The calls earned Bobby a total of $700, while the stock lost $300. Of
course, with this type of trade, it is not relevant which leg was a winner and
which a loser. All that matters is the bottom line. The net P&(L) on the trade
was a gain of $400. The gain in this case was mostly a product of IV’s
rising. Exhibit 12.10 shows the P&(L) per greek.
EXHIBIT 12.10 Profit breakdown by greek.
Delta
The position began long 0.20 deltas. The 0.30-point rise earned Bobby a
0.06 point gain in delta per contract.
Gamma
Bobby had an initial gamma of +1.8. We will use 1.8 for estimating the P&
(L) in this example, assuming gamma remained constant. A 0.30 rise in the
stock price multiplied by the 1.8 gamma means that with the stock at $50,
Bobby was long an additional 0.54 deltas. We can estimate that over the
course of the 0.30 rise in the stock price, Bobby was long an average of
0.27 (0.54 ÷ 2). His P&(L) due to gamma, therefore, is a gain of about 0.08
(0.27 × 0.30).
Theta
Bobby held this trade for three days. His total theta cost him 1.92 or $192.
Vega
The biggest contribution to Bobby’s profit on this trade was made by the
spike in IV. He bought 30 volatility and sold 35 volatility. His 1.20 position
vega earned him 6.00, or $600.