Essay on Harvard Business Case: Options

1071 Words Nov 24th, 2014 5 Pages
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
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To calculate the return at T, several calculations have to be performed. The following formula is applied to calculate the future value of the loan taken, in other words, what Jim has to buy back at T:
〖FV〗_l (T)=〖PV〗_l (t)e^r(T-t) with 〖PV〗_l (t) = $4,999,516.42 (90% of totally used money), rl = 8%, and T-t = 23/365. This results in 〖FV〗_l (T) $5,024,783.10 which Jim has to pay back to the bank. The same formula can be applied to calculate the expected future value of the own funds with 〖FV〗_o (T) = $502,478.31 (it also assumes r = 8% interest). The underlying stock which Jim bought at t can be sold for S(T) at March 21st. As Jim bought the underlying he will also receive dividends worth $12,371.48. With regard to the short futures, Jim has to buy shares at S(T) which he then can sell at a price of $5,016,800.00 (see Figure 2).

Question 3: What rate of return can Jim expect to earn on his position?

As shown by Figure 2, the total return from these transactions will be $1861.72. Based on the input of own funds, the total annualized return on that transaction would be 6.076%. Figure 3 shows in addition the return on the overall employed funds.

Question 4: Who, in addition to security dealers, would you expect to engage in index-futures arbitrage?

Besides dealers, following people engage in index future arbitrage for a variety of reasons: Speculators Institutional Investors High frequency traders Investors that have the…