GMBA 767 Homework ch 21 22 problem
Question # 00022011
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Updated on: 08/04/2014 03:08 PM Due on: 08/27/2014
PROBLEM 10 (a-c)
The treasurer of a middle market, import-export company has approached you for advice on how to best invest some ofthe firm's short-term cash balances. The company, which has been a client of the bank that employs you for a few years,has $250,000 that it is able to commit for a one-year holding period. The treasurer is currently considering two alternatives:
(1) invest all the funds in a one-year U.S. Treasury bill offering a bond equivalent yield of 4.25%; and
(2) invest all the funds in a Swiss government security over the same horizon, locking in the spot and
forward currency exchanges in the FX market. A quick call to the bank's FX desk gives you the
following two-way currency exchange quotes.
Swiss France Per U.S. Dollar Per
U.S. Dollar Swiss Franc (CHF)
Spot 1.5035 0.6651
1-year CHF Futures ------- 0.6586
a. Calculate the one-year bond equivalent yield for the Swiss government security that would support the interest rate parity condition.
b. Assuming the actual yield on a one-year Swiss government bond is 5.50 percent, which strategy would leave the treasurer with the greatest return after one year?
c. Describe the transactions that an arbitrageaur could use to take advantage of this apparent mispricing and calculate what the profit would be for a $250,000 transaction.
Problem
Consider the following questions on the pricing of options on the stock of ARB Inc.,. a. A share of ARB sells for $75 and has a standard deviation of 20 percent. The current risk free rate is 9% and the stock pays two dividends:
(1) $2.00 dividend just prior to the option s expiration date, which is 91 days from now (exactly one-quarter of a year); and (2) a $2.00 dividend 182 days from now (i.e., exactly one-half year). Calculate the Black-Scholes value for a European-style call option with an exercise price of $70.
b. What would be the price of a 91-day European-style put option on ARB Inc., having the same exercise price?
c. Calculate the change in the call option s value that would occur if ARB’s management suddenly decided to suspend dividend payments and this action had no effect on the price of the company s stock?
d. Briefly describe (without calculations) how your answer in Part a would differ under the following separate circumstances: (1) the volatility of ARB stock increases to 30%, and (2) the risk free rate decreases to 8%.
The treasurer of a middle market, import-export company has approached you for advice on how to best invest some ofthe firm's short-term cash balances. The company, which has been a client of the bank that employs you for a few years,has $250,000 that it is able to commit for a one-year holding period. The treasurer is currently considering two alternatives:
(1) invest all the funds in a one-year U.S. Treasury bill offering a bond equivalent yield of 4.25%; and
(2) invest all the funds in a Swiss government security over the same horizon, locking in the spot and
forward currency exchanges in the FX market. A quick call to the bank's FX desk gives you the
following two-way currency exchange quotes.
Swiss France Per U.S. Dollar Per
U.S. Dollar Swiss Franc (CHF)
Spot 1.5035 0.6651
1-year CHF Futures ------- 0.6586
a. Calculate the one-year bond equivalent yield for the Swiss government security that would support the interest rate parity condition.
b. Assuming the actual yield on a one-year Swiss government bond is 5.50 percent, which strategy would leave the treasurer with the greatest return after one year?
c. Describe the transactions that an arbitrageaur could use to take advantage of this apparent mispricing and calculate what the profit would be for a $250,000 transaction.
Problem
Consider the following questions on the pricing of options on the stock of ARB Inc.,. a. A share of ARB sells for $75 and has a standard deviation of 20 percent. The current risk free rate is 9% and the stock pays two dividends:
(1) $2.00 dividend just prior to the option s expiration date, which is 91 days from now (exactly one-quarter of a year); and (2) a $2.00 dividend 182 days from now (i.e., exactly one-half year). Calculate the Black-Scholes value for a European-style call option with an exercise price of $70.
b. What would be the price of a 91-day European-style put option on ARB Inc., having the same exercise price?
c. Calculate the change in the call option s value that would occur if ARB’s management suddenly decided to suspend dividend payments and this action had no effect on the price of the company s stock?
d. Briefly describe (without calculations) how your answer in Part a would differ under the following separate circumstances: (1) the volatility of ARB stock increases to 30%, and (2) the risk free rate decreases to 8%.
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Solution: GMBA 767 Homework ch 21 22 problem