16 – M4 L3b 16 IVol Arbitrage Risk V3

Not all arbitrage opportunities are created equal. If you found two similar stocks with similar mispricing, all else being equal, you’d prefer to act on the stock that is less risky. For example, let’s imagine we have identified through a model in which we have high confidence two stocks, A and B, which are each undervalued by 10 percent. However, stock B typically fluctuates two times as much as stock A. If we’re limited to our capital deployment, which is how much cash we can invest, and we can only choose one stock, we would likely choose to buy stock A since our expected Sharpe ratio will be much higher. Remember, in neither case are we guaranteed to make money, we just have a model in which we have high confidence. Now take this example and think of the universal effect. All savvy arbitragers like us, would prefer stock A, and the opportunity in stock A might get arbitraged away before we even have a chance to buy the stock. If that’s true, then in fact, we may be better off trying to capture the discount in stock B as there will be less competition to capture the opportunity presented there. That’s the gist of this paper. The risk that acting on an arbitraged opportunity may actually yield a loss is called arbitrage risk. As you may have guessed from the example, one source of arbitrage risk is the volatility of the stock, defined as the standard deviation of returns.