6 December 2013
- 15 minute read

These are now all traded on the CME except: (1) Eurex, (2) TSE, (3) OSE, (4) HKFE, (5) SFE, (6) LIFFE, (7) LME. (8) We synthesise prices for a Copper futures contract with a fixed expiry date, rather than a fixed time to expiry as found on the LME.

Returns are not compounded and volatility is determined by a 100-day exponentially-weighted estimate. The Sharpe ratios are 0.87, 1.12 and 0.81 for the fast, medium and slow strategies, respectively, for the 30-year period. The standard error on the Sharpe ratio is approximately 0.2 for 30 years of data. The realised volatility is around 10.5% for all three strategies.

The standard error of these estimates is shown in grey around the results of the medium-speed strategy. Dashed lines give the average Sharpe ratio for the individual asset return; these appear to mimic the performance of the portfolio, indicating that the decline at the portfolio level is due to the decline of performance of underlying assets and not an increase in between-asset correlation.

Where Δ is the difference between the first and last 10-year periods, and t and p are the corresponding t-statistic and p-value. The p-value estimates the probability of achieving the observed Δ value under the null hypothesis that the true performance did not change in these two 10-year periods, and the difference is just due to sample error. All strategies have seen a decline in performance, but this is most significant for the fastest system.

For each portfolio 20 markets are selected at random from a total list of 38. The median results are plotted for each strategy speed, and the 15th to 85th percentile ranges from 1,000 realisations.

The Dow Jones Industrial Average futures have only existed since 1997 we synthesise a rolled futures series using dividend yields and interest rates going back to 1900.

“Of all the potential embarrassments to market efficiency, momentum is the primary one"

[1] T. J. Moskowitz, Y. H. Ooi, L. H. Pedersen, Time series momentum, Journal of Financial Economics, vol 104, 228-250, 2012.

[2] N. Jegadeesh, S. Titman, Returns to Buying Winners and Selling Losers: Implications for Stock Market Efficiency, Journal of Finance, vol 48, 1993.

[3] A. W. Lo, A. C. MacKinlay, When Are Contrarian Profits Due to Stock Market Overreaction?, Review of Financial Studies, vol 3, 175-205, 1989.

[4] M. M. Carhart, On Persistence in Mutual Fund Performance, Journal of Finance, vol 52, 57-82, 1997.

[5] E. F. Fama, K. R. French, Size, Value, and Momentum in International Stock Returns, Journal of Financial Economics, vol 105, 457-472, 2012

[6] We define the turnover of a system as: the ratio of the mean absolute position to the mean absolute five-day change in position, roughly indicating how many weeks it takes to close a position but ignoring small trades back and forth on a daily level.

[7] Lean hogs, silver, natural gas, soybeans, aluminium, Eurostoxx 50, DAX, Kospi, Nasdaq, Hang Seng, Euribor, short-sterling, bobl, US 5-year T-notes, schatz, Australian dollar, Mexican peso, New Zealand dollar.