Better Than An Equity Curve
Consider the example equity curve below from our recent test of the DVI Indicator (strategy in red, S&P 500 in grey).
[logarithmically-scaled, growth of $10,000]
I fear that when I show an equity curve like this the conclusion that folks come to is that prior to 2000 or so the strategy didn’t outperform buy and hold.
That is precisely the wrong conclusion.
The problem is that from this 30,000 foot view we can’t see all the hundreds of drawdowns and the unnecessary volatility that the strategy would have prevented. In other words, we see absolute returns and not risk-adjusted returns.
But back in the real world, drawdowns and volatility hurt. They lead to poor decision making. They make us abandon well-devised strategies and perpetually chase the hot hand. Anyone who says that absolute returns are all that matter has no experience trading actual capital.
Summary statistics like the ones I include in all of my tests help put returns into some perspective, but even those are insufficient because numbers don’t have the visceral, gut impact of an equity curve.
What to do…what to do…
Better Than An Equity Curve
Occasionally I’ve shown a graph of rolling volatility-adjusted returns, like so…
This is a rolling graph of the 5-year annualized return divided by annualized standard deviation of the strategy (red) versus the S&P 500 (grey) since 1970.
Here we’re not looking at returns in the absolute sense, but returns relative to volatility (and to some degree risk) over time. Without a doubt, when comparing a strategy to a benchmark, I think this is a far superior measure of the magnitude and consistency of the kind of outperformance that really matters.
We can even take this a step further and subtract the grey line from the red line to produce a graph of rolling excess volatility-adjusted return…
It should now be abundantly clear that the strategy has, with the exception of a few brief periods, trounced the benchmark. This is a much better representation of what investors would have actually felt month-to-month and year-to-year.
So why not always use this better approach?
I’m in a constant balancing act between making this blog smart enough to attract like-minded geeks and accessible enough that any reasonably intelligent person could follow along, and I worry that the enormous significance of this rolling approach is lost on some readers.
But I’m thinking now that when faced with this kind of problem I should err on the side of geekiness. Expect to see much more of the rolling vol-adjusted return graphs in the future (and if I forget, be sure to hold my feet to the fire).
Happy Trading,
ms
P.S. rather than returns versus volatility we could be looking at other measures of risk-adjusted performance such as average drawdown, the Ulcer Index, etc. Also note that I usually use a 5-year rolling window because it’s a nice middle-ground between results that are too noisy and too lumbering, but there’s no reason we couldn’t use 1-year, 20-years, etc.
. . . . .
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Filed under: Random Stuff | 9 Comments
How about showing a leveraged version, perhaps with the amount of leverage scaled to equal the ratio of strategy’s annualized volatility to that of the S&P 500.
RE to Josh: smart comment sir. What I wouldn’t like about that is that “risk” as defined by annualized volatility is very different than true “risk”. For example, a strategy that is 200% invested on half of all days and 0% invested on the other half may look on paper to have similar annualized volatility when in truth there is much, much higher potential risk (should the market make a big move against us).
I think that unless we’re managing actual potential risk (such as with a pairs-trading strategy) then it’s not fair to add the leverage.
Just my $0.02. Great comment. michael
Michael,
That’s a good point about annualized volatility. Then how about de-leveraging (i.e. holding some cash) the S&P so their vol is the same. My suggestion was intended more for making the risk-adjusted performance visually clear to readers who might be quick to think the strategy underperformed pre-2000, than staying true to the maths of annualized return/volatility. ;)
On a somewhat related note, I wonder how the DVI does on US bonds? And how does a DVI strategy applied to bonds and the S&P compare to the classic 60/40 portfolio?
Josh
Thanks, Michael. Nice post.
I wonder if you would get a smoother graph by using a rolling EMA instead of a rolling MA. The severe rises and falls (e.g., 1988(?) and 1993(?)) look very strange. I suppose ’88 was a particularly bad year, which fell off the average in ’93 just as 2008 will fall off the average in 2013. It would be interesting to see how a graph of the rolling return EMA divided by the rolling vol EMA compares to a graph of a long period EMA of return divided by a long period EMA for the vol.
RE to Blue: I’m guessing that’s October 1987 (this particular strategy was long on Black Monday). Good point re: using an EMA vs SMA. Would have smoothed the later jump (but increased the size of the first jump). Will have to try it out the next time I show one of these. michael
I have been debating (internally) also about how to “normalize” returns and decided to go with Drawdown, namely MaxDD – it is not ideal though, as it is a more error-prone stat – but from a practical investment perspective I find that it describes risk better and ultimately drives what sort of leverage you could have applied (ie 2x notional funding on 50% DD would wipe you out, etc.)
I guess, like most performance metrics what really matters is how it affects you and there will not be any ideal solution though…
RE to Jez: I personally don’t put too much importance on Max DD because it does such a poor job representing the entire period tested. Let’s say you’re testing two long-only strategies. Strategy A could be far, far better than strategy B but because A happened to be long in October 1987, it gets marked as worse than B. Too much importance on (potentially) one single day I think. I much prefer the Ulcer Index or annualized return vs average drawdown or something to that effect. Just my $0.02. michael
Looks like a Sharpe Ratio analysis?
And suggests a mean reversion trade…. Buy when below zero and crosses above, sell when above zero and crosses below?
RE to Carl: exactly like a rolling Sharpe Ratio without the risk-free discount. A Sharpe Ratio would have worked perfectly well, Ulcer Index, etc.