# A Sentimental Skew Strategy

[Part of a series on timing the S&P 500 by using the implied skew index, begin here]

Over the previous days, the skew strategy has had improving, but alas, abominable Sharpe ratios.

I have finally stumbled upon a recipe which beats the S&P 500 Sharpe over the last quarter of a century (and now a less than 1% chance of the strategy being noise).

Now our indicator doesn't depend on the level of the skew index but the change in skew month over month.

The assumption is that movements in sentiment are better indicators than the current level of sentiment.

To be specific our weighting of the S&P 500 when the skew index increases (i.e. greater chance of crash) is:

`-ln(Skew(t)/Skew(t-1))`

and double when it drops

`-2*ln(Skew(t)/Skew(t-1))`

On average our portfolio is ~2% long the S&P 500 and 98% cash.

Without the doubling we would have something closer to a type of symmetry and on average just have 0.03% of our portfolio in the S&P 500. The doubling is pretty arbitrary (perhaps there's a more solid reason?) but being slightly net long gives the strategy a little more pep.

The cumulative Sharpe over 25 years diverges during the dot-com days. Our skew strategy stays remarkably steady however for 20 years.

2008 sees a large drop but a very quick bounce back - much quicker than the S&P 500.

Also, our strategy is finally showing positive skewness.

This histogram shows the monthly returns of the S&P 500 over the last 25 years. The skewness statistic is about -1.

The left tail is far longer than the right.

Quite the opposite with our skew strategy. Losses are a lot more limited in magnitude than gains. The skewness statistic is about 3 or 4.

To top it off the beta between the S&P 500 and our strategy is only 0.02.

Let's not get too carried away. We have barely beaten the vanilla S&P 500. Plus I have happily ignored trading fees and other factors.

Not sure how much more can be reasonably pulled from the skew index as an estimator. I am surprised it's performed as well as it has done.