- CFA Exams
- CFA Level I Exam
- Study Session 14. Derivatives
- Reading 37. Pricing and Valuation of Forward Commitments
- Subject 3. Equity Forward and Futures Contracts

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**CFA Practice Question**

A portfolio manager took a long position on a 180-day forward contract on the S&P 500 stock index 30 days ago. The no-arbitrage forward price was $1263.87. The index was at $1245. Now (30 days later) the index is still at $1245. Suppose that the continuously compounded dividend yield is 1.45%, and the discrete risk-free rate is 4.6%. neither of these two rates have changed since the contract initiation date. What is the current value of the forward contract?

A. $0, since the index price and two rates are still the same.

B. -$3.11

C. $3.72

**Explanation:**

*r*= ln(1 + r) = ln(1 + 0.046) = 0.045

V

_{t}(0, T) = Vt(0, T) = S

_{t}e

^{-δ(T-t)}- F(0, T) e

^{-r(T - t)}= 1245 x e

^{-0.0145 x (150/365)}- 1263.87 e

^{-0.045 x (150/365)}) = -$3.11

This is a loss to the long position.

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**User Contributed Comments**
8

User |
Comment |
---|---|

danlan2 |
Discret risk-free rate is 4.6%, so continuous risk-free rate is ln1.046=0.045 |

danlan2 |
Dividend yield and risk-free rate are different, so we use both rates. |

danlan2 |
We use dividend yield for index and risk-free rate for forward price. |

frankal101 |
In 30 days the index value must be at least 1245e^(0.046-0.0145)(30/365) (number bigger than 1245). Since it is the same, the return must be negative... |

MonkeySee |
No calculation is needed in this case. Since the situation shows an asset price that has appreciated at a rate of less then the risk free rate, we know it is a loss for the long. Only one answer is negative and therefore is correct. |

broadex |
Why do we discount the index since its the current price? The forward price is 150 days fro m now hence we need to discount by 150 days. |

DCPWS |
Current price includes value of dividends. These must be discounted out since they do not accrue to the holder of the futures. |

DevanCFA |
RFR is higher than div yield and the index hasnt increased, so it will be a neagtive value. is it not that simple? |