Fully automated futures trading

[traider]

Carry and momentum are diversifying, so barring any information about performance (and there isn't any statistically significant difference between them) you'd want to split your portfolio 50:50 (assuming you have the same number of trading rule variations in each camp) for optimal expected performance. An institutional fund like AHL's flagship fund has to allocate more than 50% to momentum, so has a suboptimal portfolio.



Forecasts are proportional to sharpe ratio (mean / vol), a diff of EMA is a return in delta(price) space, so the correct forecast is proportional to diff of EAM/ vol (delta(price))

GAT

Thanks for the reply. Sorry but I still don't quite understand (2). Put it in another way, say I have a signal -20 to 20 for a mean reversion asset. When the signal is at 20 means that the asset is very far from what I estimate to be fair value, hence I'm willing to bet more on the reversion. I'm not sure how this intuition works for a trend rule.

I found this old comment on your blog:
I probably missed it but do you explicitly test that forecast magnitude correlates with forecast accuracy? For example, do higher values of EMAs result in greater accuracy? I'm assuming there's an observed albeit weak correlation. I haven't yet immersed myself in your book so I may be barking up the wrong tree.

Rob Carver8 May 2016 at 17:10
I have tested that specific relationship, and yes it happens. If you think about it logically most forecasting rules "should" work that way.

Could you elaborate more on how to go about testing the relationship? The reason I ask is because if there wasn't a strong relationship, it might be more appropriate to setup the trading rule as a classifier problem: trend vs no trend.

 

[globalarbtrader]

Hi GAT,
In your chapter 15 portfolio from your first book, you have multiple versions of EMAC rules and only one Carry rule, yet you still weight the Carry forecast at 50%. This seems different from how you are weighting trading rules in your own portfolio. Why is this? Thanks.

From my second book:

"Consider the simple three asset portfolio I used when I introduced the handcrafting method: UK equities, US bonds, and US equities. The grouped weights of this portfolio that maximise Sharpe Ratio are 50% in US bonds, 25% in UK equities, and 25% in US equities. These are all risk weightings which assume the volatility of each asset is identical.

Now suppose I do something stupid and add another 20 Developed equity markets to the menu: Germany, Canada, Japan …. and so on. This doesn't sound too idiotic, but I'm also not going to add any more bond markets, sticking with just US bonds. Now it’s a crazy idea.

Using the handcrafted method I still have one huge group for equities with a 50% weight, or 2.27% for each of the 22 countries. The other group for bonds still has just one asset, US bonds, with 50% weight in the overall portfolio.

Would you be comfortable with that? I wouldn't be; I'd feel dangerously exposed to an event which specifically affected US interest rates, like an unexpected result in a US presidential election.

Having half my portfolio in a single bond market is uncomfortable but it is also theoretically incorrect. I can demonstrate this by examining the bond and equity sub portfolios. Because the equity sub portfolio has a large number of countries which aren't perfectly correlated, it will be less risky than any individual country.

The bond sub portfolio however has only one asset inside it: it's risk will be the same as for each individual equity country (as we're using risk adjusted returns). So the equity sub portfolio has slightly less risk, and because I assume all assets have the same arithmetic mean of returns it also has a slightly higher geometric return and better Sharpe Ratio. I can improve on equal weights in an unbalanced portfolio by increasing the weight on the larger group of assets.

Of course in practice I wouldn't actually construct a portfolio with a single bond market, and 22 equity markets. Usually I'll be trying to keep groups similar in size, but this isn't always possible."

1Technical note: There is also a theoretical formula for dealing with this problem which is in Appendix C (page 493).

The formal method for dealing with this is as follows:

Calculate the diversification multiplier within each group
Given N assetswithin each each group, with a correlation matrix of returns r and risk weightsw summing to 1, the diversification multiplier will be 1 ÷ [ √( w’ r w) ].

You will get a higher diversification multiplier for larger groups, those with closer to equal weighting, and those with lower correlations. In a spreadsheet for a three asset portfolio if the correlation matrix is in cells A1:C3, and the weights are in cells F1:F3 then the diversification multiplier will be:

1/SQRT(MMULT(TRANSPOSE(F1:F3), MMULT(A1:C3,F1:F3)))

Multiply each group weight by it's diversification multiplier
This will give certain types of group a larger relative weight: larger groups, groups with lower correlation, and groups that are closer to equal weighting.

Renormalise the weights
The sum of the weights for each group will now be much greater than 100%. Renormalise them so they add up to 100% by dividing them by the total weight across all groups.

GAT

 

[Napoleon@Dynamite]

I agree that NQ and ES have a strong correlation. However, the value volatility of the ES contract is lower than the NQ contract. So for a given amount of risk capital could you have more contracts ES than NQ. For a small account is therefore ES better than NQ, in my opinion. This criteria might not be applicable to you.

