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19 Questions on Derivatives

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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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Solution Summary

Answers to 19 Questions on Derivatives dealing with 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.

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25 multiple choice questions on derivatives, international finance, investments

MULTIPLE CHOICE QUESTIONS
1. In a forward contract the party who commits to sell an asset at a specified date in the future takes a(n) position, and the party who commits to buy an asset at a specified date in the future takes a(n) position.
(a) risk seeking; risk averse
(b) open; closed
(c) closed; open
(d) short; long
(e) long; short

2. Assume the one year forward rate for a share of stock is $45, the spot price is $41 and the risk free rate is 5% pa. The observed forward price is and the implied forward price is :
(a) $45; $41
(b) $45; $43.05
(c) $41; $45
(d) $41; $43.05
(e) $45; $38.95

3. An investment strategy that requires no outlay of an investor's own money to generate positive riskless profits is:
(a) arbitrage
(b) risk seeking
(c) portfolio replicating
(d) beta adjusting
(e) minimum variance

4. An OTC forward contract is:
(a) an option to call
(b) a forward contract for which the payback is outside the contract period
(c) a customised agreement that is not traded on an exchange
(d) a standardised agreement that is traded on an exchange
(e) a forward contract in which the spot price of the asset at maturity is over the contract forward price

5. The NZ dollar risk free rate is r$ = 3.0% pa, the euro risk free rate is r? = 7.0% pa, the euro is currently trading at NZ$2.04 per ?. The implied forward NZ dollar against euro exchange rates at 3 months and at one year are:
(a) NZ$2.06 per ?; NZ$2.12 per ?
(b) NZ$2.12 per ?; NZ$2.06 per ?
(c) NZ$2.02 per ?; NZ$1.96 per ?
(d) NZ$2.00 per ?; NZ$1.96 per ?
(e) NZ$1.96 per ?; NZ$2.00 per ?

6. A dealer in a commodity is considering a trade in a forward contract. The current spot price of the commodity is $500 per unit, the forward price for delivery in 1 year is $540 per unit and the annual inventory costs are 2% of the current spot price. The implied risk free rate is , and the arbitrage profit that could be earned per unit of the commodity in period 1 if the risk-free rate of return is 5% pa in period 0 is .
(a) 4.0%; $4.20
(b) 5.5%: $5.09
(c) 5.5%; $2.70
(d) 6.0%; $5.00
(e) 6.0%; $5.40

Questions 7-12 refer to the following information.
Consider a market consisting of only two assets, A and B. There are 100 shares of asset A in the market and the price per share is $1.00. There are 100 shares of asset B in the market and the price per share is $2.00.
Asset A has an average rate of return, A = 10%.
Asset B has an average rate of return, B = 6%.
The risk free interest rate is 5%.
The standard deviation of the market return is 20%.
Assume the market satisfies the CAPM.

7. The asset allocation in the market portfolio is:
(a) A = 1/2 ; B = 1/2
(b) A = 1/4 ; B = 3/4
(c) A = 3/4 ; B = 1/4
(d) A = 2/3 ; B = 1/3
(e) A = 1/3 ; B = 2/3

8. The expected return from the market portfolio is:
(a) 7.00%
(b) 7.33%
(c) 8.00%
(d) 8.67%
(e) 9.00%

9. The betas of assets A and B are:
(a) A = 1.36 ; B = 0.82
(b) A = 1.36 ; B = 0.27
(c) A = 1.15 ; B = 0.69
(d) A = 1.67 ; B = 0.33
(e) A = 2.14 ; B = 0.43

10. The covariance of the market with asset A is:
(a) 0.0857
(b) 0.0784
(c) 0.0667
(d) 0.0545
(e) 0.0500

11. The equation of the CML is:
(a)
(b)
(c)
(d)
(e)

12. An investment opportunity in the market offers an expected return of 6% with a standard deviation of 19%. If you invested all your money in this opportunity where would your portfolio lie in relation to the CML?
(a) at the point of intersection of the CML and the vertical axis
(b) at the point of intersection of the CML and the horizontal axis
(c) above the CML
(d) below the CML
(e) cannot be determined from the information given

Questions 13-14 refer to the following information.
Consider an economy in which the risk free interest rate is 5%, the return to the market portfolio is 15% and the standard deviation of the return to the market portfolio is 20%.
A firm's shares are currently trading at $20 per share.
A market analyst reports that the firm's expected dividend is $2 and it is expected that the share price will remain constant.
Assume the firm's beta is 0.1.

