COMMENTAR Y
This shows that all else equal, the stronger the persistence in the roll adjustment, the stronger the persistence in the futures return. Therefore, Equation 10 makes clear that trend following has a strong connection to the behaviour of the roll adjustment. In fact, our previous white paper4 showed that nearly half of the cumulative performance of a trend-following strategy was attributable to roll yield.
“The long-term persistence across multiple roll days suggests that roll yield is more predictable than spot price.”
Implications for carry strategies It would be nice if we could get direct exposure to the roll adjustment due to its high persistence, but it does not represent the return of any instrument. However, what if the price change of the front contract (the “noisy” part) averaged out to zero over time? Then, Equation 2 gives:
EQUATION 11: Futures Return Over Life of Trade ≈ Roll Adjustment over life of Trade
We want to emphasise that this holds only if the front contract price change is small compared to the roll adjustment. Nevertheless, it immediately suggests an actionable trading strategy, called the “Carry” trade:
Under certain conditions, the roll adjustment contains information about expected profit. If the sign and magnitude of the roll adjustment are not expected to change quickly, then we can use today’s roll adjustment as an estimate going forward. Thus, using Equation 11, we can write:
EQUATION 12: Futures Return Over Life of Trade ≈ Today’s Roll Adjustment * Time in Trade
We can exploit this by going long markets for which the roll adjustment is positive (i.e., backwardated) and short markets for which the roll adjustment is negative (i.e., in contango).
We are not claiming that we are obtaining direct exposure to the roll adjustment. But under a specific set of assumptions, the roll adjustment can behave like a ‘real’ P&L in a sense captured by Equation 11.
The carry trade is not riskless, however. Let’s revisit Equation 12, putting back in the spot return:
EQUATION 13: Futures Return ≈ Spot Return + Today’s Roll Adjustment * Time
As long as the roll adjustment exceeds any adverse moves in the spot, the carry trade will be
Fig.3 Decomposition of joined price – spot, basis and roll adjustment contributions The Joined Price is equivalent to the Basis + Cumulative Roll Adjustment + Spot Price
10 15 20 25
-10 -5 0 5
0 Spot Price Basis Front Price Cumulative Roll Adjustment Joined Price
profitable. Thus we can think of the roll adjustment as a “buffer” against adverse spot price moves.
Furthermore, Equation 13 shows that risk-adjusted performance of a carry strategy will depend on the relative magnitude of the roll adjustment versus volatility of spot moves. Therefore, performance can be improved by reducing the impact of adverse spot price movements in a way that does not significantly degrade the roll adjustment.
Equation 13 and the subsequent discussion provide a framework to develop ‘enhanced’ carry strategies through the prediction and mitigation of adverse spot price moves. THFJ
NOTES
1. In saying that the futures price converges to the spot price at expiration, we are somewhat idealising things; each sector has its own idiosyncrasies that make this statement inexact.
2. For simplicity, we say that one contract corresponds to one unit of the S&P 500 index. The actual e-Mini contract gives exposure to 50 units of the underlying index.
3. To simplify the discussion, we assume that all trades are done without commissions, slippage, or other transaction costs.
4. ‘Prospects for CTAs in a Rising Rate Environment’, Campbell White Paper Series, January 2013.
Source: Campbell & Company
The roll adjustment is calculated to exactly offset this artificial price jump
On roll dates, the basis 'jumps' downward since deferred price < front price 5 10 15 20 25
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