Literature on allocation across multiple strategies on the same asset

[cjbuckley4]

Consider a situation where we attempt to trade multiple strategies on the same asset with varying returns, volatlities, trading frequencies, and holding periods. Obviously, you should (will automatically) "internally match" (I'm not Citadel...) when your short term strategy is short (long) and your long term strategy is long (short). This dynamic is really where things get complicated in my eyes. How would I best combine these strategies in practice to maximize risk adjusted returns?

The way I view this problem, I have three choices:
1. Fixed allocation per strategy, floating cumulative risk. Use Backtest returns and risks to construct portfolio of strategies on efficient frontier. My concern here is that if my strategies are highly correlated, they will lead me to over leverage myself. The pro that jumps out immediately is that I will never be in a situation where I miss out on trading opportunities because I am already fully invested. I think we can probably do better than this approach.
2. Fixed cumulative risk, floating allocations. This seems like a good idea. It will (hopefully) allow me to always remain below a specified VaR. The downside is that strategies will compete for capital. That's not unheritly a bad thing, but how to implement this is the question.
3. Fixed cumulative risk, single boosted strategy. We could combine the signals of several strategies into one signal using machine learning techniques. This is an idea I like a lot, and perhaps it may be the best framework going forward because I can do away with the idea of even coming up with individual strategies and just come up with predictors.

Let me know what approach you believe is best and in the likely event it is approach 2, please do hook me up with any literature on this you know of as it sounds like a complex but very interesting idea. I know a bit about mean variance optimization, but I don't really know how to apply it to a situation where the strategies returns are all dependent on the same underlying process. Thanks.

 

[globalarbtrader]

My concern here is that if my strategies are highly correlated, they will lead me to over leverage myself.

Think you mean uncorrelated?

I'd allocate a fixed proportion of my risk and leverage up my portfolio according to how diversified the strategies are (but you knew that, right?). A key ratio is the average vs the peak diversification benefit of running multiple strategies. This is a function of higher correlated moments of the forecasts. If this ratio is high, then you have strategies that are probably mostly uncorrelated but ocasionally all point in the same direction. When they do you'll have to put on multiples of your average risk, at least in theory.

Is the portfolio long only, unleveraged? If so then you'll end up holding a lot of cash a lot of the time to cope with the peaks. Or you wind up the risk target and end up with a more binary system.

If you have access to leverage, then you can probably want to cap at a maximum leverage (or maximum total forecast). But if you spend a lot of time capped then again your system becomes more binary in nature.

There is no easy answer to this question. A non linear solution like (3) isn't the easy answer eithier. It will just hide this problem under layers of darkness.

GAT

Consider a situation where we attempt to trade multiple strategies on the same asset with varying returns, volatlities, trading frequencies, and holding periods. Obviously, you should (will automatically) "internally match" (I'm not Citadel...) when your short term strategy is short (long) and your long term strategy is long (short). This dynamic is really where things get complicated in my eyes. How would I best combine these strategies in practice to maximize risk adjusted returns?

The way I view this problem, I have three choices:
1. Fixed allocation per strategy, floating cumulative risk. Use Backtest returns and risks to construct portfolio of strategies on efficient frontier. My concern here is that if my strategies are highly correlated, they will lead me to over leverage myself. The pro that jumps out immediately is that I will never be in a situation where I miss out on trading opportunities because I am already fully invested. I think we can probably do better than this approach.
2. Fixed cumulative risk, floating allocations. This seems like a good idea. It will (hopefully) allow me to always remain below a specified VaR. The downside is that strategies will compete for capital. That's not unheritly a bad thing, but how to implement this is the question.
3. Fixed cumulative risk, single boosted strategy. We could combine the signals of several strategies into one signal using machine learning techniques. This is an idea I like a lot, and perhaps it may be the best framework going forward because I can do away with the idea of even coming up with individual strategies and just come up with predictors.

Let me know what approach you believe is best and in the likely event it is approach 2, please do hook me up with any literature on this you know of as it sounds like a complex but very interesting idea. I know a bit about mean variance optimization, but I don't really know how to apply it to a situation where the strategies returns are all dependent on the same underlying process. Thanks.

 

[cjbuckley4]

My concern here is that if my strategies are highly correlated, they will lead me to over leverage myself.

Think you mean uncorrelated?

I'd allocate a fixed proportion of my risk and leverage up my portfolio according to how diversified the strategies are (but you knew that, right?). A key ratio is the average vs the peak diversification benefit of running multiple strategies. This is a function of higher correlated moments of the forecasts. If this ratio is high, then you have strategies that are probably mostly uncorrelated but ocasionally all point in the same direction. When they do you'll have to put on multiples of your average risk, at least in theory.

Is the portfolio long only, unleveraged? If so then you'll end up holding a lot of cash a lot of the time to cope with the peaks. Or you wind up the risk target and end up with a more binary system.

If you have access to leverage, then you can probably want to cap at a maximum leverage (or maximum total forecast). But if you spend a lot of time capped then again your system becomes more binary in nature.

