Table 10-4 compares two bullish strategies in two market scenarios.Rows 1, 2, and 3 contain the assumptions about the stock price, the days to expiration, and the level of implied volatility,and rows 4 and 5 contain the prices of the 70 Call and the 70–75 call spread. The price of the 70–75 call spread is calculated by subtracting the price of the 75 Call from the price of the 70 Call. To avoid confusion, the price of the 75 Call is not shown.Column 1 contains the initial market assumptions and the initial prices.
The initial stock price is $70.00, there are 35 days to expiration, and the implied volatility is 31 percent.Columns 2 and 3 in Table 10-4 show the estimated option prices and profit of the first scenario in which the stock price rises to 73.50 (row 1),three weeks pass, leaving 14 days remaining to expiration (row 2), but the implied volatility remains unchanged at 31 percent (row 3).
In this scenario, the 70 Call rises in price to 4.11 for a profit of 1.29 (row 4), and the 70–75 call spread rises to 2.92 for a profit of 1.12 (row 5). In the second scenario, the stock price (73.50) and time to expiration (14 days) are the same as in scenario 1, but the implied volatility has declined to 24 percent. This scenario is presented in columns 4 and 5 of Table 10-4. The 70 Call rises in price to 3.85 for a profit of 1.03, and the 70–75 call spread rises to 3.05 for a profit of 1.25. In this scenario, the profit from the 70–75 call spread increases by 0.13, whereas the profit of the 70 Call declines by 0.26.
Profits from these two strategies change because implied volatility decreases—this is the only difference between the two scenarios. Table 10-4 demonstrates that vertical spreads sometimes can perform better in an environment of declining implied volatility than outright long options.Any calculation of position risks is only a snapshot that catches the situation at one stock price and at one point in time. Position risks change if stock price, time, or implied volatility change, as they inevitably will. In Table 10-3, the stock price is 70, so the 70 Call is at the money, and the 75 Call is out of the money.
The Greeks of the 70 Call therefore are larger, in absolute terms, than the Greeks of the 75 Call.Table 10-5 calculates position risks of the 20 long 70–75 call vertical spreads assuming a stock price of 75, at which point the 70 Call is in the money and the 75 Call is at the money.A comparison of Table 10-5 with Table 10-3 reveals how—and by how much—the Greeks change when the stock price is 75 versus 70.With the stock price at 70, the 20 long 70–75 call vertical spreads have a position delta of 546, a positive gamma, a positive vega, and a negative theta.
With a stock price of 75, the position delta is 512,which is lower than with the stock price at 70. The gamma is now negative,and the vega also has changed from positive to negative. The theta, however, is now positive rather than negative.The message of Table 10-5 is that a stock price rise of $5.00 causes the position risks to reverse completely. The position delta now will change in the opposite direction from the change in price of the underlying stock.
The position now will be hurt if implied volatility rises and helped if it declines. Finally, the passing of time now will help this position.The difference in position Greeks caused by the rise in stock price from 70 to 75 means that the strategy’s primary source of profit has changed. When the stock price is 70 (see Table 10-3), a bull call spread is a bullish strategy that profits primarily from a stock-price rise and is hurt by the passing of time.
When the stock price is 75 (see Table 10-5), however, a bull call spread is more of a neutral strategy; it still has a positive delta, but now the position will profit from time decay.The change in position risks from Table 10-3 to Table 10-5 is only one example of how position risks change. Given the interaction of the changing Greeks of long and short options, it is not always easy to anticipate how position risks will change as market conditions change.
Traders must continuously update their risk analysis of positions because those risks can change in unanticipated ways.Changing Risks Graphed:The position risks of 20 of the 70–75 bull call spreads are illustrated in Figures 10-1 through 10-5. In all these figures, the straight line graphs risk at expiration, and the curved lines represent the risk at 35 and 17 days to expiration. It can be difficult determining which curved line is 35 days and which is 17 days because they cross, so attention to detail is important. Figure 10-1 graphs position value against stock price (underlying).