GOAL RISK KEEPER Considering all (long-dated) options – how to stay invested

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GOAL RISK KEEPER Considering all (long-dated) options – how to stay invested

Goldman Sachs GOAL Risk Keeper

Why and which long-dated calls - drivers of convexity and performance

The performance of long-dated call options is driven by several distinct forces.

Breaking the total return into components helps clarify how the choice of expiry and

moneyness affects performance and in which regimes long-dated calls are more likely to

outperform a simple equity investment.

We can decompose the total performance of the strategy (buying call options on the

S&P 500, with the remaining cash invested in T-bills) into five components:

1. ‘Starting delta‘ (initial market exposure): the P&L from holding a fixed position in

the S&P 500 equal to the option’s delta at the moment of purchase. This isolates the

return you would have earned if the exposure never changed.

2. ‘Path delta‘ (changing exposure over time): the additional P&L generated because

the option’s delta moves over its life. As the market rallies, the delta of the strategy

rises, increasing its exposure to equity price moves (and vice versa as prices trend

down).

3. ‘Vega‘ (sensitivity to implied volatility): the P&L from changes in the option’s

implied volatility, holding other factors constant.

4. ‘Option carry‘ (time decay net of realized volatility): the P&L from changes in the

option’s value that remains after stripping out the delta and vega contributions

above. This captures the option’s theta, gamma, and higher-order sensitivities.

5. ‘Funding‘ (cost of leverage plus cash return): the P&L of being long an equity

forward (sized to the initial option delta) plus the return earned on the T-bills held in

the portfolio, minus the total return on the equivalent S&P 500 position. This