On September 13, 2009, the S&P 500 Index futures settlement price was 1016.70 fo
ID: 2815695 • Letter: O
Question
On September 13, 2009, the S&P 500 Index futures settlement price was 1016.70 for December 2009 delivery contract. The actual S&P 500 index (spot market) was closed at 1003.35 on 09/13/2009. The dividend yield is estimated currently at 2.12% (source: http://www.indexarb.com/dividendAnalysis.html). The actual delivery date of the December contract is 12/19/2009. The LIBLOR rate is 3.675% on September 13, 2009, which can be treated as a risk-free rate. Asssume the dividend yield and LIBOR rate are continously compounded.rates. Use the actual/360 day count method.
A) Are the futures price and the spot index in equilibrium? That is, is there an arbitrage opportuity between the futures market and the spot market? What is the basis for your answer?
B) Show the steps to find any arbitrage profit opportunity. Calculate the arbitrage profit which should be zero if the market is in equilbrium, positive if not. Be sure to show your calculations step by step.
S0= 1,003.35 9/13/2009 T= 97 days 12/19/2009 f(0,T)= 1,016.70 Rf= 3.675% DivYld 2.120%Explanation / Answer
Soln : Step 1 : We have to calculate the price as per the risk free rate and spot price with interest compounding is continuous.
Forward price = , F = S * e(r-q)*t
Here, S = spot price = 1003.35, r = risk free rate = 3.675%, q = dividend yield = 2.12% , t = time to maturity = 97 days = 97/360 = 0.269
F = 1003.35 *e(3.675%-2.12%)*0.269 = 1007.56
Step 2 : Forward price of index given, V = 1016.70
We can see that V> F , as this induced an arbitrage opportunity here. As we can see that with the market forces , price is lower than the price provided by buyers in the market.
(b) We can sell these forward contracts and at the time of delivery when price will become in equilibirium, buying these contracts at spot and complete the contract to deliver at 1016.70
Net profit = 1016.70 - 1007.56 = $9.14
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