Finance 475

Solutions to Problem Set #9

1)      You are expecting revenues of Y100,000 in one month that you will need to covert to dollars.  You could hedge this in forward markets by taking long positions in US dollars (short positions in Japanese Yen).  By locking in your price at \$1 = Y105, your dollar revenues are guaranteed to be

Y100,000/ 105 = \$952

On the other hand, you can wait and use the spot markets.

 Exchange Rate Probability Revenue w/ out Hedge Revenue  with Hedge Value of Hedge 90 Y/\$ 2% \$1,111 \$952 -\$159 95 Y/\$ 25% \$1,052 \$952 -\$100 100 Y/\$ 45% \$1,000 \$952 -\$48 105 Y/\$ 20% \$952 \$952 \$0 110 Y/\$ 8% \$909 \$952 \$43

Expected Value = (.02)(-159) + (.25)(-100) + (.45)(-48) + (.20)(0) + (.08)(43) = -\$46.34

You could replicate this hedge by using the following:

a) Borrow in Japan

b) convert the Yen to dollars

c) invest the dollars in the US

d) Pay back the loan when you receive the Y100,000

2) We need to solve the problem in two regions:

For e > \$1.80, the call option has value

For e < \$1.80, the call option is worthless

For e > \$1.80,

Cost with call option = \$1.80 + \$.04 = \$1.84

Cost With Partial Hedge = (1/3)(\$1.80) + (2/3)(e)

\$1.84 > (1/3)(\$1.80) + (2/3)(e)

e < \$1.86

For e < \$1.80,

Cost with call option =e + \$.04

Cost With Partial Hedge = (1/3)(\$1.80) + (2/3)(e)

e + \$.04 > (1/3)(\$1.80) + (2/3)(e)

e > \$1.68

3) A straddle hedge involves buy both a put ad a call option.  The advantage is that it protects you from both currency appreciations and depreciations.  The disadvantage is that it is generally a pretty expensive strategy (it involves buying two contracts).

4) You could cover this with a bullish spread.  That is, buy a call option with a strike price of 8 pesos per dollar and sell a call option at a strike price of 10 pesos per dollar.  You will only be hedged for the range from 8 to 10 pesos per dollar, but the revenues from the call sale will cover the call purchase.

5) The cost of Euros with the call will be the strike price plus the premium.  Therefore, the spot rate would have to rise by at least the value of the premium for the call option to be valuable.