DERIVATIVE INVESTMENTS

MODULE TITLE: Derivatives Investments

(MSc Finance & Investment)

Learning outcomes and pass attainment level: 1. Assess derivative contracts and their appropriateness and suitability for investment and management of different risks. 2. Construct derivative contracts to get exposure to investments in different markets & asset classes. 3. Evaluate different risks associated with investments & financing and use derivative contracts to hedge the relevant risks.

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Indicative marking guide

	0 – 39% Fail	40 – 49% Fail	50 – 59% Pass	60 – 69% Strong Pass (merit)	70 – 79% Very Strong Pass (distinction)	80 – 100% Exceptionally Strong Pass (distinction)
Criterion 1 Mark:	Assess derivative contracts and their appropriateness and suitability for investment and management of different risks.
	No evidence of assessment of derivative contracts and their suitability for investment and risk management found. The submitted work does not accurately describe the use of different derivative contracts for given scenarios.	Some evidence of assessment of derivative contracts and their suitability for investment and risk management found. The suitability of different derivative contracts s partially correct and the analysis of derivative contracts is inadequate.	Good evidence of assessment of derivative contracts and their suitability for investment and risk management found. However, the analysis of derivative contracts and their suitability should have been more detailed and objective.	Strong evidence of assessment of derivative contracts and their suitability for investment and risk management found. The analysis of derivative contracts and their suitability have been discussed adequately.	Very strong evidence of assessment of derivative contracts and their suitability for investment and risk management found. The analysis of derivative contracts and their suitability have been very well explained and discussed.	An outstanding assessment off derivative contracts and their suitability for investment and risk management have been provided. The analysis of derivative contracts and their suitability have been exceptionally well explained and discussed.
Criterion 2 Mark:	Construct derivative contracts to get exposure to investments in different markets & asset classes.
	The submitted work fails to show evidence of setting up derivative contracts to get exposure to investment in different markets and asset classes. The calculations and/or analysis are not correct.	The submitted work shows some evidence of setting up derivative contracts to get exposure to investment in different markets and asset classes. However, the calculations and/or analysis are not correct and inadequate.	The submitted work shows evidence of setting up derivative contracts to get exposure to investment in different markets and asset classes. However, the calculations and/or analysis should have been more been more detail and well explained.	The submitted work shows strong evidence of setting up derivative contracts to get exposure to investment in different markets and asset classes. The calculations and/or analysis have been more detailed and adequately explained.	A very strong evidence of setting up derivative contracts to get exposure to investment in different markets and asset classes is evident. The calculations and/or analysis have been very well explained and discussed.	Excellent ability in setting up derivative contracts to get exposure to investment in different markets and asset classes is evident. The calculations and/or analysis have been exceptionally well-explained and discussed.
Criterion 3 Mark:	Evaluate different risks associated with investments & financing and use derivative contracts to hedge the relevant risks.
	Different risks associated with investment and financing have not been evaluated. Derivative contracts have not been used to hedge risks in given scenarios or have not been correctly used at all.	Different risks associated with investment and financing have been evaluated partially and inadequately. Hedging of risks using derivative contracts in given scenarios is partially correct and inadequate.	Different risks associated with investment and financing have been evaluated adequately. Hedging of risks using derivative contracts in given scenarios is correct, however, the evaluation of risks should have been more detail and the hedge results well explained.	Good evaluation of different risks associated with investment and financing is evident. Hedging of risks using derivative contracts in given scenarios is correct as well as adequately explained. The evaluation of different risks is very detailed and the hedge results well explained.	Very good evaluation of different risks associated with investment and financing is evident. Hedging of risks using derivative contracts in given scenarios is correct as well as very well explained. The evaluation of different risks is very good and hedge results are very well explained.	Excellent evaluation of different risks associated with investment and financing is evident. Risks have been hedged accurately using derivative contracts. The evaluation of risks as well as the explanation of the hedge results is exceptional.

Question 1

Jason Roy is the portfolio manager and CEO of Roy Investments. At present he is very busy and has a number of important issues that must be dealt with before the end of the week. Roy manages a portfolio that consists of $40 million in bonds and 460 million in equity securities. The bonds in the portfolio have a modified duration of 6.3 and beta of the equity portion of the portfolio is 1.25. For each the holding period is one year and Roy has the authority to borrow up to $25 million for investing on short term basis to earn any spread as the difference between borrowing and lending rates.

