The delta of a derivatives portfolio measures the sensitivity of the portfolio's value to changes in the underlying asset (in this case, the S&P 500 index). A delta of -2,100 means that for every 1-point increase in the index, the value of the portfolio decreases by $2,100, and for every 1-point decrease in the index, the value of the portfolio increases by $2,100.
To estimate what happens to the value of the portfolio when the index increases from 1,000 to 1,005, we can use the delta and the following formula:
Change in portfolio value = Delta × Change in underlying asset value
In this case, the change in underlying asset value is:
Change in underlying asset value = 1,005 - 1,000 = 5
Substituting the given values, we get:
Change in portfolio value = -2,100 × 5
Change in portfolio value = -10,500
Therefore, when the S&P 500 index increases from 1,000 to 1,005, the value of the derivatives portfolio is to decrease by $10,500.