# Dissecting Volatility

It is one thing to say that the market is volatile.  It is quite another to appreciate fully what that really means.  So let’s spend a moment to dissect volatility.

## The Current Level Of Volatility

The first thing to make clear is how is volatility measured.  One way is to use historical data.  The data necessary to estimate historical volatility is not a series of past prices, but past daily returns.  The return is the percentage change in price adjusted for any payouts.  Because payouts during that last couple of months have miniscule compared to price fluctuations, you can think of the return as the percentage change in price.  To measure volatility, you cannot average past returns because positive and negative returns cancel each other leading to a vast underestimate of volatility.  Therefore, volatility is measured by either the standard deviation of the returns, or more simply by the average of the absolute values of the returns.  In most cases, the two estimates are quite similar.

By these measures, how volatile has the aggregate value of all U.S. publicly traded stocks been over the last three weeks?  The average daily absolute price change comes to about 6.5% (with some negative and some positive).  This level of volatility means that every day you can expect the market to move 6.5%.  To appreciate how astonishing this is it is helpful to keep two observations in mind.  First, remember that the value of the aggregate stock market is the present value of the cash flows to equity owners expected to be produced by all listed companies in all future years.  Second, that present value is a big number.  At the end of 2019, the data base maintained by the Center for Research in Securities Prices calculates it to be \$41.14 trillion.  Of course, it has declined since then by an amount that depends on the day you do the calculation, but to keep things easy let’s use \$35 trillion.

## How To Measure Volatility

Based on that number, the current level of volatility implies that every day the market value of publicly traded American business can be expected to change by about \$2.25 trillion.  It takes a moment for that number to sink in.  On average, based on whatever information comes in that day, the market is revaluing total equity by \$2.25 trillion – and it is doing it day after day.  While one may think that on a day or two, in response to major news, a move of this magnitude might be warranted, to have it occur day after day, often without the arrival of much in the way of value relevant new information is remarkable.

All that said, there is one factor, news about which may be driving the market up and down and that is the term of the lockdown associated with the virus.  In a previous post, The Market and the Virus: Deconstructing the Drop, I calculated that the impact of the virus should be less than 10%.  Ironically, if we use January 1, 2020 as the starting point, we are getting back to that level after the run-up of the last three days.  The good news is that this interpretation implies that the market should sustain this level, but the offsetting bad news is that no further increase would be warranted.  Of course, all of this depends on the assumptions used in modeling the duration of the virus-related economic shutdown, a number which, like the market, changes daily.

## VIX Index Has Risen 5x

It is also possible to calculate forward looking measures of volatility.  By far the best known is the VIX index which calculates the volatility implied by the prices of options on the S&P 500 index.  Between the beginning of the year and the close on Thursday, the VIX index has risen by a factor of about five times.  Options on individual stocks have seen their implied volatilities rise by similar factors.  For those who employ hedging strategies using options, as we do at Cornell Capital, the pickings were slim prior to the virus crisis because volatility, and therefore option premia, were near historic lows.  Needless to say that has changed dramatically.  Option premia are at levels last seen at the height of the 2008 financial crisis.

In closing, it may seem that investing based on fundamental valuation is fruitless during times when the large daily price changes seem to have little relation to changes in value, but the reverse is true.  Given the unpredictability of the massive short-term price movements, attempting to play a pricing game is ill advised.  The best an investor can do is take positions based on his or her fundamental valuations and maintain sufficient reserves to ride out the bumps in both direction that are highly likely to occur.  Those bumps can be softened by careful use of options, particularly in light of the current high option premia.