This makes sense to me, @HobbyTrading . GAT, why do you consider NQ a better instrument than ES for smaller traders who are building up their list of instruments? On the other hand, I feel like I have to trade US2 every day with every little blip in the market, since my max forecast right now is about 10 contracts (250k account at 30% volatility). I wonder if I could save trading costs if I used US5 or 10, since I wouldn't be trading those every day as my max forecast would probably be a lot less than 10 for those.

 

[globalarbtrader]

Thanks for the reply. Sorry but I still don't quite understand (2). Put it in another way, say I have a signal -20 to 20 for a mean reversion asset. When the signal is at 20 means that the asset is very far from what I estimate to be fair value, hence I'm willing to bet more on the reversion. I'm not sure how this intuition works for a trend rule.

I found this old comment on your blog:
I probably missed it but do you explicitly test that forecast magnitude correlates with forecast accuracy? For example, do higher values of EMAs result in greater accuracy? I'm assuming there's an observed albeit weak correlation. I haven't yet immersed myself in your book so I may be barking up the wrong tree.

Rob Carver8 May 2016 at 17:10
I have tested that specific relationship, and yes it happens. If you think about it logically most forecasting rules "should" work that way.

Could you elaborate more on how to go about testing the relationship? The reason I ask is because if there wasn't a strong relationship, it might be more appropriate to setup the trading rule as a classifier problem: trend vs no trend.

You do a scatter plot of the ex-post risk adjusted return vs the ex-ante forecast (both in risk adjusted return units). You will normally see a linear relationship; stronger forecast, stronger risk adjusted return and vice versa. If you saw a binary relationship (positive forecast, positive risk adjusted return of unvarying magnitude and vice versa) then yes you should stick to a binary classifier. But I've never seen that for any trading rule.

Ocasionally you'll see an apparent non linear relationship (eg reversion for very strong trend forecasts AKA the dead cat bounce), but it's rare there's enough statistical evidence to justify fitting a non linear mapping which involves multiple additional parameters.

If there isn't a strong relationship (a regression would have painfully low R2 and no significance) then you'd normally be downweighting the rule full stop rather than mucking about with a non linear mapping between forecast and expected risk adjusted return.

GAT

 

[globalarbtrader]

This makes sense to me, @HobbyTrading . GAT, why do you consider NQ a better instrument than ES for smaller traders who are building up their list of instruments? On the other hand, I feel like I have to trade US2 every day with every little blip in the market, since my max forecast right now is about 10 contracts (250k account at 30% volatility). I wonder if I could save trading costs if I used US5 or 10, since I wouldn't be trading those every day as my max forecast would probably be a lot less than 10 for those.

I agree that NQ and ES have a strong correlation. However, the value volatility of the ES contract is lower than the NQ contract. So for a given amount of risk capital could you have more contracts ES than NQ. For a small account is therefore ES better than NQ, in my opinion. This criteria might not be applicable to you.

When I last did this exercise ES was a little more value volatile than NQ. But now because volatility in ES has been crushed the order has been reversed. So I'd agree that ES is better for a small account.

GAT

 

[traider]

You do a scatter plot of the ex-post risk adjusted return vs the ex-ante forecast (both in risk adjusted return units). You will normally see a linear relationship; stronger forecast, stronger risk adjusted return and vice versa. If you saw a binary relationship (positive forecast, positive risk adjusted return of unvarying magnitude and vice versa) then yes you should stick to a binary classifier. But I've never seen that for any trading rule.

Ocasionally you'll see an apparent non linear relationship (eg reversion for very strong trend forecasts AKA the dead cat bounce), but it's rare there's enough statistical evidence to justify fitting a non linear mapping which involves multiple additional parameters.

If there isn't a strong relationship (a regression would have painfully low R2 and no significance) then you'd normally be downweighting the rule full stop rather than mucking about with a non linear mapping between forecast and expected risk adjusted return.

GAT

Yes I remember that you mentioned the dead cat bounce was not statistically significant in one of your talks.

Say my rule is EMA (4,16) and I have a forecast for day 1. What number do I choose for the Nth day return so that my test makes sense?
My guess is for shorter rules, a smaller N but I don't really know the exact number.
If it's too length to explain, could you point to some academic reference which elaborates on how to setup such a test properly?

 

[globalarbtrader]

Yes I remember that you mentioned the dead cat bounce was not statistically significant in one of your talks.

Say my rule is EMA (4,16) and I have a forecast for day 1. What number do I choose for the Nth day return so that my test makes sense?
My guess is for shorter rules, a smaller N but I don't really know the exact number.
If it's too length to explain, could you point to some academic reference which elaborates on how to setup such a test properly?

