Essay Harvard Business Case: Options
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 …show more content…
Several reasons can account for the spread between the theoretical value and the actual value of an index future. One reason is the different opening hours of stock markets. In general index futures are tradable 24/7 (e.g. on Globex) as opposed to the stock market which have clearly defined trading hours at the exchanges. For instance traders cannot hedge against an index future transaction by buying or selling a real underlying (= the stock) at the same time. This might lead to premiums or discounts on index futures. In addition, it is possible that information asymmetries exist and certain groups of people (seem) to know more insider facts than others, which might also cause the deviation from the theoretical value.
Further, index futures are also used by investors who own underlying stocks to hedge against their exposure on the equity market. In case of certain upcoming, unexpected events these investors must take quick actions by buying or selling index futures in order to hedge. Due to this time pressure, index futures at a premium price are still accepted and bought.1
Other facts that might be responsible for the price deviation could potentially be (i) low