If you belong to the tiny group of non-random traders, then you may find this article interesting. If not, then this article is probably a must read.
Note that random trading is a valid method. As a matter of fact, random trading may be more profitable than algo trading under certain conditions.
Below are simulations of random SPY trading and year-to-date results. All simulations are based on coin tosses. Starting capital is $100,000 and commission is set at $0.01 per share. Equity is fully invested at each new position. All trades are entered and exited at the close (this is realistic since random trading does not involve calculation of signals.) Random year-to-date results are repeated 20,000 times to determine the distribution of the net return of random systems. There are five cases included, with results summarized on a table at the end.
Case 1: Fair coin. Long (heads)/Short (tails) positions.
Probability of a positive return is 44.52% and probability of a return above buy and hold is 35.6%. A 10% test return is not significant (p-value = 0.216)
Case 2: Fair coin. Long (heads) positions only (exit signal: tails)
Probability of a positive return is 55.2% and probability of a return above buy and hold is 37.2%. A 10% test return is not significant (p-value = 0.118)
Case 3: Fair coin. Short (tails) positions only (exit signal: heads)
Probability of a positive return is 34.1% and probability of a return above buy and hold is 19.3%. A 10% test return is significant (p-value = 0.039)
Case 4: Biased coin. Long (heads, p = 75%) positions only (exit signal: tails)
Probability of a positive return is 69.9% and probability of a return above buy and hold is 17.5%. A 10% test return is significant (p-value = 0.000)
Case 5: Biased coin. Short (tails, p = 75%) positions only (exit signal: heads)
Probability of a positive return is 54.9% and probability of a return above buy and hold is 2.1%. A 10% test return is significant (p-value = 0.000)
Summary
Note that uses of biased coins at p = 75% for heads results in position trades that last about 8 days on the average.
| Trade and coin type | Prob. ret. > 0 | Prob. ret. > b&h | 10% ret. p-value |
| Long/Short fair | 49.5% | 35.6% | 0.216 |
| Long fair | 55.2% | 37.2% | 0.118 |
| Short fair | 34.1% | 19.3% | 0.039 |
| Long bias (75%) | 69.9% | 17.5% | 0.000 |
| Short biase (75%) | 54.9% | 2.1% | 0.000 |
Conclusions
- A random long-only position trader has higher probability to win but lower probability of outperforming buy and hold
- A random EOD trader has lower probability to win but higher probability of outperforming buy and hold
- Random EOD traders (long/short) have high probability (about 36%) of outperforming buy and hold
Note that the probabilities are not stationary but change with market conditions. However, over the longer-term high probabilities increase and low decrease.
More details can be found in chapter four of my new book.
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