Testing the Futures Leverage Effect with Monthly Returns and Volatility

Summary

The method tests whether negative futures returns are associated with higher subsequent volatility. It recommends using adjusted historical futures prices that account for contract rolls, then calculating a monthly volatility measure from squared daily log returns. For each month, pair that volatility with the previous month’s return, producing observations for a scatter plot and a regression. A negative relationship and a statistically significant regression slope would support the presence of the leverage effect over the sample period.

The answer presents a simple diagnostic, not a definitive causal test. It recommends several years of daily history, but the result can depend on the construction of the continuous contract, the monthly aggregation, and the regression assumptions. It does not specify corrections for serial dependence, changing volatility regimes, or other confounding effects. The procedure therefore offers an exploratory way to assess the relationship and its statistical significance, rather than establishing that falling prices cause volatility to rise.

Key ideas

• Use adjusted continuous futures prices to account for rolling between contracts.
• Calculate monthly volatility from the mean of squared daily log returns, followed by a square root.
• Pair each month’s volatility with the return from the preceding month.
• A negative regression slope indicates an inverse relationship, and its significance can be tested.
• The method is a simple diagnostic whose conclusions depend on data construction and statistical assumptions.

Tags

# The leverage effect for futures contract


# The leverage effect for futures contract












Given the daily price data of equity and government-bond futures contracts, how can I identify the leverage effect (when prices move down, the volatility of prices increases), and see if it is statistically significant on the given time period?

## Answer by nbbo2 (score 1, accepted)

https://quant.stackexchange.com/a/41754

A simple way to show the Leverage Effect (not necessarily the only way) is:

Collect daily futures price data for at least 5 years. Use Adjusted historical data (sometimes called continuous contract data), which incorporates the effect of changing or rolling from one futures contract to the next.

For each calendar month in the period compute two numbers:

- The daily volatility for this month, which is the square root of average value of $(\ln(P_t/P_{t-1}))^2$ for t ranging over all days of the month. (This will be the average of about 20 numbers, since there are about 20 (or 21) trading days each month.)

- The return in the prior month. For example if the current month is June, then the prior month is May so we would compute the return from the last trading day of April to the last trading day of May.

Plot these 60 (or more) pairs of numbers, with prior month return on the x axis and volatility on the y axis. There should be a negative (downward sloping) relationship visible. Fit a regression line and test whether the slope of the regression line is significant.

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This summary was written by Stratmill's research agent from the original; it is not a copy of the source.