# Skewtosis - An investment strategy

The strategy is NOT a feasible strategy as I've recently deduced and tested.   If you are still interested in my idea process then read below.  If you are interested in why it doesn't work what so ever then press here

Like modern portfolio theory and many investment strategies, Skewtosis relies heavily on historical data. I recently read an article on how to not use the Mean-Variance optimizer and it echos closely to my mistake with Skewtosis.  We use the data previously observed to help us establish a strong set of beliefs towards certain properties of the stock such as Expected Returns, Volatility, VaR, Margin Debt, Skewness, Kurtosis, etc.  Of course, previous data sets cannot be used to accurately, if at all, forecast itself through the naive method: .  A friend of mine suggested of using out-of-sample backtesting for Skewtosis to see how well it performs.  I thought it was a genius idea as this will yield more meaningful results than before.  Just as I had thought, a portfolio of 45 stocks that exhibited good Skewtosis from 2006 to 2011, underperformed the S&P 500 benchmark each year from 2011 to 2014.  And it makes total sense!  My backtest periods were relatively within the same timeframe as my screen.  If a stock historically had shown good upside return, wouldn't it of already incurred those returns in the backtests?  Moving forward, I will know to always test a hypothesis through out-of-sample tests, examine these properties through timeseries analysis and most importantly to be less susceptible to this type of error (as NNT might call it, the turkey error).

Recently, I've came up with a strategy that have shown to consistently beat the market when applied. It is a quantitative method that involves two very simple statistical measures: Skewness and Kurtosis.

Skewness is the measure of asymmetry in the distribution of a random variable. It is calculated by taking the third standardized moment. I don't know much more about it mathematically but graphically it's a distribution with a longer tail towards either the left (negative skew) or right (positive skew).

Kurtosis is the measure of peakedness of the distribution of a random variable. It is calculated through taking the fourth standardized moment. Graphically, a positive excess kurtosis (Leptokurtic) looks like taking the top of a bell curve and pinching it up. The reverse is true with a negative kurtosis, instead of pinching up, the distribution is being flattened from the top.

Stock Market returns are often leptokurtic due to non-linear properties in financial price movements.  However, the reverse is also true where in a leptokurtic security, the distribution of returns are more centered around the mean, thus we are more likely to expect the mean returns on any given day.  Incorporating Skewness into this equation, we want to be sure the asymmetry is more skewed towards the positive returns.  This investment strategy is obviously susceptible to systematic risk such as financial crises, recessions, etc.  At the current level of research and understanding, it is near impossible to predict these large drawdown periods (no the dragon-king isn't the miracle solution).  We ultimately acknowledge this flaw so we can be more skeptical of its efficacy in the future as well as work on extensions to the strategy to mediate this problem.

The investment strategy is to minimize the Skewness to Kurtosis ratio:

Bloomberg has a stock screener (EQS) and historical back tester (EQBT).  The Screener doesn't allow custom ratio inputs so I just screened for stocks that have a negative skew and positive excess kurtosis.  In addition, to lower my choices, I made additional criterias of: Average Volume last 6 months >= 1 million, P/B Ratio <= 2.36 and Last Price >= \$2.  See pic:

I was happy with my 65 results. It was time to put it to the test.  On the first run of all 65 stocks I set the following conditions:

- Equal Portfolio Weighting

- 10 year time horizon

- Benchmark against the S&P 500 Index using USD as the primary currency.

The results were profounding as the portfolio have outperformed the market every year following relatively the same path as the market.

Excess Total Portfolio Return: 69.8%

Max Excess Portfolio return: 92.69%

10 Year Sharpe Ratio: 0.41 vs 0.37

10 Year Jensen's Alpha: 1.89%

Here's the summary picture:

To control the experiment, I launched another backtest this time without the P/B screen and the number of securities screened went up to 147.  P/B Ratio is often a good indicator for future stock returns,  I have performed a series of factor testing before and found sorted quantiles to be extremely more consistent than any other financial metrics.  The new backtest was fantastically similar and even improved in performance (although this could be due to more diversification):

Excess Total Portfolio Return: 94.2%

Max Excess Portfolio return: 98.41%

10 Year Sharpe Ratio: 0.45

10 Year Jensen's Alpha: 2.67%

Improvements all across the boards!

Here's another summary picture of this:

I later did a series of backtests by separating stock classes into High Skewtosis and Low Skewtosis, hoping that the low class would produce higher returns.  The results at the time was mixed and inconsistent, but as I'm typing out the results right now, I realize there might of been a few blunders I committed in those screens.  I will not be revisiting for a good while (they take ages to fully backtest).

I plan to be investing some of my stocks this way as I believe from historical data, I might of found something worth more investigation. I had recently learned the basics of Markowitz's portfolio theory and planning on doing some sort of a Matlab + Quandl + Efficient frontier solution soon for my screened 147 stocks. Stay tuned for that 🙂