13. What is the expected return from the stock and the stock's risk premium?
(a) 17%; 12%
(b) 25%; 5%
(c) 25%; 20%
(d) 10%; 15%
(e) 10%; 5%

14. What is the risk premium suggested by CAPM? According to CAPM are the firm's shares over-priced or under-priced?
(a) 10%; over-priced
(b) 10%; over-priced
(c) 1%; under-priced
(d) 1%; over-priced
(e) 5%; correctly priced

15. Assume the standard deviation of the market return is 0.2, the standard deviation of asset k is 0.45 and the beta of asset k is 0.675. The correlation coefficient between the return from asset k and the return from the market is:
(a) 0.900
(b) 0.658
(c) 0.444
(d) 0.300
(e) 0.133

16. A portfolio comprises two risky assets. As the correlation between the two assets decreases the standard deviation of the minimum variance portfolio and the standard deviation of the tangency portfolio :
(a) increases; decreases
(b) increases; increases
(c) remains unchanged; decreases
(d) decreases; increases
(e) decreases; decreases

17. A call option is in-the-money if the:
(a) strike price of the option is less than the current price of the underlying asset
(b) strike price of the option is greater than the current price of the underlying asset
(c) strike price of the option is equal to the price of the underlying asset
(d) intrinsic value of the option is zero
(e) settlement date is less than one month from the current date

18. The forward short position with a forward price of E has the same gross return as the combination of which two option positions, each with strike price E?
(a) long call and short put
(b) long put and short call
(c) long call and long put
(d) short put and short call
(e) none of the above

19. The price of a put option as the volatility of the returns of the underlying asset increases, and the price of a put option as the time to expiration decreases.
(a) decreases; remains unchanged
(b) decreases; decreases
(c) increases; increases
(d) increases; remains unchanged
(e) increases; decreases

20. Which of the following statements is NOT true of the Black-Scholes model?
(a) vega is always positive
(b) N(d1) is the  of the call option
(c) N(d2) is the  of the put option
(d) the volatility of the underlying asset is the annualised standard deviation of its returns
(e) the volatility of the underlying asset is assumed to be constant

Questions 21-25 refer to the following information.
Assume the current price of a stock is $43 and the volatility is 0.2. Assume the stock is not expected to pay dividends during the next 6 months. Assume the risk-free interest rate is 10% pa.

21. The Black-Scholes model suggests that the price of a 6 month European call option on the stock where the exercise price of the option is $40 is:
(a) $6.29
(b) $5.56
(c) $4.83
(d) $3.72
(e) $1.86

22. What is the intrinsic value of the call option? What is its the time value?
(a) $4.00; $0.35
(b) $2.72; $1.00
(c) $3.00; $2.56
(d) $3.00; $3.29
(e) $0; $4.83

23. The probability that the call option expires in-the-money is approximately:
(a) 0.94
(b) 0.83
(c) 0.79
(d) 0.17
(e) 0.06

24. The Black-Scholes model suggests that the price of a 6 month European put option on the stock where the exercise price of the option is $40 is:
(a) $0.61
(b) $0.78
(c) $0.84
(d) $1.34
(e) $2.63

25. The call option is , and the put option is :
(a) in-the-money; at-the-money
(b) out-of-the-money; in-the-money
(c) at-the-money; at-the-money
(d) in-the-money; out-of-the-money
(e) out-of-the-money; at-the-money

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