less than

d. actually the convexity will decrease

10. Assume you are short 2 futures contracts for 100 ounces of gold with initial margin of $2,000 each; maintenance margin is $1,500 per contract. Assume the price is initially $500 per ounce. If the price at the end of day 1 is $495 and $493 on day 2, how much money do you have in your margin account (assuming no withdrawals and assuming you make all margin calls) at the start of day 3?

11. Which of the asset A or B has the higher volatility? Both calls have one year to expiration and the riskless rate is 3%.

Option Exercise price Stock price Option price

Call on asset A 95 100 13.7

Call on asset B 60 50 6.10

12. Briefly explain why you think the Palm/3COM story is relevant to the study of financial markets.

13. The following diagram shows the beta calculation for a given firm using weekly data. What can you say about its performance over the time period represented by these data? Why?

The diagram below plots the value of a put option with an exercise price of $100 and one year to maturity.

14. Draw the value of a put option on the same security as in the previous question with an exercise price of $100 and 6 months to maturity.

For each of the following 3 questions determine whether or not an arbitrage opportunity exists. If one exists, describe how you could exploit this arbitrage. All options are written on the same underlying stock, which has a current price of $100 with annual standard deviation of return = .3. The riskless return is 4%.

15. Call with exercise price of 100 costs $20; Call with exercise price of 110 costs $13; Call with exercise price of 120 costs $5. All three options have a one-year maturity.

16. Call with a one-year maturity and an exercise price of 100 costs $20; put with a 2-year maturity and an exercise price of 100 costs $16.

17. The current one-year riskless rate in the U.S. is .05 and the current one-year riskless rate in Canada is .04. The spot rate shows that a Canadian dollar is 0.846 US$. The 6-month forward rate for converting Canadian to US dollars is 0.88.

18. Data have shown that the implied volatility of SPX puts is higher than the historical volatility of the SPX. How could you take advantage of this phenomenon?

19. Suppose you enter into a floating to fixed swap (i.e., you want to have certainty in your interest payments). The current swap rate for a 3-year maturity is LIBOR for 4.9% fixed. Assume that you are borrowing $10 million at LIBOR. Assume the swap payments are made annually. If at the end of year 1 LIBOR is 4.0%, how much do you pay to (or receive from) the swap counterparty?

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