# Continuous returns for negative roll-adjusted futures data

I've generated roll adjusted notional futures data by adding a roll adjustment to the settlement price then multiplying by contract multiplier through time. For example, for crude oil CL, on 15 March 2013, the settlement price of the CLJ3 contract was 93.45. The cumulative roll adjustment was -70.80 and the multiplier is 1,000. My roll adjusted notional is then $(93.45-70.80)/*1,000=22,650$.

This is great but take for example 12 Feb 2009 where settlement price was 33.98 and cumulative roll adjustment was -33.99. This gives me a negative roll adjusted contract value of $(33.98-33.99)*1,000=-10$.

The implication of a negative roll adjusted notional value on futures is that you have literally lost money through the cost of carry for this product. I am using a method dictated by my client otherwise the ratio method, described here, may have been implemented. This person is intent on capturing potential loss due to carry, however.

I'm challenged in my attempt to compute continuous returns for the series because of the negative values. Taking the log of a negative number in MATLAB returns an imaginary number and Excel can't handle it at all.

Does anyone have experience or advice in computing continuous returns for negative roll-adjusted futures notionals?

• I wouldn't expect negative values if I were calculating a continuous futures contract. For the client, why don't you figure out a way to express what they want as a trading strategy first. Perhaps there is a way to express it in another way (like the difference in the return between the nearest continuous contract and the second nearest continuous contract). – John Jun 6 '13 at 20:15
• That's basically what we're doing. When the deferred month open interest exceeds the active contract open interest, we simulate the roll by taking the difference between the deferred and active contract prices which is the roll adjustment. This value is accumulated through time as discussed above to represent the cost of carrying the contract. – strimp099 Jun 6 '13 at 20:21
• You should not derive cumulative roll adjustments. Simply calculate the roll adjustment each time you actually roll the contract and then derive the backward adjustment factor. This adjustment factor will never be negative and because you multiply/divide it with your past pricing data you should never arrive at a negative price at any point. – Matthias Wolf Jun 7 '13 at 1:42
• Would the backward adjustment factor computed for a given roll apply to all previous contracts strung together or just the last contract? I.e. do you multiply every previous price by the factor in the series or just the price for the last contract? – strimp099 Jun 8 '13 at 1:34