Can someone please help me out with the following:
Context
This is about a delta hedge that is “short six month calls on 50,000 shares”
Text
When you look at the graph of a short call, it is evident the hedge will not perform perfectly and should systematically underperform as the down side of the short call position exceeds the upside.
Question
(1) What does under-performance mean? Does it mean that hedge position would always be loss making?
(2) Why does it systematically under-perform? I do not understand the above text.
Underperformance means the hedge will not fully match the change in price of the underlying, creating a loss on the hedged position. It is because shorting options means shorting convexity (gamma). Like for a bond, convexity diminishes price drops if rates increase and amplifies price increases if rates decrease. The shape of the short call payoff diagram shows that the price change is indeed convex and not linear (prior to expiration). If the underlying increases by 10% the call may increase by more than that due to convexity which is a loss for the short.
Another way to think of it is that rebalancing a delta hedged position means you’ll be buying high and selling low (a losing strategy). If you’ve shorted calls and the underlying increases in value and the delta on your short calls have increased as well you will have to buy more shares to delta hedge. Same if underlying decreases you need to lower the delta of your hedge by selling shares at a lower price.