I recently had a conversation with a work friend of mine, Kate, who was interested in seeing whether or not random stock picking could consistently beat the market. Kate’s original idea was to randomly pick one stock at the beginning of each week to purchase, hold for twelve months and then sell at the end. As an avid investor, who struggles with finding new stocks to invest in, and also determining when to buy and sell, I feel that if a strategy like this could work, it would take away a significant amount of mental effort on my part when investing. After a few conversations back and forth with Kate, who originally wanted to tackle this project herself, and an agreement to share the process, she finally relented and allowed me take her idea and test it out, thanks Kate!

In this post I will perform a statistical hypothesis test to determine whether or not random stock picking can consistently beat the market, this will be limited to the market context of the ASX.

## Hypothesis

My hypothesis when Kate was originally talking about the idea, was that a random selection would not be statistically significantly different to the performance of the overall market. I believe that the average return of random stock picking would normalise to be the same as the overall market over the same period. However, as I consider the problem in greater detail, the stocks in the market do not all have a equal weighting to the total performance as some have significantly more market capitalisation compared to others. This difference in contribution, depending on market performance of the stocks may temper or bolster the average percentage movement of all stocks. Statistically, there is more probability of the random choice landing on a smaller capitalisation stock, than one of the market behemoths, like Commonwealth Bank (CBA) or BHP Billiton Limited (BHP). Which make up approximately 12% of the ASX in market capitalisation, whilst being 0.00086% of the unique stocks available on the ASX as of August 2018.

Therefore, the hypotheses I am testing are:

**H0:**Random selection is equal to performance of overall market.**H1:**Random selection is not equal to performance of overall market.

## Assumptions

The hypothesis test will make the following assumptions:

- Stocks will be picked at random.
- A new stock will be picked each week for 52 weeks and “purchased” at close price of the first working day of the week.
- Each stock will be held for 52 weeks and then “sold” at close price of first working day of the 53rd week after purchase.
- Profit or loss of a stock will be the difference between “purchase” and “sold” price.
- Profit or loss of all stocks will be the average percentage difference of all 52 random stocks picked.
- Total Market performance will be the difference between the All Ordinaries index close price on the first “purchase” date and the close price on the last “sell” date. The All Ordinaries index was chosen as it is considered to be the ‘total market barometer for the Australian market’ and ‘accounts for 93% (March 2018) of the Australian equity market’ [1].
- Sample is normally distributed.

## Test statistic

As we do not truly know the population\ variance, it is appropriate to test the hypothesis using a Students T-Test.

The sample fails the assumption of being normally distributed, as you can see below.

However, the T-Test is also heavily effected by outliers, after removing the outliers, using a Median Average Diversion test with a threshold of 3.5 s.d, the sample falls much closer to normal distribution allowing the T-Test to be used. Removing the outliers results in a skewness of 0.735 and a kurtosis of 0.440

## P-Value

The one sample T-Test results in a test statistic of -5.02 and a P-Value of 5.28e-07.

## Conclusion

As the P-value is so small, there is strong evidence against our H0, indicating that random stock selection does not have the same performance of the market. As the test statistic results in a negative number, random stock picking performs worse than the market.

This experiment was relatively simple, and does not implement any investment trading plans that many use to dictate how they trade. it simply picks a random stock, and holds it for 12 months before selling the stock regardless of market movements over the 12 month period. This raises the question, would the performance of the random stock picking change if a set of the rules were implemented? In a later post I will see how the implementation a set of standard rules for stop loss, and profit take will effect the performance of random stock picking.

For those interested, please see this GitHub repository which holds the data, and the statistical tests that were performed.

## References

- MarketIndex.com.au. (2018, August 09).
*All Ordinaries.*Retrieved from Market Index: https://www.marketindex.com.au/all-ordinaries

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