# Any topic (Writer’s choice)

1) What are the main advantages, and disadvantages, to entering a futures hedge? Explain your answer with reference to a futures contract on wheat. Assume the current price is 400 cents per bushel and the futures price is 410 cents per bushel, and cover both the short and long positions.

The main advantages of entering a futures hedge are reduction in risk, reduction in bankruptcy costs and tax advantages (Janakiramanan, 2011). For instance, hedging will ensure that instead of paying a piece of 410 cents per bushel on wheat in the future, only 400 cents per bushel resulting in a saving of 10 cents per bushel.

The main disadvantages of entering a futures hedge are elimination of the opportunity to take advantage of the favorable market conditions and giving misleading impression regarding the amount of the risk reduced (Janakiramanan, 2011). For instance, when the price of wheat decreases to 390 cents per bushel, the buyer will not be able to take advantage of the favorable opportunity.

2) Explain the structure of each of the following types of swaps; what is exchanged between the parties?

- a) Interest rate swap – An interest rate swap is structured in a way that two parties agree to exchange the respective interest rate cash flows; fixed interest rate is exchanged for floating interest rate and vice versa (Janakiramanan, 2011).
- b) Currency swap – A currency swap is structured in such a way that two parties agree to exchange a loan’s principal and/or interest payment in one currency for equivalent net present amounts in another currency (Janakiramanan, 2011). Here, the parties exchange currencies.
- c) Equity swap – An equity swap is where two parties agree to exchange a set of future cash flows at set dates in the future (Janakiramanan, 2011).

3) For each of the following situations, describe the risk that you face and an appropriate futures hedging strategy to hedge that risk:

- You own a portfolio of $20 million of equity securities.

The risk in this situation is equity risk, financial risk of owning equity in a specific investment and an appropriate futures hedging strategy to hedge that risk is diversification, holding a spread of asset classes (Janakiramanan, 2011). Also, using options-based products such as covered warrants, traded options and turbos will help.

- You are an airline, and you expect to need to buy 20 million gallons of jet fuel in January of 2016.

Quantity risk as they are not certain of the quantity of the gallons. An appropriate futures hedging strategy to hedge that risk is Standard Power Options (Janakiramanan, 2011).

- You plan on borrowing 50 million in 12 months at LIBOR plus 50 basis points.

In this situation the risk is interest rate risk which is the unfavorable change in the LIBOR. This kind of risk is hedged by interest rate swaps to ensure the desired interest rate is the one paid for in 12 months even if it changes (Janakiramanan, 2011).

- You are a yogurt manufacturer, and plan on buying 800,000 gallons of milk in the next 60 days.

Here, the risk is *transaction risk* which is the *risk* that there will be unfavorable fluctuation in the relevant exchange rate during the time lag, resulting in potentially serious losses to the yogurt manufacturer. This risk is hedged by forward market to help in locking in an exchange rate today at which the purchase of the gallons of milk will occur at the future date (Janakiramanan, 2011).

4) Assume that you make a one year, $30 million notational principal, plain vanilla interest rate swap, with the fixed rate leg at 7%, paid quarterly on the basis of 90 days in the quarter, and 360 days in the year. The floating leg of the swap is based on LIBOR, and that the actual LIBOR rate for the preceding 4 quarters is 7.0%, 6.0%. 7.5% and 7.7%.

- a) Calculate the net payments over the life of the swap, and identify who is responsible for making each payment.

**1 ^{st} Quarter: **= $0, LIBOR and fixed rate are the same, hence no particular person will pay the party.

^{2st}** Quarter: **= $75,000, paid by fixed rate payer to the floating rate payer

**3 ^{rd} Quarter:** = $37,500, paid by floating rate payer to the fixed rate payer

**4 ^{th} Quarter:** = $52,500, paid by floating rate payer to the fixed rate payer

The fixed rate payer will pay a total of $75,000 while floating rate payer will pay a total of $90,000. Therefore, the net payment will be $90000-75000) $15,000 to be paid by the floating rate payer to the fixed rate payer.

- b) What happens to the $30 million at the end of the swap?

The $30 million is the notional principal which never changes hands in the transaction. It is just theoretical and no party will pay or receive it; only the interest rate payments will change hands.

5) Find the optimal stock index futures hedge ratio if the portfolio is worth $100,000,000, the beta of the portfolio is 1.15 and the S&P 500 futures price is 2,300 with a multiplier of 250. Show the structure of the hedge.

Appropriate hedge ratio is

N_{f} = −(β_{S}/β_{f})(S/f)

Where,

S = price of spot instrument

F = price of hedging instrument

β_{S} is the beta from the CAPM

β_{f} is the beta of the futures

= 1.15/250)(100,000,000/2300) = 200

6) You hold a portfolio of stocks with a value of $1,000,000. You expect that you will be selling the stocks in the portfolio in one year. You are considering hedging your market risk by using the 1-yr S&P 500 Index Future. The price of the future is currently at 2,000. The multiplier for the future is 250; the margin requirement is 10% of the total futures position.

- a) What side of the futures position will you take? Long or short, and why?

I will take a short hedge because I own an asset I plan to sell later. In case the market falls, the losses in portfolio stocks will be offset by the gain in index future.

- b) What is your initial cash flow?

The dollar value of the index is thus: $250 x 2,000 = $500,000 x 10%= required margin of $50,000

Initial cash flow = $500,000-50,000 = $450,000

- c) If the price of the futures falls to 1,900, what will happen to your margin account?

If the futures price falls to 1,900, the decline in the futures price is 2,000-1,900 = 100.

The decrease in the margin account would be 100 x $250=$25,000.

- d) If, in exactly one year, the futures contract is trading at 1,800 and your stock portfolio has fallen in value by 10%, what will be your overall profit?

The new dollar value of the index is $250 x 1,800 = $450,000

Required margin = 450,000 x 10% = $45,000

The cash flow = 450,000 – $45,000 = $405,000

New value of stock portfolio = $1,000,000 (1-0.01) = $900,000

Overall profit = $900,000-$405,000 = $495,000

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