Dynamic Arbitrage II
In the last commentary (October 5, 1999) we considered a stock selling for $50 a share and a call option on the stock with strike price 50, expiration 30 days away, value $5 and asking price $2. At a purchase price of $2, this call is underpriced and perhaps appeared in one of the underpriced lists on the site. I suggested that this was an arbitrage situation, since the call is underpriced relative to the stock, and the natural inclination is to buy the call and sell the stock.
Before modern communications, it was not uncommon to find a stock, say IBM, selling for one price on one exchange and another price on another. For instance, the NYSE ask for IBM might be 34 1/8 and the bid at the Pacific Stock Exchange in San Francisco might be 34 3/8. So if you acted quickly, you could purchase IBM for 34 1/8 in New York and simultaneously sell it to the bidder in San Francisco for 34 3/8, locking in a profit of 2/8. You merely has to act quickly and make certain that you bought and sold the same number of shares of stock.
Even as late as the 1970s, there were arbitrage firms that made a decent living by finding situations like this. In fact, Joe Ritchie of CRT started out in this business doing precisely this kind of arbitrage between the Chicago and New York silver markets, graduating later to options arbitrage. The simultaneous purchase and sale of an item is called “riskless arbitrage,” because any risk of adverse movement in the stock is factored, or hedged, out.
P>You can consider the option opportunity to be an arbitrage situation, and deal with it in the same way, purchasing the underpriced item, the call, and selling the overpriced item, the stock. However, as in riskless arbitrage you have to make certain that you are purchasing and selling the quantity of each.
The delta of the option tells you how the option will move with changes in the stock price. A delta of 50 tells you that the option behaves like 50 shares of the stock. So to purchase the equivalent of 100 shares of the stock, you have to purchase two of the calls.
This position, long two calls and short 100 shares of the stock, is a spread, but it is a special kind of spread: it is a delta neutral spread. It is an arbitrage, but it is different from a riskless arbitrage. Small movements in the stock price will be met with offsetting movements in the option value, and so the value of the position will change little, and the risk is low but the arbitrage is not riskless. Larger movements in the stock price will cause the delta to change, and the position will have to be adjusted to maintain neutrality.
More on this next time.