CFA Practice Question

There are 206 practice questions for this study session.

CFA Practice Question

Continue with question 1. Assume a stock price is $55 and in the next year it will either rise by 20% or fall by 16%. The risk-free interest rate is 5%. A call option on this stock has an exercise price of $60. Suppose the call option is selling for $4. Show how to execute an arbitrage transaction that will earn more than the risk-free rate. Use 1000 call options.
Correct Answer: Sell the call and buy the underlying stock.

As the current price is higher than 3.33, it is overpriced. We should sell the call and buy the underlying stock. As n is 0.303 (from question 2), for every option sold we should purchase 0.303 shares of stock.
  • Sell 1000 calls at 4: 4,000
  • Buy 303 shares at 55: -16,665
  • Net cash flow: -12,665
At expiration the value of this combination will be
  • 303 x 66 - 6 x 1000 = 13,998 if ST= 66
  • 303 x 46.2 - 0 x 1000 = 13,998 if ST= 46.2
The rate of return is (13,998 - 12,665)/ 12,665 = 10.53%, which is higher than the risk-free rate of 5%.

User Contributed Comments 8

User Comment
PhiWong Total cash outflow: 55 x 303 + 4 x 1000 = -16,665 + 4000 = -12,665
If St=66, net income = 4 x 1000 + -6 x 1000 + (-55+66) x 303 =1,333.6
If St=46.2, net income = 4 x 1000 + (46.2 - 55) x 303 = 1,333.6
Rate of Return = 1,333.6/(-4 x 1000 + 55 x 303) = 10.53%
PhiWong Total Cash out flow shoud be: -55 x 303 + 4 x 1000 = -12,665
JVAC but what if you don't have 12665 to purchase 303 stocks? you have to borrow @5%. that makes your ROR (1333.6-0.05*12665)/12665= 5.5%
ehc0791 The funding cost should be considered. The cost of 12,665 can be put into bank and make 5% return.
AusPhD Absolutely, but what we have shown is that if you fund this strategy at the risk free rate you make risk free profit.
MonkeySee This is assuming that you have correctly estimated the volatility for the upcoming year. A powerful yet inconvient truth.
mazen1967 the issue here is to gain more than rf
Paulvw I always understood that the arbitrageur would sell the call, buy the underlying stock, AND buy a put of the same strike and borrow the present value of the future strike. This would balance the expensively sold call with the cheaper underlying, earning a profit up front (why would the arbitrageur want to wait around until expiry?) and leaving her in a riskless position where all positions net out at expiry (assuming a central clearing house with no credit risk etc etc). Am I missing something?
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