- CFA Exams
- CFA Level I Exam
- Study Session 16. Derivatives
- Reading 49. Basics of Derivative Pricing and Valuation
- Subject 11. Binomial Valuation of Options

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**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

- 303 x 66 - 6 x 1000 = 13,998 if S
_{T}= 66 - 303 x 46.2 - 0 x 1000 = 13,998 if S
_{T}= 46.2

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**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? |