Question

3. Hikoru Sulu and Nyota Uhura are tired of being bossed around by their egomaniac Captain Therefore, they are studying together for the CFA Level 1 exam in hopes of eventually transferring to the Finance Department within the United Federation of Planets (UFP). They were unable to answer the following questions. Can you help them out? a. The 1F500 stock index pays no dividends. The continuously compounded risk free rate is 5%. The price of a prepaid 2-year forward contract is $2,016.00. What is the 18-month forward price of the IF500 stock index? b. The RP3000 stock index has a current price of $1,898.60. The two-year forward price of the index is $2,016.00. The continuously compounded risk-free rate is 5%. The stock index pays dividends continuously at a rate of 6 per year. Determine 6.

Answer 1

3a. The formula to calculate the forward price of a stock after t years given the risk free rate r and no dividend payment is as follows:

Forward price    = Spot price * e^(rt)

Given forward price for 2 years IF500 stock index is $2016, the spot rate of the index can be calculated as follows:

2016 = Spot price * e ^ (5%*2)   = Spot price * e ^(0.1)

Thus, spot price                                = 2016 / e^(0.1)                                =2016/1.105171                =1824.152

Thus, the 18 month forward contract on the same index is given as below:

Forward price    = 1824.152 * e ^ (5%*1.5)             = 1824.152 * e ^(0.075) =             1824.152*1.077884

                                = 1966.225

Thus, 18 month forward on the index will be priced at $1,966.23

Note – e to the power x can be calculated either using excel function EXP(number) (number is the raised to number) or a financial calculator

3b. The formula to calculate the forward price of a stock after t years given the risk free rate r and continuous dividend payment δ is as follows:

Forward price    = Spot price * e^[(r- δ )*t]

Using the above formula and the given information,

2016 = 1898.6 * e^ [ (5% - δ)*2]

1.0618 = e^ [ (5% - δ)*2]

Taking natural log ln on both sides, we get the equation,

(5% - δ)*2 *ln e = ln 1.01618

Ln e =1 and ln 1.01618 = 0.01605

Thus, (5% - δ)*2 = 0.01605

5% - δ = 0.008025

δ = 0.05 - 0.008025 =0.041975 =4.2%

δ = 4.2%