Oct

4

Even if there were no drift and you could make an equal case for the long or short based on studies, since the thing is for the most part random it is good to think about what happens when you get it wrong. If you limit yourself to long only, there is one way to screw up instead of two:

Position: Long
MKT:      DN

Position: Long Short
MKT:      DN    UP

One could consider limiting trading directions as risk reduction (i.e., less ways to lose). But in that risk should be compensated, should not trading both long and short, on average, produce higher returns? Or is the long-only advantage completely attributable to drift?

SPY daily returns for the past 10 years were (expressed as decimal fraction):

avg    1.00038
stdev 0.01200

This standard deviation was plugged into a random number generator, which simulated 2500 daily returns having a normal distribution with a mean of 1.0 (or zero daily return — a simulated market without drift). Then twenty different traders held these daily returns either only long, or half long and half short. Here is data for 20 longholders, with the product being the final compounded amount:

avg     stdev   prod
0.9996 0.0120 0.3410
0.9996 0.0122 0.3387
0.9996 0.0118 0.3445
0.9997 0.0124 0.4210
0.9998 0.0117 0.4857
0.9998 0.0122 0.5506
0.9999 0.0118 0.6535
0.9999 0.0123 0.6779
1.0000 0.0122 0.7678
1.0000 0.0121 0.9391
1.0001 0.0121 1.1213
1.0001 0.0119 1.2052
1.0002 0.0121 1.2838
1.0002 0.0121 1.3532
1.0002 0.0120 1.3768
1.0002 0.0122 1.4747
1.0003 0.0122 1.6099
1.0003 0.0121 1.8312
1.0003 0.0125 1.9530
1.0004 0.0122 2.0176

av daily  sd  cpd ret
1.0000 0.0121 1.0373

As expected, the overall average daily return for being long all the undrifting days was 1.0, and the average compounded return was 1.037 (+4%).

Here is the data for the strategy of long 1/2 the time and short 1/2 the time:

avg     stdev   prod
0.9995 0.0121 0.2469
0.9996 0.0124 0.2683
0.9997 0.0122 0.3479
0.9997 0.0118 0.3713
0.9997 0.0121 0.4079
0.9998 0.0123 0.5301
0.9998 0.0117 0.5398
0.9998 0.0122 0.5621
0.9999 0.0120 0.6176
0.9999 0.0122 0.6380
0.9999 0.0118 0.7248
0.9999 0.0121 0.7264
0.9999 0.0119 0.7374
1.0001 0.0122 1.1389
1.0001 0.0120 1.1730
1.0001 0.0121 1.1836
1.0002 0.0125 1.2056
1.0002 0.0122 1.4407
1.0002 0.0122 1.5368
1.0004 0.0120 2.2918

av daily  sd  cpd ret
0.9999 0.0121 0.8344

As expected, the mean daily return was essentially 1.0. However the average compounded return was 0.83; futher away than long-only (I suspect this is due to too few cases, and with more traders than 20 this would be closer to 1).

One measure of risk is the dispersion in compound returns. Long only ranged from 0.3410-2.0176. Long/short ranged 0.2469-2.2918, which is substantially larger.

So while long only and long/short simulated strategies give similar average returns in a no-drift market, the greater dispersion of long-short suggests greater risk.

Now if you put the drift in …


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