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Curve fitting a portfolio

Devising a system to look good on a set of past data is the worst form of self-deception a trader can perpetrate upon himself. It cannot fail to disappoint in the future and if leverage is used the effect is likely to be a dangerously exaggerated draw down. Even if the traders account is not wiped out, the psychological damage is likely to be profound.

Choosing a portfolio which looks good in a back test is one of the best examples of curve fitting. For the examples in this post I used futures and an effective but simple envelope breakout system which I have traded in the past.

A moving average of the close is surrounded by an upper band and a lower band. The moving average period has been chosen such that the system’s average trade lasts around 3 months. The bands are based on the moving average + and – a measure of volatility. When the price exceeds the upper band go long; exit when the price penetrates the moving average on the downside. Short trades are triggered when the price penetrates the lower band and are excited when the price goes back above the moving average.

A profit taking mechanism is employed to reduce volatility.

Trades are not taken if the absolute correlation of the proposed new trade / instrument exceeds a given level measured against any one instrument in the existing positions or if the average correlation of the portfolio as a whole would exceed a certain level when including a proposed new instrument / trade.

Fixed fractional volatility base position sizing is used.

The first equity curve below results from trading a carefully balanced portfolio of 25 instruments which I happened to choose from those available for trading from a particular UK based spread betting firm. Performance in recent years looks good.

The City Index 24 portfolio was a genuine attempt to reach a sensible and balanced portfolio:

ECX EUA Emissions -ICE                         Wheat-Kansas City-KCBT

Petroleum-Crude Oil Light-NYMEX        Petroleum-Gas Oil

Cotton #2                                                     Hogs-Lean

FX-Euro-CME                                             Index-Nikkei 225-CME

Index-U.S. Dollar                                        Palladium-NYMEX

Euro German Bobl-EUREX                      Platinum-NYMEX

Intrbank Offer Rate-EURIBOR                Rapeseed(Canola)

Sterling Rate-3Mth-LIFFE                        Soybeans-CBT

Gold-COMEX                                             Sugar #11

Petroleum-Heating Oil #2                       Index-S&P 500-CME(Floor Trading Only)

FX-Japanese Yen-CME                            Index-Swiss Market-EUREX

Coffee                                                         Index-CBOE Volatility-CFE

But why should the portfolio necessarily perform as well in the future as it seems to have done over the past few years? How would different 25 instrument portfolios have performed using the same system and parameters?

I took 100 futures markets and ran tests on 230 randomly chosen portfolios of 25 instruments out of the total potential of 100.

Here are histograms of the results and a chart which matches achieved CAGR and max DD on each test:

Here by contrast are the results of a test run on a portfolio of all 100 futures with a suitable reduced position size:

Note the performance has been flat as a pancake since 2011, much more in line with what we have seen reported by CTAs in general.

I am happy with the system – it is simple and generic. What about the portfolio? I am not unhappy with the City Index 24 portfolio – it is reasonable balanced. But the outperformance since 2011 is very probably pure chance. The monte carlo, bootstrapping like tests suggest a likely CAGR of 10% for a max drawdown of 30% hence a MAR of 0.33 – not unlike what has been achieved by CTAs in the real world over the past decade.

But still no guarantee for the future. And perhaps after all the 100 instrument portfolio is a safer bet although it will take a much bigger account size to trade.

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