Implied and Realized Components of the S&P 500 3-month Variance Futures

Because S&P 500 3-month Variance Futures are based on the realized variance of the S&P 500 Index, the price of the front-month contract can be stated as two distinct components: the realized variance and the implied forward variance. CFE will disseminate both of these values at the end of each trading day under the following tickers:

Realized Variance - RUG: An indication of the realized variance of the S&P 500 Index corresponding to the front-month Variance futures contract.

Implied Forward Variance - IUG: An indication of the future variance of the S&P 500 Index that is implied by the daily settlement price of the front-month Variance futures contract

Variance futures contracts are forward starting three-month variance swaps. Once a futures contract reaches front-month status, it enters the three-month window during which realized variance is calculated.

To calculate the variance, sum the daily returns of the S&P 500 from the swap-start date through futures expiration, then annualize the number. Because the daily returns are additive, on any day, it is possible to know both the realized variance since the first day of the swap period (RUG) and the implied variance of the S&P 500 derived from the price of the variance futures contract (IUG).

For example, on March 4, 2005, the front-month Variance futures contract (VT/H5) had 10 business days remaining until settlement. Because the entire three-month swap period encompassed 62 business days, 83% of the contract's settlement value has been realized (RUG). The RUG reported by CFE that evening was 94.97 and the VT/H5 daily settlement price was 99.50. Using the following formula, we can calculate the implied forward variance (IUG) for the remaining ten days.

Where,
VT is the daily settlement price for the front-month Variance futures contract.
RUG is realized variance so far in the life of the contract.
T is the total number of business days in the Variance futures.
t is the number of business days left until options expiration.

Taking the square root of the IUG, one finds the futures price is implying an annualized S&P 500 return standard deviation or volatility of 11.09% over the next ten days.