
HitmanH


Total Posts: 498 
Joined: Apr 2005 


Question on how to / what is market standard to calculate risk metrics like Sharpe ratio  for a strategy which doesn't trade every day. As well as not trading, it has no positions  so there is never any PNL on those days.
If you include them at a zero, then it dampens the mean return an awful lot
However if we null them, and don't include the data point, i feel that it inflates the numbers, and it is simply not possible to trade the strategy ever day. However, as there is no capital / margin / risk budget used up, it maybe feels better this way.
Open to suggestions / inspiration. 




goldorak


Total Posts: 1091 
Joined: Nov 2004 


I guess it all boils down to what you can do with the money when you are not invested.
If you never know when cash will be needed to be put to work because you never know in advance when a trade will occur, then zero is the right number (or "cash rate" depending on the time horizon) because you always need to be ready to invest. Otherwise you may assume that you need to delay your investment in the strategy by N days if you know that another (less seducing) strategy in the portfolio has an investment horizon strictly inferior to N days. I guess this reduces the inflation in the numbers if you just remove periods of inactivity.
The market standard to solve that kind of problematic? I know people who would call for an IRR...

If you are not living on the edge you are taking up too much space. 


 


> However if we null them, and don't include the data point,
This isn't the right approach. A strategy that trades everyday, caeteris paribus, has an inherent advantage over one that trades fewer times a year. Normally we think of diversification in the space of assets, but there's also diversification over time. If every trading day samples from the same distribution, then a 252 trading day strategy can achieve the same expected returns with 1/16 the volatility, drawdown, and VaR compared to a strategy with one day a year. Nulling the nontraded days ignores this disadvantage and pretends that the 252day and 1day strategy are equivalent. Reductio ad absurdum.
> If you include them at a zero, then it dampens the mean return an awful lot
This also isn't the right approach. At least in most cases. The question boils down to what's the investor's next best opportunity? Let's pretend your strategy *did* trade 252days/year. Where would your typical investor be allocating money from to fund the investment? I'm guessing it's very unlikely that the opportunity cost is cash. Very likely the funding competes with allocation to some liquid risktype asset.
The proposition is very simple. If you were selling a fulltime strategy, you'd have to convince the client that your strategy is better than their next best opportunity. Now all you're saying instead is "my strategy's better than your next best opportunity 30 days of the year. But the other 220 days when it's not available just do what you were doing before. You're better off some days, and no worse off the rest of the time".
In short pick some standard "ambient risk asset". Probably the S&P 500, but maybe you can get fancier. Interlace the ambient returns on top of the strategy's censored trading days. E.g. if you're only tradable on Tuesday and Friday, the returns for the week become [SPY, Strat, SPY, SPY, Start]. With the full interlaced series in hand, calculate the standard portfolio statistics. Also to be serious you should add the transaction costs to toggle in/out of the ambient asset, but for SPY on a daily horizon that's gonna be de minims. 
Good questions outrank easy answers.
Paul Samuelson 


HitmanH


Total Posts: 498 
Joined: Apr 2005 


Thanks for this, it's superlogical to follow. Have been looking at this in terms of assessing internal strategies  so the ambient risk asset is actually a function of what else we have on at the time, and how they're performing (as if not allocating here  everything else is a higher % of the risk budget).
One last question, and mathematically there is no difference, but if there are two types of occasional trading strategies, one which only trades on news, or a breakout, or vol etc, and another that only trades set days per year (say expiry dates). Mentally I want to treat them different, but not sure I should. Thoughts? 




goldorak


Total Posts: 1091 
Joined: Nov 2004 


I tend to favour the second kind.
The first kind is pretty hard to manage, especially if you are an outsider with limited knowledge of their inner workings. They tend to cluster in time which strongly limits their profit potential. I hate those. The best way to manage them is to have lots of strategies (but REALLY a lot), applying to lots of assets as uncorrelated as possible, and to build portfolio of fixedsize boxes, which you then fill one by one when strategies trigger. Even in such a setup, particular geopolitical configurations or market panics tend to bring back time clusters, and in a matter of no time you end up with a portfolio full of correlated trades.

If you are not living on the edge you are taking up too much space. 


HitmanH


Total Posts: 498 
Joined: Apr 2005 


Oh I'm with you, much prefer the latter  but more looking for metrics if we have both in our wheelhouse, to review / assess them... 




goldorak


Total Posts: 1091 
Joined: Nov 2004 


Sorry, I quit using frequentist statistics a long time ago for that kind of job. Not the right tools to analyze trading strategies. So no metric for you.
My scheme is more inclined towards bayesian thinking. Use your understanding of the inner workings of a trading strategy to tweak priors away from uniform (I do such a bold move in very seldom cases), observe performance and build posteriors. Iterate. 
If you are not living on the edge you are taking up too much space. 



