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The Siren of Statistics

A siren was a mythological being who lured sailors with their enchanting music to shipwreck on the rocky coasts of their island. Their songs were almost impossible to resist. But more generally a “siren” is a bad thing that we are attracted to, either physically or psychologically.
For investors, an example of a siren’s song is simplicity. Many investors are prone to looking for just a few metrics to evaluate a fund or a strategy. This is a problem. It is a problem for me because my answers to reasonable sounding questions will be incomplete. “What is your Sharpe ratio?” sounds reasonable enough. But the answer on its own is close to meaningless without a much more detailed elaboration. What is the sampling error around the point estimate? How constant has it been across sub-periods? How distorted is it due to the shape of the full return distribution? But, more importantly, it is a problem for the investor because the simple answer gives a false sense of certainty.
Is the Sharpe rat…
Recent posts

The VIX is Not Broken

On April the 24th, the Wall Street Journal ran a story detailing the huge move of the VIX index in the opening 30 minutes of trading on the previous Wednesday. The VIX spiked up 12% in 30 minutes despite the underlying S&P 500 index not moving much at all. To put this 12% move into perspective, the current expected move in a 30-minute period is less than 2%. In addition to being a large move, the timing was suspicious. It was during this period that the settlement price for the April VIX futures was calculated. Anyone holding a long futures position would have benefitted greatly, at the expense of the shorts.
There have been rumors about the manipulation of the VIX index for many years. Whether or not the anomalously large S&P 500 option trades during the settlement period are evidence of manipulation, part of an arbitrage or just coincidence, the fact is that the VIX settlement period is often atypically volatile. This is alarming for market-makers and professional arbitrage…

New Volatility Regime

The equity market hasn’t really decided what it wants to do. However, we are now very clearly in a new volatility regime. From the start of 2017 through to the end of this January, realized volatility was 6.9%. In February and March, it was 23.6%. 

Below I show the S&P 500 from the start of 2017 until the end of this March.


Things have changed.

But what is particularly interesting to me is how exactly things have changed, because that is a little unusual. 

Generally periods of high volatility have one major cause: the Asian crash, LTCM blowup, the dot-com bubble or the housing credit crisis. But this year we have had two distinctly different periods.

The start of the turmoil was on Friday, February 2nd, when the S&P 500 dropped 2.1% and the VIX rallied 28.5% from 13.47 to 17.31. This was a large move: the 34th largest in history. But Monday the 5th was truly exceptional. The S&P 500 dropped 4.2%, but the VIX rallied 115.6%. This was the largest VIX move ever, and nearly twice t…

Adversity and the Variance Premium Part 2

Following on from the last post we will now look at how the concept of adversity can lead to the variance premium.
Let’s think about a $100 stock and the $100 strike call and put. Assuming no interest rates or dividends, and a volatility of 30%, both the one-year call and put will each be worth $9.92. One trader sells the put, and another buys the call. Now let’s look at two price paths for the stock.
Case One:
On the first day, the stock jumps to $119.84. It stays there until expiration. Each trader makes $9.92 at expiry, but the PL evolves slightly differently over time.


Figure One: PL for short put.


Figure Two: PL for long call.
Now consider the case when the jump happens right at expiration.


Figure Three: PL for short put.



Figure Four: PL for long call
My contention is that the shape of Figure Four is the one most preferred by investors. That the long option maintains the ability to “snatch victory from the jaws of defeat” is important. People prefer this, which points to options…

Adversity and the Variance Premium

Recently I’ve come to believe that we don’t know nearly as much as we think we do. Specifically the history of markets is nowhere near as big as we often assume. For example, equity options have only been traded in liquid, transparent markets sine the CBOE opened in 1973. S&P 500 futures and options have only been traded since 1982. The VIX didn’t exist until 1990 and wasn’t tradable until 2004. And the average lifetime of a S&P 500 company is only about 20 years. 
This might seem like a decent length of history that we can study and look for patterns in. But I doubt that it is. I think that while there appear to be many thousands of data points, there might only be dozens. Options and volatility wiggle around a lot but their long-term values are related to macro variables such as inflation, monetary policy, commodity prices, interest rates and earnings. And these change on the order of months and years. Even worse, they are all co-dependent.
I think this …