问答题
4.For a number of years Daikon Co has been using forward rate agreements to manage its exposure to interest rate fluctuations. Recently its chief executive officer (CEO) attended a talk on using exchange-traded derivative products to
manage risks. She wants to find out by how much the extra cost of the borrowing detailed below can be reduced,when using interest rate futures, options on interest rate futures, and a collar on the options, to manage the interest
rate risk. She asks that detailed calculations for each of the three derivative products be provided and a reasoned recommendation to be made.
Daikon Co is expecting to borrow $34,000,000 in five months’ time. It expects to make a full repayment of the borrowed amount in 11 months’ time. Assume it is 1 June 2015 today. Daikon Co can borrow funds at LIBOR plus 70 basis points. LIBOR is currently 3·6%, but Daikon Co expects that interest rates may increase by as much as 80 basis points in five months time.
The following information and quotes from an appropriate exchange are provided on LIBOR-based $ futures and options.
Three-month $ December futures are currently quoted at 95·84. The contract size is $1,000,000, the tick size is 0·01% and the tick value is $25.
Options on three-month $ futures, $1,000,000 contract, tick size 0·01% and tick value $25. Option premiums are in annual %.
Initial assumptions
It can be assumed that settlement for both the futures and options contracts is at the end of the month; that basis diminishes to zero at a constant rate until the contract matures and time intervals can be counted in months; that margin requirements may be ignored; and that if the options are in-the-money, they will exercised at the end of the hedge instead of being sold.
Further issues
In the talk, the CEO was informed of the following issues:
(i) Futures contracts will be marked-to-market daily. The CEO wondered what the impact of this would be if 50 futures contracts were bought at 95·84 on 1 June and 30 futures contracts were sold at 95·61 on 3 June, based on the $ December futures contract given above. The closing settlement prices are given below for four days
Initial assumptions
It can be assumed that settlement for both the futures and options contracts is at the end of the month; that basis diminishes to zero at a constant rate until the contract matures and time intervals can be counted in months; that margin requirements may be ignored; and that if the options are in-the-money, they will exercised at the end of the hedge instead of being sold.
Further issues
In the talk, the CEO was informed of the following issues:
(i) Futures contracts will be marked-to-market daily. The CEO wondered what the impact of this would be if 50 futures contracts were bought at 95·84 on 1 June and 30 futures contracts were sold at 95·61 on 3 June, based on the $ December futures contract given above. The closing settlement prices are given below for four days
问答题
(a) Based on the three hedging choices available to Daikon Co and the initial assumptions given above, draft a response to the chief executive officer’s (CEO) request made in the first paragraph of the question.(15 marks)
【正确答案】Borrowing period is 6 months (11 months – 5 months)
Current borrowing cost = $34,000,000 x 6 months/12 months x 4·3% = $731,000
Borrowing cost if interest rates increase by 80 basis points (0·8%) = $34,000,000 x 6/12 x 5·1% = $867,000
Additional cost = $136,000 [$34,000,000 x 6/12 x 0·8%]
Using futures to hedge
Need to hedge against a rise in interest rates, therefore go short in the futures market.
Borrowing period is 6 months
No. of contracts needed = $34,000,000/ $1,000,000 x 6 months/3 months = 68 contracts.
Basis
Current price (on 1 June 2015) – futures price = total basis
(100 – 3·6) – 95·84 = 0·56
Unexpired basis (at beginning of November) = 2/7 x 0·56 = 0·16
Assume that interest rates increase by 0·8% (80 basis points) to 4·4%
Expected futures price = 100 – 4·4 – 0·16 = 95·44
Gain on the futures market = (95·84 – 95·44) x $25 x 68 = $68,000
Net additional cost = ($136,000 – $68,000) $68,000
Using options on futures to hedge
Need to hedge against a rise in interest rates, therefore buy put options. As before, 68 put option contracts are needed
($34,000,000/$1,000,000 x 6 months/3 months).
Assume that interest rates increase by 0·8% (80 basis points) to 4·4%
(*The put option is exercised, since by exercising the option, the option holder has the right to sell the instrument at 95·50 instead of the market price of 95·44 and gain 6 basis points per contract. The call option is not exercised, since by not exercising the option, the option holder can buy the instrument at a lower market price of 95·44 instead of the higher option exercise price of 96·00)
(*The put option is exercised, since by exercising the option, the option holder has the right to sell the instrument at 95·50 instead of the market price of 95·44 and gain 6 basis points per contract. The call option is not exercised, since by not exercising the option, the option holder can buy the instrument at a lower market price of 95·44 instead of the higher option exercise price of 96·00)
【答案解析】
问答题
(b) Discuss the impact on Daikon Co of each of the three further issues given above. As part of the discussion,include the calculations of the daily impact of the mark-to-market closing prices on the transactions specified by the CEO.(10 marks)
【正确答案】Mark-to-market: Daily settlements
2 June: 8 basis points (95·76 – 95·84) x $25 x 50 contracts = $10,000 loss
3 June: 10 basis points (95·66 – 95·76) x $25 x 50 contracts + 5 basis points (95·61 – 95·66) x $25 x 30 contracts =
$16,250 loss
[Alternatively: 15 basis points (95·61 – 95·76) x $25 x 30 contracts + 10 basis points (95·66 – 95·76) x $25 x 20
contracts = $16,250 loss]
4 June: 8 basis points (95·74 – 95·66) x $25 x 20 contracts = $4,000 profit
Both mark-to-market and margins are used by markets to reduce (eliminate) the risk of non-payment by purchasers of the derivative products if prices move against them.
Mark-to-market closes all the open deals at the end of each day at that day’s settlement price, and opens them again at the start of the following day. The notional profit or loss on the deals is then calculated and the margin account is adjusted accordingly on a daily basis. The impact on Daikon Co is that if losses are made, then the company may have to deposit extra funds with its broker if the margin account falls below the maintenance margin level. This may affect the company’s ability to plan adequately and ensure it has enough funds for other activities. On the other hand, extra cash accruing from the notional profits can be withdrawn from the broker account if needed.
Each time a market-traded derivative product is opened, the purchaser needs to deposit a margin (initial margin) with the broker, which consists of funds to be kept with the broker while the position is open. As stated above, this amount may change daily and would affect Daikon Co’s ability to plan for its cash requirements, but also open positions require that funds are tied up to support these positions and cannot be used for other purposes by the company.
The value of an option prior to expiry consists of time value, and may also consist of intrinsic value if the option is in-the-money. If an option is exercised prior to expiry, Daikon Co will only receive the intrinsic value attached to the option but not the time value. If the option is sold instead, whether it is in-the-money or out-of-money, Daikon Co will receive a higher value for it due to the time value. Unless options have other features, like dividends, attached to them, which are not reflected in the option value, they would not normally be exercised prior to expiry.
【答案解析】