Single Stock Futures and Stock Index Futures
(i) How would you arbitrage?
(ii) On December 29, the market has moved down, and the index value is 5,850. What would be your arbitrage prot?
Solution to Problem 7.20
Step 1: Calculate the theoretical futures value:
F = S × e
(r–d)T
= 6,200 × e
(0.08–0.018)(68/365)
= 6,272.09
Step 2: Find which is overpriced and which is underpriced.
Since the futures price is 6,260 and the theoretical value is 6,272.09, the futures are underpriced and the
index is overpriced relative to each other.
Step 3: Undertake an arbitrage transaction by taking a long position in the underpriced security and a short position
in the overpriced security and the appropriate investment in the risk-free assets. ...