Forward rate FX agreements and options.

1. Unit 8 Foreign Exchange and Contingent Risk

2. Pricing forward FX rates Calculate the forward rate one might obtain to convert £/Euro in 6 months time. The spot rate today is £1= euro 1.4286 Interest rates for 6 months are 7% pa in the UK and 4% pa in the euro zone.

3. Pricing forward FX rates The spot rate today is £1= euro 1.4286. Interest rates for 6 months are 7% pa in the UK and 4% pa in the euro zone . You wish to convert £ to euro Borrow Euro1 You accrue Euro1x 4% x 6/12 = 0.02 So you need E1.02

4. Pricing forward FX rates The spot rate today is £1= euro 1.4286. Interest rates for 6 months are 7% pa in the UK and 4% pa in the euro zone . You wish to convert £ to euro Borrow Euro1 You accrue Euro1x 4% x 6/12 = 0.02 So you need E1.02 Converts to £ 0.7000 This earns £0.7x7%x6/12 = 0.0245 So you have £0.7245

5. Pricing forward FX rates The spot rate today is £1= euro 1.4286. Interest rates for 6 months are 7% pa in the UK and 4% pa in the euro zone . You wish to convert £ to euro Borrow Euro1 You accrue Euro1x 4% x 6/12 = 0.02 So you need E1.02 Converts to £ 0.7000 This earns £0.7x7%x6/12 = 0.0245 So you have £0.7245 So the conversion rate needs to be £0.7245 = E 1.02 or, £1 = 1.02/0.7245 = Euro 1.4079

6. Pricing forward FX rates – Why does this have to happen? Let us assume that the forward rate is not £1=E 1.4070 but £1 = E1.38 Borrow £1 You accrue £1x 7% x 6/12 = 0.035 So you need £1.035 Converts to Eu 1.4286 This earns EU 1.4286x4%x6/12 = 0.0286 So you have Eu 1.4572

7. Pricing forward FX rates – Why does this have to happen? Let us assume that the forward rate is not £1=E 1.4070 but £1 = E1.38 Borrow £1 You accrue £1x 7% x 6/12 = 0.035 So you need £1.035 Converts to Eu 1.4286 This earns EU 1.4286x4%x6/12 = 0.0286 So you have Eu 1.4572 So you convert your E 1.4572 @ 1.38 = £1.0559. Pay off your loan you have a profit of 1.0559-1.035 = £0.0209. For doing nothing – arbitrage prevents this. There would be large demand on borrowing sterling so sterling rates would rise. At the same time there would be increased demand for euro deposits, so euro deposit rates would drop. This would continue until the relative rates remove the risk-free profit.

8. Options There are two main types of options: A call option is an option to buy the underlying commodity (shares, interest rates, pork bellies etc) A put option is an option to sell the underlying commodity

9. Options You can buy either a call or put option. You can later decide to sell the option to someone else, when your involvement is at an end. The person who acts on your option is called the writer.

10. Options Options give the owner a right to exercise. This right has value and so therefore does the option. The price of an option is called the premium. Futures are “free” as there is no “right” – both the seller and buyer have entered a commitment to each other – with options only the writer has a commitment.

11. Options Options give the owner a right to exercise. This right has value and so therefore does the option. The price of an option is called the premium. Futures are “free” as there is no “right” – both the seller and buyer have entered a commitment to each other – with options only the writer has a commitment. If you exercise a call option the writer must sell you the product at the agreed price (the exercise or strike price). If you exercise a put option the writer must buy from you the product at the strike price.

12. Options – Payoff Diagrams You buy a call option for 10p on MBA plc shares, just about to expiry. The strike price is £2. The shares are trading today (spot) at £1.30 First map a table showing the profit/losses for the share price going from , 50p (say) to £4.50. What if the market price (spot) is £1.50? £3.5? £2.05? Would you exercise yes or no? What is your profit or loss?

13. Options – Payoff Diagrams You buy a call option for 10p on MBA plc shares, with just aboutto expiry. The strike price is £2. The shares are trading today at £1.30 First map a table showing the profit/losses for the share price going from , 50p (say) to £4.50. Then draw the graph of profit vs share price

14. Options – Payoff Diagrams

15. Options – payoff diagrams You buy a naked put option for MBA plc. The premium was 10p. The strike price is £2. Draw the payoff diagram. (would you exercise at £2.50? £1.50? £1.95?)

16. Options – payoff diagrams

17. Options – example Edward owns 1,000 shares in MK plc which he bought today for £4.07. He wants to hedge his portfolio against falling prices. The following options are available. Type Call Put Strike price £4.20 £4.20 Premium 13.6p 20.2p (one option for one share) Advise Edward as to which type of option to buy. Show the payoff diagram

18. Options – example Edward owns 1,000 shares in MK plc which he bought today for £4.07. He wants to hedge his portfolio against falling prices. The following options are available. Type Call Put Strike price £4.20 £4.20 Premium 13.6p 20.2p (one option for one share) He wishes to be able to sell his portfolio for a given price. So he must buy put options. If the spot price is £4.50 he will not exercise his option. So he will sell his shares at £4.50 making a profit of 1,000 x (4.50-4.07) = £430. He will have spent 1,000 x 20.2p buying options = £202, an overall profit of £228.

19. Options – example Edward owns 1,000 shares in MK plc which he bought today for £4.07. He wants to hedge his portfolio against falling prices. The following options are available. Type Call Put Strike price £4.20 £4.20 Premium 13.6p 20.2p (one option for one share) He wishes to be able to sell his portfolio for a given price. So he must buy put options. If the spot price is £4.50 he will not exercise his option. So he will sell his shares at £4.50 making a profit of 1,000 x (4.50-4.07) = £430. He will have spent 1,000 x 20.2p buying options = £202, an overall profit of £228. If the spot is £3.50 he will exercise his option making 1,000 x (4.20-3.50) = £700 less the option cost (£202) = £498. He will sell his original shares for £3.5 (less purchase price £4.07) giving a loss of £570. An overall loss of £72 (= 4.2-4.07-.202 x 1000). [Without the options he would have lost 4.07-3.5 x 1000 = £570.]

20. Options example

21. Options – example A call option has a strike price of £2. The premium is 15p. Draw the payoff diagram of the writer.

22. Options – example A call option has a strike price of £2. The premium is 15p. Draw the payoff diagram of the writer.

23. Options – example So recall the graphs. A buyer of a call option can make unlimited profits. A writer (of either option) has a capped profit. Buyer of a naked put option Buyer of a call option (or put with share) Writer of a put option Writer of a call option