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Harvard Business Case: Options

In: Business and Management

Submitted By snehalss8
Words 1074
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Question 1: What is the theoretical price of the MMI March ’86 futures contract?

To calculate the theoretical price of the MMI March ‘86 futures contract, we applied the formula:
F(t,T) = S(t) * Exp(r(T-t) - y)
Here, we assume 23 days from February 26 to March 21 and used 23 days as “t to T”. We used dividend yield (3.41/1374.5 = 0.25%) as y, the cash index $311.74 as S(t), and one month treasury 6.8% as r. According to our calculation, the theoretical price will be $ 312.30.

Question 2: Assume that Jim is subject to a $5,000,000 position limit. What position should he take to exploit the mispricing for the March '86 MMI futures?

In order to decide which position Jim should take to earn a profit, we have to compare the theoretical futures price with the actual futures price. In order to make a profit, one has to "buy low, sell high". As Ft(t,T) = $312.30 < Fa(t,T) = $313.55 Jim should short March'86 MMI futures contracts. Thereby, he can buy them at the theoretical price of $312.30 and sell them at $313.55.
To short the futures, Jim has to buy the underlying. Therefore, he has to invest some money. Part of it will be the company’s own funds; the major part comes from borrowed funds. Jim can have a total position of $5,000,000. Jim has the restriction that 10% of this amount must be kept as margin. Therefore, he would borrow $4,999,516.42 from the bank at a borrowing rate of 8%. The cost of capital for company funds is expected to be higher. However, as this number is not explicitly given in the case, we assume that it is 8% too.
The total price for the index is adjusted by a mark-up of 0.0025% for a round-trip impact. As he cannot buy partial stocks, he will only make use of $4,999,516.42 (see Figure 1). Jim will use this amount to buy 3628 shares of the index (more precise, shares of each component stock) on February 26th. Moreover, he shorts…...

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