Past Rolling Hills to Smoother Pastures
Often when analyzing the historical volatility of future contracts, it is useful to look at continuity symbols. For these synthetic symbols the price on each day represents the price of the nth expiring future. Using this to construct a time series, an issue arises when a future expires. On the day following the expiry of the next future, the price for the continuity time series comes from a new future. As such the return between the current day and previous day’s prices represents the return between two different contracts.
In any contract, this causes a problem, but this is especially evident for seasonal commodities where the spread between consecutive future prices is large. The realized historical volatility of futures is overstated as the roll contributes significantly to the volatility of the continuity time series. The solution to eliminate this is elegant in its simplicity. Whenever analyzing the returns in the time series, replace each return on the first day using a new contract, with the actual return of the new contract. In this way one can effectively construct a synthetic time series containing adjusted returns, where on any given day, the return represents the return of the actual nth expiring future, rather than the price. This has the effect that when the future rolls, it resets the cost basis so all returns are reflected in the same basis.
Lean Hog Front Month
– Adjusted Returns in Red / Unadjusted in Blue
The effect is stark. Note that significant jumps in the blue time series due to the rolling of contracts have been adjusted (most significant roll dates circled), while the actual fluctuations in price remain represented. This provides more consistent and accurate realized volatility calculations and accurate correlations between continuity symbols.
Front month correlation with underlying index, .SSMI
– Adjusted on left / Unadjusted on right
In addition to viewing position-by-position results and portfolio totals, you can aggregate positions by parameters such as Industry or Currency to display meaningful breakdowns of the stress-test results.
Effect on Holding VaR
Imagine stores the adjusted continuity time series using specific symbols, with three years of price data available at any time. These follow the Refinitiv continuity symbol format with a “-S” suffix. E.g. CLc1-S represents the adjusted returns for CLc1. The prices are constructed by taking the current day value to be the current unadjusted price, calculating the adjusted returns, then working backwards to construct the rest of the time series. This creates a consistent time series which is maintained daily, with the entire time series being refreshed on the first day of a new expiry.
These symbols are used in Imagine’s RCYS extension roll curves. At present approximately 700 of Imagine’s roll curves are using these adjusted returns. To understand whether a roll curve is using adjusted returns, one can look for the “–S” suffix to the symbols in the “Risk Symbol” column of the roll curve.
Adjusted Risk Factor Roll Curve:
Unadjusted Risk Factor Roll Curve:
The examples described in this blog post illustrate one possible scenario and are intended to be used in general as guidance towards risk management of market events.
Please contact Consulting or your Imagine representative for help with constructing your own scenario analysis.
When newcomers to the field of quantitative finance are assigned the task of writing up an analysis, they will often show numbers using five, six or even more digits to the right of the decimal point. This may be driven by the part of the brain that craves precision and exactness. Given the unstable nature of financial data, does that mean it is a fool’s errand to try to estimate risk?