In general, investors cling to rather boring strategies.  Very few investors short stocks so the vast majority of trades revolve around long positions with hopes of getting timing right via momentum or valuation plays.  When investors get scared about their long positions they tend to buy puts (even though long volatility might serve as more efficient protection) or sell out of positions.

Today, let us broaden our horizons.

First, let me say that I am tired of hearing and reading about fat tails.  I really liked Nassim Taleb’s Fooled By Randomness, but when Black Swan became a hit, the meme became overwhelming.  The book, along with the 2008 crash, gave everyone the full and utter knowledge about how fat tails happen often and how you would be stupid to believe otherwise.  When you talk about selling options, you often get harassed by those who know the truth.  I say bullocks and read through this link first if you want to argue about it.

Most things in life cannot be distilled to one sentence.  With  regards to the topic of fat negative return tails, this is also the case.

Positive and Negative Tails on the S&P 500

The chart above is extremely interesting because it depends on the time window you are looking at.  When I looked at daily returns, the distribution was definitely skewed towards negative returns.  When you look above you still see the effect in weekly and monthly returns.  With quarterly data you start to see this relationship break down with a greater number of +20% returns than negative 20% and nearly equal observations of +/-30% and +/-40% quarterly returns.

Looking further, when you compare the option implied quarterly return probabilities to the historical observations, put options look massively overpriced whereas some call options look underpriced.  Then you get the idea of stock replacement.

A stock replacement strategy can mean many things, but generally it means that you replicate a long stock position with derivatives.  The truest form would be the purchase of a call, sale of a put at the same strike and investment of the notional amount of the options in a risk free bond for the tenor of the options.  The strategy can be tweaked by selling puts of different tenors and strikes of the purchased calls.  By selling a longer maturity put that is further out of the money, you reduce the probability of losses by giving yourself a buffer for stocks to drop.  Regardless of what strikes and maturities you choose,  stock replacement strategies in which calls are purchased through a subsidy of written puts should outperform long only positions.