Roy fears a rise of 25 basis points in the interest rates over the near future and hence desires to decrease the duration of the bonds in the portfolio to 5.0 for a short period of time. He prefers to use futures contracts to implement this change as it is temporary as well as he does not want to sell the bonds and incur higher transaction costs. Treasury bond futures contract have a modified duration of 4.2, a yield beta of 1.1, and a price (including the multiplier) of $245,000.

Roy desires to borrow funds three months from today so that he can take advantage of higher interest rates and invest at higher expected interest rates. However, for this to be advantageous he must lock in today’s interest rates for the loan. Therefore, Roy is considering a forward rate agreement (FRA) to lock in the rate on the loan. This FRA will be settled in cash based on the prevailing actual interest rates relative to the FRA interest rate three months from now. This strategy involves Roy to borrow $20 million at 5 % for 9 months and the loan will be obtained three months from now.

The equity portion of the portfolio has performed extremely well over the recent past and Roy must decide on one of the following two options:

Option 1: Roy could hold on to his current profits for the next six months which should make the reported annual return rank in the top one percentile of similar portfolios. Again, Roy prefers to use futures contracts instead of selling stocks to lock in the profits. The portfolio is composed of the same stocks and sector weightings as the S&P 500. The contract on the index is at 2000 (with a multiplier of 250), and it expires in 6 months. The risk free rate is 2% and the dividend yield on the index is 3%.

Option 2: Roy believes there is a chance the market may move significantly over the next six months. To benefit from the expected move in the market, Roy could increase the equity portion of the portfolio from its current beta of 1.25 to 1.4 by using equity index futures. The appropriate equity index futures contract that Roy is considering using has a beta of 0.90 and a price (including the multiplier) of $335,000.

Finally, Roy Investments expects to receive $6 million cash in 4 months and the desire is to pre-invest the funds to create the same exposure to the bond and stock market that is found in the original portfolio. The relevant stock index futures contract for accomplishing this has a total price (including the multiplier) of $315,650 and a beta of 1.10. The relevant bond index futures contract has a total price of $115,460, a yield beta of 1.05 and an effective duration of 6.2.

Required:

i. Assume Roy Investments uses a FRA to hedge the loan rate. If interest rates are 4.85 percent at expiration of the FRA, calculate the settlement payment. Provide details of your calculations and explain. (8 marks)

ii. What is the value of the bond portfolio given a 25 basis point increase? Explain your calculations. (4 marks)

iii. How many Treasury bond futures contracts are needed to reduce the duration of the bonds in the portfolio. Explain. (6 marks)

iv. As the beta of the equity portfolio to be increased to 1.4, explain the expectations about the market as well as the required number of contracts that needs to be traded to achieve the target beta. (6 marks)

v. Determine the number of S&P index futures contracts that need to be traded (bought or sold) to create a six-month synthetic cash position. (4 marks)

Question 2

a) Karim works as an option trader at Gold Star Securities. He just sold one-month put options on 2,000 shares of James Steel Inc. to Ian Smith. These options carry an exercise price of €1,300 with an option premium of €19.09 per share. James Steel Inc. equity is currently trading at €1,340 per share. The options were priced using a volatility of 24%. Karim’s calculations show the delta of the options to be –0.3088.

To hedge this exposure, Karim requires to trade in the shares of James Steel Inc.

Required:

i. To hedge the exposure from the put option, what action should Karim take i.e. buy or sell shares of James Steel Inc. (2 marks)

ii. Determine the number of shares that need to be traded. Show your calculations in detail and explain. (4 marks)

b) The risk manager at Gold Star Securities is interested to know about the sensitivity of the price of the put options to develop better understanding of the process of risk management involved. Karim responded that option deltas are frequently used by traders for estimating the sensitivity of the options to changes in the price of the underlying. However, the actual price changes of options differ from those estimated using options’ deltas.

