5% annual return inflation in simulation return

hi,

somebody may have figured out the answer to the issue i have at hand. But not me so far. Here is the situation. I created the following simulation:

Benchmark: SP500
Universe: SP500
Transaction price: next close
Number of stocks:5
Ranking system: Random
Transaction cost: zero
Rebalance: weekly
Buy rules: None
Sell rules: Rank < 101

Using the “optimize” under tool, I repeated the simulation many times and only to find that the annualized return is always around 10%, 5% higher than the annualized return of the benchmark SP500. In my mind, the random function will create an average simulation return very close to the Benchmark. But it is not the case.

Does that mean in my other simulations there is such inflation as well?


What happens if you compare your optimization to the benchmark S&P500 Eq Weight?
Steve

Thanks Steve,

I tried re-running the simulation with “S&P 500 Eq Weight”. In this case, the benchmark’s annualized return increased to 8% from 5%. However, there is still a gap of 2% per year. I guess that is better than the previous 5%, where the comparison is not really apple to apple.

SH

Dividends.

hmm, if the benchmark, “S&P 500 Eq Weight”, doesn’t include dividends then the gap of 2% could be explained as we know the simulation results include dividends.

SH

Use 1 stock sims instead of 5 and download the weekly performance data for many runs of random. For every week, you now have a sample of a single stock’s return (equal weighted including dividends just as your regular sims calculate return). Average enough of those samples and you’ll have a more accurate benchmark. I believe you’ll find that 5 stock random sims do, on average, measureably worse than the average of the universe as a whole. The distribution of single stocks within most any broadly defined universe are very far from normal, so it takes at least 30 stock sims for the law of large numbers to bring the sample averages into alignment with the population average.

I am not sure what ranking system you are using. I found that mine, when I did the same experiment, was not random - it was selecting the same stocks over and over. I found the following random ranking on P123 and have been using it. It does give me random results in a simulation (over say 100 runs):
https://www.portfolio123.com/rank_about.jsp?rankid=252484

Here is the sim I created:
https://www.portfolio123.com/port_summary.jsp?portid=1311036

I remember now that the random function does not work in a ranking system. I think it has to do with caching.
Steve

Use the benchmark SPDR S&P 500 ETF Trust. It includes the dividends.

The random function does recreate new random ranks every time it is run. At one time in the past the rank values of the Random function used to be cached, but Marco fixed that a number of years ago.

But the ETF is not equal weighted, I assume

Do you just want the mean of the population (and not the standard deviation of your sample population)? If you want the mean of the population find it directly:

Use the screener with SP500 as the universe. Set Max No. Of Stocks (0 for all) to zero. Set slippage and carry cost to zero. Adjust the start and end date to the desired period. SH, I assume you will want to keep weekly rebalance. Click Run Backtest.

As SUpirate1081 has mentioned in a previous post on a similar subject, you will have to think about the effect of compounding: if you run more than a year do you want the arithmetic mean or the geometric mean? I do think this might be better than running multiple samples if you are interested in the population mean.

[quote]
I believe you’ll find that 5 stock random sims do, on average, measureably worse than the average of the universe as a whole. The distribution of single stocks within most any broadly defined universe are very far from normal, so it takes at least 30 stock sims for the law of large numbers to bring the sample averages into alignment with the population average.
[/quote]I created a screen here to test random portfolios. I was surprised to see how much returns vary from one run to the next even for 250 random stocks.

Thanks all. I guess the equal weighted SP500 index is the most comparable benchmark. Probably it is difficult to get exact the same return as that of the benchmark. 2% difference is unlikely to render the simulations invalid.