Option Greeks and Stock Prices

The option Greeks indicate current P&L potential of the option portfolio. But identical Greek values may have significantly different impacts on the P&L potentials of portfolios. It depends on the prices of the stocks/indices present in the portfolio. Let's take a look at a SPY and SPX beta-weighted portfolio as an example in part 2 of this series of posts.

Due to the following factors:

• SPX is roughly 10x SPY,
• Delta of one stock is always less than 1 regardless of stock prices
• Gamma is the rate of Delta change per unit price of stock
• Theta is time decay in dollars per day
• Vega is option price change per implied volatility point change

we have the following relationships for SPY/SPX beta-weighted portfolios:

• SPX delta    = SPY delta / 10
• SPX gamma = SPY gamma / 10
• SPX theta    = SPY theta x 10
• SPX vega    = SPY vega x 10

Let's say SPX beta-weighted portfolio has delta of 100, then the equivalent SPY portfolio delta is 1000. If the SPX gamma is 10, the equivalent SPY gamma is 100. If the SPX theta is 40, the equivalent SPY theta is 4 (SPX portfolios offer more theta). If the SPX vega is 150, then the equivalent SPY vega is 15 even if there are similar volatilities between SPX and SPY.

Finally, there is one less trading day for SPX than that of SPY.