Feb

9

When the market gets going in one direction like it has lately I usually get a bit frustrated. Not so much because I am losing (I have given up trying to pick tops and bottoms when there is anything beyond my opinion at stake) but more just because the market has such a propensity to go to extremes and it is hard to handicap extremes. Usually I swear off shorting and make general untested comments like “buying over the long haul is the only way to go” right before a big reversal.

I decided to test this phenomenon by looking at the close/open change in the SPY from 1/2000 to end of Jan 2012. I found the average result was -0.01%. Max was +8.43%, min -8.99%, st dev 1.16%. Of the 3039 days, 51.5% were up. I found this to be interesting because the distribution was fairly normal. This could all be a function of the central limit theorem (CLT) but regardless of reason, sort of renders my conclusion that it pays to only go long wrong. As an aside, it is interesting to consider the CLT as a trading device, I do not believe it can be proven wrong over enough observations and time—solvency remains the concern.

Anyway, I next examined the calendar years and found that there are biases within years. They are subtle but they exist. More evidence of the CLT causing the near zero expectation over the long haul. I drilled further (weekly/daily) and found more biases.

Looking at it this way, I would say that it pays to be both long and short, the distribution is approximately normal over the long haul and therefore there is no great bias to long vs. short. The frequency goes to the longs but the magnitude advantage of the shorts renders the longs neutralized. On shorter horizons the biases become more evident. If you can pick the sub periods correctly, you will outperform.

But stepping back, I look at it another way. If I go long every day I would be down very small. If I go short every day I would be up very small. If I go long and short my outcomes vary. If I hit every day correctly, I will drastically outperform. If I hit every day incorrectly, I will drastically underperform. Given the distribution is normal, the expected return of batting 50/50 with a long/short approach is about break even.

So while the simple math indicates I am equally benefited in being long or short, the reality is I have to be right. Therefore I believe it may make more sense to just be directionally biased. Over time the central limit theorem will bail me out. If I use counting or fundamentals or value or common sense or some combo of these I can likely find more opportune times to be in/out of my directional play, upping my chances of success with a CLT kicker. Adding a trailing stop would likely help. I could, in theory be directionally biased picking every single day wrong, but the odds of this generally seem less likely than getting chopped up being long/short. I have not quantified this however.

Thoughts?

Rocky Humbert writes: 

Without commenting directly, there are two big things you didn't mention:1. Convexity. This is a fancy way of saying that, stock prices cannot go below zero. But they can rise infinitely. This may seem like a nonsense statement, but I raise it because you raised the central limit theorem. If the stock market is truly and completely random (and has no long term drift), if you play a monte carlo simulation long enough, the S&P will print at a price of 0.0000000001. It will also print at a price of X–>infinity. Hence, there is a clear mathematical benefit to being long versus being short, ceteris paribus…. because the sum of infinity and zero is a BIG positive number … 2. Cost of carry. Again, assuming that there is no drift, when the risk free rate is substantially below the dividend yield, there is a (perhaps illusory) bias to holding long positions. When the risk free rate is substantially above the dividend yield, there is a (perhaps illusory) bias to holding net short positions. And, unless you are always 100% long or 100% short, there is also the cash yield on uninvested cash. Perhaps some other specs have studied the market behavior when stocks have positive/negative carry — I haven't. However, it's generally accepted that a substantial portion of the return in stocks is attributable to dividend yield, so this should be considered. To repeat, I'm not directly responding to your question. I'm pointing out two considerations that you didn't mention.

Tim Melvin writes:

While not the worlds greatest math or stats guy I think your test period may be giving you information that becomes less true with time. The period you use has two major market crashes in less than decade giving more bias to the short side results than you might have gotten if you studied 1988 to 2000. if you believe the next twelve years will look like the last 12 in terms of market behavior and volatility then you study holds up well if it doesn't then perhaps not so much…

George Coyle responds: 

Interesting point Tim and Rocky. When I graduated college (2000ish) it was a forgone conclusion you could expect the stock market to return 8% or so a year, year in and year out (well over a horizon at least). The last 10 years have proven otherwise. Ever changing cycles. Would be interesting to study the impact of generally accepted academic market conventions and what happens in reality once they become doctrine. Hard parameters to concisely define though.


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