That's a really interesting topic but above my paygrade at the moment. This is probably a naive solution but what if we overweighted assets that are inversely correlated to broad market correlation. For example, in 2008 most assets tumbled but VIX and VIX implied vol shot up like a rocket.
Fully automated futures trading
- Thread starter globalarbtrader
- Start date
That's a really interesting topic but above my paygrade at the moment. This is probably a naive solution but what if we overweighted assets that are inversely correlated to broad market correlation. For example, in 2008 most assets tumbled but VIX and VIX implied vol shot up like a rocket.
I've thought long and hard about this problem. Here's what I've tried:
* @globalarbtrader 's method - bootstrap portfolio weights to optimise overall Sharpe ratio. Possible risk: overfitting (e.g. heavy equities, heavy VIX)
* Some kind of max separation based on the correlation matrix of weekly returns. In principle this works well, because it doesn't take many periods to get high statistical significance of the correlation matrix (1 year is enough data). Assumes that the expected return of each instrument is identical.
In the end, I realised the best thing to do is a 'common sense' approach. It's obvious that the TF hypothesis that the expected return isn't going to be the same- some instruments trend nicely, others never seem to. While being careful to avoid implicit overfitting (e.g. by dropping instruments that were never profitable in backtest), the best thing, in my opinion, is a mixture of @globalarbtrader 's method + handcrafting.
In other words:
- Reduce the set of instruments by taking out obvious pairs - e.g. Nasdaq, S&P500 & Russell 2000 are all basically the same.
- Bootstrap portfolio weights, again applying common sense.
Interesting question. As mentioned by other posters, it's a tough one.
There are some papers out there suggesting that reducing risk (volatility target) in response to increased correlation between markets produces better results -- I believe that is in one of the Baltas papers. I've not verified this specifically in my system yet.
What I've done so far is something relatively simple conceptually, but was a pain in the butt for me due to the way my backtesting framework is implemented. Essentially, I started with static weights calculated using bootstrapping as outlined by GAT. Then, on every trading day, I "adjusted" (raised or lowered) the weight of a market based on it's "relative correlation" with the system equity curve. To do that, I calculated the correlation (using a relatively short look-back) of each individual market equity curve (trading that single market using the system signals for that market) with the system equity curve (for all markets in my security universe) -- this is why it was a pain in the butt, I had to have a separate equity curve for each market in addition to the equity curve for the complete system trading all markets using the unadjusted weights. Once I had the correlation between each market's equity curve and the system equity curve, I calculated the weight "adjustment" for a market based on the distance of that market's correlation from the average market correlation -- this way, markets for which the correlation between their equity curves and the system equity curve was further away from the average market correlation got a bigger adjustment (you can get into all sorts of non-linear scaling algos here -- I believe I did something based on normal distribution). Markets with smaller correlation than average ended up with a positive adjustment and markets with higher than average correlation would end up with lower weights.
Anyhow, the above did reduce the maximum draw-down by about 10% or so -- from 25% to 22.5% if I remember correctly -- I'm traveling and don't have my notebook with all the notes and results from that experiment, thus I'm going off memory. I don't think the Sharpe ratio was affected much at all -- which I suppose makes sense since you're boosting the weight of loosing markets during times when your overall system is making money.
Anyhow, (as mentioned) while the above approach is simple conceptually, the implementation complexities made it so that I never put it into practice live trading my system.
I have used hierarchical clustering in a GTAA system in the past to aid in portfolio construction, but have not had a chance to try it out on the diversified futures trend and carry system.
I suppose the whole question of whether some sort of dynamic portfolio construction based on changing correlations would produce "better" results comes down to whether changes in correlations have any staying power. For example, using historical instrument volatility to adjust position sizes going forward works because of volatility clustering -- we know that once we get to higher volatility, that higher volatility will stick around for a while on average. Does the same happen with correlations? We know that correlations change in the long run, but do they exhibit clustering in the short run?
There is a paper -- "Momentum and Markowitz: a Golden Combination" -- that I think is very much on point here. The authors of the paper use a much shorter "formation" period than the years and years of returns and correlation data that most academic papers use. The paper seems to suggest that using correlations from much shorter time frames (less than a year) for portfolio construction does produce some impressive results and avoids many of the down-sides of MV optimizations. Alas, I have not had a chance to test out this approach in my system yet since it requires a very efficient optimizer (the paper suggests Critical Line algo), and I've not had the time to implement one myself yet (yes, I know, I could probably use one off the shelf ... I may get there someday).
Anyhow, that's my $0.02.
--Maciej
Last edited:
I realize my reply above does not answer the original question (arguably it doesn't even touch on the original question). But, the original question got me thinking about using correlation info for portfolio construction (which is pretty close to the spirit of the original question at least) and thus that's how I ended up with my post above. A bit of a tangent, but I hope you guys don't mind too much.
For calculating the correlation, what time period (lookback period) do you use? I assume that you have been using daily price bars to calculate this.
I was "playing" myself with correlation calculations and found that it makes a lot of difference whether you use a short period or a long period.
I think this chart could be easily misinterpreted. The performance is very strong for the first five years. Rebase the graph at 1990, what would you see?
Secondly, these lines don't look they've had the volatility normalised, so I'm not sure it makes sense to compare them on a chart like this. (@globalarbtrader care to help out here?)
And lastly, with respect to the shape of the breakout curve- the curve with the highest sharpe ratio will be an almost flat slope up and to the right (the strong performance at the beginning might lower the sharpe).
In any case, perhaps I missed something, so I will go back and test again
The chart isn't vol normalised: breakout had a higher allocation.
But we're talking about two different things: the SR of a single curve, and the difference made when you add that to your existing system.
GAT