Required:

iii. Determine whether the change in the price of the put option will be greater for an increase or decrease in the price of the underlying equity. Explain in detail. (6 marks)

Note: Assume the increase and decrease are immediate and of equal value.

c) Karim sold 3,000 three-month equity call options with an exercise price of €825 to another client. The price of the underlying equity is €800 per share with each call option priced at €29.42. To hedge this position, purchased 1,322 shares of the underlying equity and calculated his net cash outlay to be €969,340. For assessing the performance of the hedge, Karim sets his performance benchmark as the net cash outlay continuously compounding at the risk-free rate of 2.25% (using days in period/365).

Five days later into the hedge period, the price of the equity is €815, and Karim calculates the new fair value of the call options to be €35.30.

Required:

iv). Calculated the percentage difference between the hedge position’s value and Karim’s benchmark. Provide detail calculations and explain. (8 marks)

v). Explain why the hedge may not be perfect. (4 marks)

Question 3

Kraig Wall and Jessy Roll share the responsibility for both interest rate and currency risk management at Reed Corporation which is a multinational firm headquartered in the United States.

Given the recent increase in the growth of global economy, Reed Corporation has experienced significant increase in its sales and now plans to increase the capacity of its factory in the U.S. as further expansion at a cost of $30,000,000. This expansion will be financed through borrowing at floating rate of LIBOR + 2% with quarterly payments over 7 years period. Kraig expects that Reed’s expansion will begin in the next six months and will receive the $30,000,000 financing at that point in time. However, he is worried that over this period the interest rates may increase and therefore it will be better to convert the loan’s floating interest rate to a fixed rate in the coming six months’ time. Kraig subsequently evaluates the forecasted future swap fixed rates and the current terms of the various swaptions. These are given below where the swaptions are for a Swap of 7 year with LIBOR flat as the floating interest rate.

Fixed rate for payer's swaption that matures in six months 7.00%

Fixed rate for receiver's swaption that matures in six months 7.10%

Projected Swap Fixed Rate in six months 7.20%

Fixed rate for payer's swaption that matures in seven years 8.40%

Fixed rate for receiver's swaption that matures in seven years 8.50%

Projected Swap Fixed Rate in seven years 9.20%

Reed Corporation has just recently opened a new factory in France to sell its products locally with a projected quarterly earning cash flows of €10,000,000. To convert these quarterly Euro cash flows into dollars, Jessy has suggested that Reed Corporation use currency swap that does not involve the exchange of notional principal. Only the quarterly cash flow in Euro will be exchanged for dollars. Jessy received the following exchange rate and annual swap fixed interest rates from a currency swap dealer.

Exchange rate (EUR per dollar) 0.72

Swap interest rate in U.S. dollars 3.40%

Swap interest rate in euros 5.80%

These rates are for 3 months’ cash flow exchange and approximately coincides with the quarterly Euro cash flows Reed will receive from its French operations. The swap has a maturity of 2 years as Jessy is not confident in projecting the earning cash flows from the French operations beyond 2 years.

Required:

Write a report which covers the following contents (word limit 1300):

i. Explain the similarities and differences between Swaps and forward contracts. (5 marks)

ii. Explain the different uses of swaps for risk management. (6 marks)

iii. Given the interest rate forecast, the most appropriate position Kraig should take to hedge the financing of the factory expansion. Provide detail justifications and calculations. (3 marks)

iv. Assume the firm buys the appropriate swaption and Kraig’s interest rate forecasts prove correct. Determine the net interest payment Reed Corporation will make on the factory expansion loan in six months. (4 marks)

v. If Kraig’s interest rate forecasts prove correct, and the appropriate hedge is enacted, what happens to the cash flow risk and the market value risk of Reed Corporation i.e. increase or decrease in each? Explain. (4 marks)

vi. Determine the periodic cash flows resulting from Reed’s hedge of the French factory sales. (4 marks)

vii. Suppose that Reed’s currency swap can be structured with fixed or floating payments. If Kraig’s interest rate concerns are correct, which of the following would be the ideal position for Reed to take in the currency swap? From Reed’s perspective, how should the swap be structured with? i.e.

a. Fixed dollar interest rate and a floating euro interest rate or

b. Floating dollar interest rate and a fixed euro interest rate or

c. Floating dollar interest rate and floating euro interest rate

Note: You must provide detail explanation of your choice. (3 marks)