## What Volatility Isn't

### And What To Do - Or Not Do - About It

I have been reading a decent amount about volatility in the financial markets of late, and with good reason: I pen this piece on March 13, 2020, during a period where markets have entered free-fall mode.

Of course, European stocks aren't alone in this vicious spill. Indeed, virtually every asset out there is ripping higher and (mostly) lower on both an intraday and interday basis.

Implied volatility indexes are screeching to some of their highest-ever observed levels. There is simply no doubt that we are in the midst of historic volatility readings.

So with context hinted at (and we'll pick up on this thread before I close this piece), I want to turn to a highly important misconception so far as it concerns volatility and risk assets. In order to address the point of confusion direction, let me introduce a brief mechanical explanation of volatility via a story problem.

**Finance Story Problem**

**Question:** A financial asset thuds lower by 6.00% each day for seven consecutive days. What is the close-to-close volatility on the asset?

**Answer:** **0%**

**Explanation:** Volatility, as measured by metrics such as "realized vol", is computed using sample standard deviations. The formula is as seen below:

I'll expound on this topic in a future piece, but as a quick thumbnail sketch, I would like to explain the above formula as being the *average distance from the average*. The terms in parentheses are each the individual deviations, or the gap between the individual observations and the mean observation. Because this is a sample standard deviation, we divide by N - 1 rather than by N, as we would for a typical average (this is due to the concept of degrees of freedom).

For the purposes of our sample problem, I present the table below:

If each of the observations is the same large, negative value, then there is no distinction between the observations and the mean. In each case, the observed deviation from the mean observed performance is zero. Because each and every observed deviation is zero, the average deviation is also zero. As such, the sample standard deviation for the problem posed above is 0.

**Back to the Real World**

A lot of investors think about - and communicate about - volatility in terms of "markets going down". As we saw in the sample problem above, that is simply not true. A steady, n-percent decline, even a large one, can result in a low or possibly non-existent standard deviation. There is no mathematical sense in which the direction of a market must be related to the volatility of that same market.

But in practice, this is in fact often the case. When equities dive, they also tend to increase in volatility:

But the key is that true volatility is marked with a great deal of observed deviation from the mean observation, which frequently entails large downswings and monster rallies. This can be seen in clips such as the one pictured below:

This after S&P futures continued to plumb new depths after-hours on March 12 of 2398, before swiftly reversing course to near 2600 before the open. The micro-narrative here will hardly matter to you, the reader, by the time you are absorbing this info. But the larger point remains: volatility does not speak so much to direction as it does to distance.

And make no mistake: the distances are blowing up, across various timeframes. There is no question that there is a strong correlation between increased vols and returns.

**What the Distinction Means For Investors**

Sometimes technicalities can obscure the broader lesson. I'd like to conclude by offering some practical advice as to what this environment means for investor portfolios.

*The volatility stops whenever it wants, not when you want.*It may be more useful to think in terms of current volatility and your portfolio as opposed to thinking about thematic ideas like "bear market". Is the current volatility for your portfolio as a whole at an appropriate level in the context of your financial goals and circumstances? If so, then taking no action is quite defensible; perhaps even buying can be a good decision. If your portfolio's volatility is outside the bounds of what is appropriate, then you should sell to cut your risk, whether the prospect of doing so appeals to you or not.*Don't read too much into any one move*. As discussed in this piece, in the short run volatility obtains its value precisely based on how far it lives from some average observed value. Investors tend to put a great deal of weight on very recent developments. Of course, the situation we are journeying through as investors and as a society is highly fluid, and I do not want to minimize that reality; still, the fact remains that markets are going to move with hypersensitivity, and can reverse course on a dime in either direction.*If you're an investor and not a trader, now is not the time to start trading*. Investors have different tools in their risk-management toolkit than do traders. It can be an excellent idea to move from one camp into the other. But doing so requires commitment, patience, and a willingness to really look at markets from a totally different perspective. Darting into and out of markets in a knee-jerk fashion in a market that currently exhibits high-percentile vol readings is really not the time to get started with such a practice. Think of the present time as providing a reason to understand why someone might want to develop such skills, but not as a time to start honing them from scratch.

Keep your nerve, slowly move forward, and make sure that you write down what your rationale is for whatever action you are considering taking. Consider that your emotions - whether characterized by greed or fear - are not your friend. Focus first on your goals and your circumstances, and on market behavior second.

In closing, for your benefit I recommend that you consider the nature of volatility from both a practical and a mechanical sense.