Daily Speculations
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Daily Speculations |
06-Jun-2006
Don't Have a Crystal Ball? from Kim Zussman
In the absence of a crystal ball (like the one with Maria wearing an "I Dream of Greenie outfit"), and beyond research results, investors might have a particular overall bias towards stocks. Bullish? Bearish? Where to you tilt when the compass of research is spinning rather than pointing?
Here is an empirical simulation of two trading firms with random strategies in an ideal world without transaction costs. Both held various days of the actual returns of ETF SPY from 1993-2006, and both had 10 traders each. Traders at 3-way LLC on any day will be long, short, or 100% cash, each with a random probability of 0.34, 0.32, and 0.34 respectively. Longjohn BFD traders could only be long or 100% cash, each with a random probability of 0.5 (these traders flipped a coin before each close to decide whether to own the next day in SPY).
Here is ANOVA comparison of 13-year means for the returns of 10 traders in 3-way, along with "day rt", which is the benchmark of holding all days (error bars are 95% confidence intervals):
Individual 95% CIs For Mean Based on Pooled Stdev.
Level N Mean StDev --------+---------+---------+---------+-
r1 3363 -0.000326 0.008935 (--------*--------)
r2 3363 0.000093 0.008846 (--------*-------)
r3 3363 -0.000070 0.009115 (--------*--------)
r4 3363 0.000095 0.009121 (--------*--------)
r5 3363 0.000097 0.009040 (--------*--------)
r6 3363 0.000091 0.008663 (--------*-------)
r7 3363 -0.000109 0.008919 (--------*--------)
r8 3363 0.000297 0.008950 (-------*--------)
r9 3363 -0.000124 0.008976 (-------*--------)
r10 3363 -0.000055 0.009109 (-------*--------)
day ret 3363 0.000441 0.010855 (--------*-------)
--------+---------+---------+---------+-
-0.00035 0.00000 0.00035 0.00070
From this we see that daily means for all of the traders were lower than all days, and since shorting is allowed some were even negative.
Longjohn traders, who can only be long or cash, are compared here with all days:
Individual 95% CIs For Mean Based on Pooled Stdev.
Level N Mean StDev -+---------+---------+---------+--------
r1 3363 0.000010 0.007705 (----------*----------)
r2 3363 0.000289 0.007622 (----------*----------)
r3 3363 0.000180 0.007925 (----------*----------)
r4 3363 0.000275 0.007870 (----------*----------)
r5 3363 0.000145 0.007880 (----------*----------)
r6 3363 0.000156 0.007569 (----------*----------)
r7 3363 0.000253 0.007780 (----------*----------)
r8 3363 0.000129 0.007906 (----------*----------)
r9 3363 0.000311 0.007957 (----------*----------)
r10 3363 0.000238 0.007575 (----------*---------)
day ret 3363 0.000441 0.010855 (----------*----------)
-+---------+---------+---------+--------
-0.00025 0.00000 0.00025 0.00050
In this group, though the limitation of no shorting prevented traders from averaging down, being in the market 100% of the time was still best (though N.S.).
How did the two trading firms do against each other, and against the market?
Individual 95% CIs For Mean Based on Pooled Stdev.
Level N Mean StDev ----+---------+---------+---------+-----
day ret 3363 0.000441 0.010855 (-----------*----------)
all 2way 33630 0.000199 0.007780 (---*---)
all 3way 33630 -0.000001 0.008969 (---*---)
----+---------+---------+---------+-----
0.00000 0.00025 0.00050 0.00075
3-way did significantly worse than 2-way (Longjohn), and significantly worse than buy and hold (day rt). Longjohn (2-way) was lower than all days, but not significantly so.
One conclusion is that for periods when one is uncertain about the market (in the absence of compelling research), over this period it was better to be long. The addition of transaction costs would exaggerate the differences, and the message for the compelling is obvious.