It depends on the turnover of the rule but a good rule of thumb for ewmac is to use n of twice the faster mav

GAT

 

[Elder]

From my second book:

"Consider the simple three asset portfolio I used when I introduced the handcrafting method: UK equities, US bonds, and US equities. The grouped weights of this portfolio that maximise Sharpe Ratio are 50% in US bonds, 25% in UK equities, and 25% in US equities. These are all risk weightings which assume the volatility of each asset is identical.

Now suppose I do something stupid and add another 20 Developed equity markets to the menu: Germany, Canada, Japan …. and so on. This doesn't sound too idiotic, but I'm also not going to add any more bond markets, sticking with just US bonds. Now it’s a crazy idea.

Using the handcrafted method I still have one huge group for equities with a 50% weight, or 2.27% for each of the 22 countries. The other group for bonds still has just one asset, US bonds, with 50% weight in the overall portfolio.

Would you be comfortable with that? I wouldn't be; I'd feel dangerously exposed to an event which specifically affected US interest rates, like an unexpected result in a US presidential election.

Having half my portfolio in a single bond market is uncomfortable but it is also theoretically incorrect. I can demonstrate this by examining the bond and equity sub portfolios. Because the equity sub portfolio has a large number of countries which aren't perfectly correlated, it will be less risky than any individual country.

The bond sub portfolio however has only one asset inside it: it's risk will be the same as for each individual equity country (as we're using risk adjusted returns). So the equity sub portfolio has slightly less risk, and because I assume all assets have the same arithmetic mean of returns it also has a slightly higher geometric return and better Sharpe Ratio. I can improve on equal weights in an unbalanced portfolio by increasing the weight on the larger group of assets.

Of course in practice I wouldn't actually construct a portfolio with a single bond market, and 22 equity markets. Usually I'll be trying to keep groups similar in size, but this isn't always possible."

1Technical note: There is also a theoretical formula for dealing with this problem which is in Appendix C (page 493).

The formal method for dealing with this is as follows:

Calculate the diversification multiplier within each group
Given N assetswithin each each group, with a correlation matrix of returns r and risk weightsw summing to 1, the diversification multiplier will be 1 ÷ [ √( w’ r w) ].

You will get a higher diversification multiplier for larger groups, those with closer to equal weighting, and those with lower correlations. In a spreadsheet for a three asset portfolio if the correlation matrix is in cells A1:C3, and the weights are in cells F1:F3 then the diversification multiplier will be:

1/SQRT(MMULT(TRANSPOSE(F1:F3), MMULT(A1:C3,F1:F3)))

Multiply each group weight by it's diversification multiplier
This will give certain types of group a larger relative weight: larger groups, groups with lower correlation, and groups that are closer to equal weighting.

Renormalise the weights
The sum of the weights for each group will now be much greater than 100%. Renormalise them so they add up to 100% by dividing them by the total weight across all groups.

GAT

Hi sorry if I am butting in again, , but interesting discussion. Reading between the lines, it seems you are saying one sensible approach is to allocate equally to carry and momentum and then apply the FDM to each style separately to alter the relative allocations? From what I recall from your posts and first book, I guess the other approach is to throw all the forecasts of all styles and variations into one optimisation (or series of optimisations when bootstrapping) and let it spit out the weights and then apply the FDM? I presume the first approach it is likely to give more stable weights?

 

[djames]

Hi all, Does anyone know why Quandl published MXP futures prices 1x10^6 times the quotes on CME?
https://www.quandl.com/data/CME/MPZ2017-Mexican-Peso-Futures-December-2017-MPZ2017
http://www.cmegroup.com/trading/fx/emerging-market/mexican-peso.html

Apologies if I am being dense! (I blame it on last nights burrito)

 

[globalarbtrader]

Hi sorry if I am butting in again, , but interesting discussion. Reading between the lines, it seems you are saying one sensible approach is to allocate equally to carry and momentum and then apply the FDM to each style separately to alter the relative allocations? From what I recall from your posts and first book, I guess the other approach is to throw all the forecasts of all styles and variations into one optimisation (or series of optimisations when bootstrapping) and let it spit out the weights and then apply the FDM? I presume the first approach it is likely to give more stable weights?

Well the discussion is about how you deal with handcrafting weights, rather than doing an optimisation. And specifically how you deal with the fact that when grouping things together, groups may vary in how they are diversified (size and correlation), and a sensible adjustment to make for that. Any optimisation across all assets together would deal with that problem, albeit at the cost of less robust weights.

Ultimately you'd still calculate a single FDM.

GAT