> Mentally I want to treat them different, but not sure I should. Thoughts?
Short answer: As long as active days infrequently overlap, then two strategies are pretty much separate things.
Long justification: Let's say strategy A and B trade occasionally on certain days throughout the year. The approximate upper bound on their correlation is basically Intersect(ADays,BDays)/Union(ADays,BDays). E.g. assume if A is active for some 126 days of the year, and B is active for some 126 days, and the active days are randomly drawn independently. Then it'd be very unlikely that their longterm aggregated correlation signficantly exceeds 33%. (63 expected coactive days divided by 189 expected active days).
To see why, consider an Astrat that trades on Wednesday, and a Bstrat that trades on Friday. Their days never overlap, so daily correlation must be zero. But is it possible that their aggregated weekly returns could be nonzero? Numerically, yes. Economically, not likely. If they had nonzero correlation, that would imply that A's Wednesday performance forward predicts B's returns on Friday. That's a clearcut violation of market efficiency.
I’m not denying that market inefficiencies exist. Otherwise I’d be a tennis instructor. But when they do they're usually rare, hard to find, and small in magnitude. For daily returns on liquid assets just stumbling on a signal with 5%+ correlation would be extremely unlikely. (And if not, consider it a mitzvah. Forget the rest of this crap, and just go print money with that thing.)
Hence the noncontemparenous portion of correlation is almost certainly puny relative to typical contemporaneous correlations. The correlation is closely upperbounded by the proportion of overlapping days. Analogous arguments can be extended to other comoments.
(Digression for pedants: This assumes all trading days within a strategy draw from the same distribution of returns. If there's heteroskedacity between different days, then the overlapping days can be more (less) volatile. In which case the upper bound is larger (smaller) relative to the disproportionate concentration of volatility on those overlapping days.)
You can approximate two strats as separate black boxes as long as 1) they both trade infrequently, and 2) their active days don't overlap significantly more than you'd expect from chance. If active days are drawn independently, two strats that trade with frequency proportion P, should overlap with frequency P^2. Hence correlation is bounded by P^2/(2*P  P^2). For small values, that approximates to P/2, which by our previous definition of P should be small. E.g. two infrequent strategies that each trade 12 randomly drawn days of the year, should have annualized crosscorrelations of less than 2.5%.
OTOH, if 1) is violated and P is large, then maybe this isn't the right approach. If we're talking about strategies that trade over 50% of the time, then it's probably time to swap back to traditional portfolio analysis. If 2) is violated, then there's probably some deeper connection between the two strategies, that warrants more than a separate black boxes approach.
For example two strategies that each trade 12 randomly drawn days a year should only overlap a handful of days a decade. But if you find them overlapping six days a year, then there's probably some underlying mechanism that's tying them together. Even if the returns themselves don't appear to correlate, it’s probably worth a deeper investigation. 
Good questions outrank easy answers.
Paul Samuelson 



goldorak


Total Posts: 1091 
Joined: Nov 2004 


Just as a side note, there is always an issue with cooccurrences, and it is stronger with "usually" non overlapping strategies. Correlations are not very useful because they rely on averages. They do not protect against single events. The day when both your strats have the same exposure and today is the 'shit hits the fan' day for this exposure, you are in trouble.
To realize how important this is, just think that you would never put both of them in the same portfolio if your past data already contained such a cooccurrence.
In my opinion, the use of correlations for risk management is a sure recipe for overleveraging positions.

If you are not living on the edge you are taking up too much space. 


ronin


Total Posts: 601 
Joined: May 2006 


> Mentally I want to treat them different, but not sure I should. Thoughts?
Just one thought. So say you take @el's example of two strategies where one trades on Wednesday, the other on Friday. You give $100 to each.
Today is Thursday. Strategy A did really well on Wednesday. Its capital is now $110. What are you giving to strat B to trade on Friday  $100 or $110?
Which ever it is, it should answer your question.

"There is a SIX am?"  Arthur 



Rashomon


Total Posts: 214 
Joined: Mar 2011 


EL: If each day pulls from the same distribution.
For US equities this is not the case. Moreover I would expect you could get a lower beta the less you engage with whatever market you are trading in.
If it were me, HitmanH, I would be asking myself my own questions about the robustness of the strategy. The way it "compounds" would be secondary.





@goldorak > In my opinion, the use of correlations for risk management is a sure recipe for overleveraging positions.
I'm not entirely unsympathetic to this criticism. But this issue goes far beyond infrequently overlapping strategies. Even a tenet as orthodox as "bonds diversify stocks" starts to look shaky if you think this way. Yes, bonds and stocks have negative correlation, but they have pretty strongly positive cokurtosis. Their prices tend to move in opposite directions but their volatility moves together. (Which can be seen by plotting VIX against TYVIX.)
For a risk metric sufficiently loaded on extreme moves, like CVaR or drawdown, the impact of cokurtosis starts to outweigh correlation. During periods of extreme stock turbulence, bonds are more likely to rise but they're also more likely to have extreme down moves. Bias your utility function enough on the latter over the former, and the Markowitz implied benefits of bond diversification shrinks or even reverses.
So yeah, you are making a very good point. One worth paying attention to. But it does open a whole can of worms that unfortunately takes the discussion way beyond the scope of the thread.
@rashomon > For US equities this is not the case [that daily distributions are identically distributed]
Definitely agree. That was just a simplifying assumption for a toy model. But the correction is relatively straightforward as long as you have a reliable estimator of the timevarying underlying vol. (Which I think is pretty easily done for US equity indices and a little harder but still doable for US singlename equities). When calculating the proportion of overlapping days, just scale the set intersect/union cardinality by the weight of underlying volatility.
Practically speaking, I can’t really see the adjusted method producing substantially different results. Unless you’re talking about strategies that almost have to be specifically constructed to give funky results. For most normal cases it’d be pretty hard to imagine overlapping days having 50% more volatility than nonoverlapping days. Most likely the difference would be substantially less than that. Going back to the original 12 day vs 12 day example, the upper bound on correlation would rise to 3.25% from 2.5%. In general, if P is O(small), then volscaledP is very likely still O(small). 
Good questions outrank easy answers.
Paul Samuelson 



HitmanH


Total Posts: 498 
Joined: Apr 2005 


@rashomon If it were me, HitmanH, I would be asking myself my own questions about the robustness of the strategy.
I think it depends. If a strategy only works when a, b then c happens in the market, that is a valid point However if a strategy targets something say on a quarterly expiry, that is different 