There is no easy answer to this question. A non linear solution like (3) isn't the easy answer eithier. It will just hide this problem under layers of darkness.

GAT

I do mean to say correlated. If the strategies trade the same asset and are any good, there should be high correlation between signals during the timeframes they overlap cumulatively. At least that would be my intuition. I hadn't even really thought of looking at higher moments though, that's a good idea.

Indeed, there will be leverage and more than I can afford to use safely on directional bets (futures markets).

W/r/t the boosting, I do agree that this is a difficult problem that might be a bad candidate for a black box. What about a bagging technique to achieve the same desired end result of an aggregated classifier that is more interpretable like random forests?

 

[globalarbtrader]

I do mean to say correlated. If the strategies trade the same asset and are any good, there should be high correlation between signals during the timeframes they overlap cumulatively. At least that would be my intuition. I hadn't even really thought of looking at higher moments though, that's a good idea.

Indeed, there will be leverage and more than I can afford to use safely on directional bets (futures markets).

W/r/t the boosting, I do agree that this is a difficult problem that might be a bad candidate for a black box. What about a bagging technique to achieve the same desired end result of an aggregated classifier that is more interpretable like random forests?

Oh I think it comes down to how you handle stuff. If I have two things that are uncorrelated, such that their average forecast is quite weak, then I leverage my system up to hit the same risk target. The disadvantage of this approach is that correlation is an average, linear, measure of similarity. If I have two predictors that are usually uncorrelated, then on the rare occasions when they point in the same direction I'll have way more risk than average. Hence my discussion on limiting this peak risk.

You seem to be talking as if you don't have this option. So if you have two highly correlated predictors, then they'll naturally have more risk than two uncorrelated ones.

I have to say I don't understand machine learning techniques in any detail, and I've never seen anyone convince me they do a better job than something simpler (like a linear combination of forecasts). From what I do know, I prefer bagging to boosting.

GAT

 

[lindq]

Let me know what approach you believe is best and in the likely event it is approach 2, please do hook me up with any literature on this you know of as it sounds like a complex but very interesting idea. I know a bit about mean variance optimization, but I don't really know how to apply it to a situation where the strategies returns are all dependent on the same underlying process. Thanks.

If you have multiple positive strategies that overlap with differing timeframes on the same instrument...there is no law against trading two accounts.

I've done it for years. And I'm still a free man.

 

[cjbuckley4]

If you have multiple positive strategies that overlap with differing timeframes on the same instrument...there is no law against trading two accounts.

I've done it for years. And I'm still a free man.

While I am aware that trading two accounts is possible and indeed may have advantages in certain cases, I'm a bit unclear as to how this would change my allocation of capital across strategies as I'm still financially on the hook for whatever gains or losses the accounts accrue. It is unclear to me how this would result in more optimal allocation of capital in terms of risk adjusted returns as just separating the accounts in which they trade does nothing to remedy the risk in trading multiple strategies who's returns ultimately depend on the same process.

 

[Martinghoul]

Why does it matter that the strategies are trading the same asset? Isn't what you have a generic portfolio construction/optimisation issue?

 

[cjbuckley4]

Why does it matter that the strategies are trading the same asset? Isn't what you have a generic portfolio construction/optimisation issue?

Well, if you look at the mean variance optimization approach (what they teach us in school), obviously, the covariance matrix depends on the correlation of assets. If we substitute in strategies for assets, it a) becomes nonlinear, but b) if you take the mesh and look at ever smaller intervals where two strategies trade the same asset, the returns of each strategy will no longer have some meaningful correlation, it will just become rho (element of) [-1, 0, 1], correct?

Does the fact that all the strategies depend on the same process not invalidate this approach to portfolio construction?

EDIT: does this site not have something LaTeX like like NP?

 

[Martinghoul]

Well, if you look at the mean variance optimization approach (what they teach us in school), obviously, the covariance matrix depends on the correlation of assets. If we substitute in strategies for assets, it a) becomes nonlinear, but b) if you take the mesh and look at ever smaller intervals where two strategies trade the same asset, the returns of each strategy will no longer have some meaningful correlation, it will just become rho (element of) [-1, 0, 1], correct?

Does the fact that all the strategies depend on the same process not invalidate this approach to portfolio construction?

EDIT: does this site not have something LaTeX like like NP?

I don't think a generic portfolio construction approach will depend on the nature of the strategies or the underlying process it is applied to. At least that has always been my understanding...

 

[globalarbtrader]

it a) becomes nonlinear, but b) if you take the mesh and look at ever smaller intervals where two strategies trade the same asset, the returns of each strategy will no longer have some meaningful correlation, it will just become rho (element of) [-1, 0, 1], correct?

I'm not convinced that non linear p&l is more likely with strategies trading the same asset, than with multiple assets.

(b) is true of any asset, since nothing trades at exactly the same time.

If I'm being honest, I'm not really understanding the perceived problem here.

GAT