By Sergei Belov, Ernest Chan, Nahid Jetha, and Akshay Nautiyal ABSTRACT We applied Corrective AI (Chan, 2022) to a trading model that takes advantage of the intraday seasonality of forex returns. Breedon and Ranaldo (2012) observed that foreign currencies depreciate vs. the US dollar during their local working hours and appreciate during the local working hours of the US dollar. We first backtested the results of Breedon and Ranaldo on recent EURUSD data from September 2021 to January 2023 and then applied Corrective AI to this trading strategy to achieve a significant increase in performance. Breedon and Ranaldo (2012) described a trading strategy that shorted EURUSD during European working hours (3 AM ET to 9 AM ET, where ET denotes the local time in New York, accounting for daylight savings) and bought EURUSD during US working hours (11 AM ET to 3 PM ET). The rationale is that large-scale institutional buying of the US dollar takes place during European working hours to pa
Lately there were a few interesting discussions in the blogosphere on the profitability of shorting the VXX-VXZ spread. (See Quantum Blog and The Speculator's Ball.) For background, VXX is an ETN that tracks the first and second month of the VIX future, which in turn tracks the VIX volatility index, which in turn tracks the volatility of SPX. VXZ is the ETN that tracks the 4th - 7th months of the VIX future. During the period 2009-2010, there were 2 different reasons why shorting this "calendar spread" was profitable:
1) The VIX futures were/are in contango: i.e. the back months' futures are more expensive than the front months'.
2) The volatility of SPX was decreasing with time.
However, some traders seem to think that either one of these conditions is enough to ensure the profitability of shorting a calendar spread. It is not. (Otherwise, life as a futures trader would be too easy!)
To see this, let's resort to a simplistic linear approximation to a model of futures prices. From John Hull's book on derivatives, section 3.12, the price of a future which matures at time T is
F(t, T)=E(ST)exp(c(T-t)),
where E(ST) is the expected value of the spot price at maturity, c is a constant, and t is the current time. If the futures are in contango, then c > 0.
If we assume that abs(c) is small, and T-t is also small (i.e. not too far from maturity), and that the expected value of the spot price changes slowly, we can linearize this formula as
F=(a+b(T-t))*(1+c(T-t))
If the market expects the future spot price to increase, then b > 0.
After a few simple algebraic steps, you can verify that the calendar spread's price is proportional to
F(t, T1)-F(t, T2) ~ bct
where T1 < T2 (i.e. F(t, T1) is the front month's price, and F(t, T2) the back month's).
This is a satisfyingly illustrative result. It says that shorting this calendar spread will be profitable if
A) futures are in contango and the expected spot price in the future is decreasing; or else
B) futures are in backwardation and the expected spot price in the future is increasing.
So what is the situation today? Will it still be profitable to short this spread? As our fellow bloggers have pointed out, VIX futures are still in contango, but the market is expecting volatility to increase in the future over the last month or so. So this may no longer be a profitable trade anymore.
1) The VIX futures were/are in contango: i.e. the back months' futures are more expensive than the front months'.
2) The volatility of SPX was decreasing with time.
However, some traders seem to think that either one of these conditions is enough to ensure the profitability of shorting a calendar spread. It is not. (Otherwise, life as a futures trader would be too easy!)
To see this, let's resort to a simplistic linear approximation to a model of futures prices. From John Hull's book on derivatives, section 3.12, the price of a future which matures at time T is
F(t, T)=E(ST)exp(c(T-t)),
where E(ST) is the expected value of the spot price at maturity, c is a constant, and t is the current time. If the futures are in contango, then c > 0.
If we assume that abs(c) is small, and T-t is also small (i.e. not too far from maturity), and that the expected value of the spot price changes slowly, we can linearize this formula as
F=(a+b(T-t))*(1+c(T-t))
If the market expects the future spot price to increase, then b > 0.
After a few simple algebraic steps, you can verify that the calendar spread's price is proportional to
F(t, T1)-F(t, T2) ~ bct
where T1 < T2 (i.e. F(t, T1) is the front month's price, and F(t, T2) the back month's).
This is a satisfyingly illustrative result. It says that shorting this calendar spread will be profitable if
A) futures are in contango and the expected spot price in the future is decreasing; or else
B) futures are in backwardation and the expected spot price in the future is increasing.
So what is the situation today? Will it still be profitable to short this spread? As our fellow bloggers have pointed out, VIX futures are still in contango, but the market is expecting volatility to increase in the future over the last month or so. So this may no longer be a profitable trade anymore.
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