What Is Risk?

My Quest to Define Investment Risk

No really, what is risk? How do we measure it? How do we even define it?

The financial industry uses CAPM measures such as beta as a proxy, which is just the volatility of the stock price relative to a benchmark. Many famed investors push back on the idea that risk and volatility are the same. After all, what does the stock price have to do with the underlying fundamentals of the business? Here are a few quotes from some of the most revered investors in history:

“If the investor fears price volatility, erroneously viewing it as a measure of risk, he may, ironically, end up doing some very risky things.” Warren Buffet

"This great emphasis on volatility in corporate finance we regard as nonsense." Charlie Munger

“We steer clear of the foolhardy academic definition of risk and volatility, recognizing, instead, that volatility is a welcome creator of opportunity.” Seth Klarman

"Not only doesn't a stock's past price volatility serve as a good indicator of future profitability, it doesn't tell you something much more important - how much you can lose. Let's repeat that: It doesn't tell you how much you can lose. Isn't risk of loss what people most care about when they think of risk?" Joel Greenblatt

“There are many kinds of risks .. But volatility may be the least relevant of them all.” Howard Marks

Okay, so we know that price volatility isn’t risk.

Howard Marks has written that true risk is the possibility for permanent loss. Joel Greenblatt’s quote above is a confirmation of that idea as well. I really like that definition as a starting point, but I think there are caveats that should be added.

If you’ve been following this blog at all, you may notice that I really like using dice throws for my examples. Today is no different.

Consider a single dice throw where you receive a 6x return if you win, otherwise surrendering your buy-in if you lose. We know the probabilities of winning a dice throw are 1 in 6. That means there is an 83% chance that you’ll lose your money if you play. That must be high risk, right?

Well not exactly. Aswath Damodaran has stated that true risk (and the risk measure you should use in your valuation) is risk that cannot be diversified away.

In our dice throw example, we can use a diversified strategy. If we play the game hundreds or thousands of times, we would expect to get exactly our total buy-in back through dispersed winnings. In this sense, the game is risk-less.

Going a step further, imagine a company that has cash flow mechanics that works in a similar manner, where at the end of the year, the CEO throws a dice and the company incurs either $1 in cashflow or nothing. The cashflow generation may look much like the graph below (first thirty years shown).

Figure 1: Lumpy Cash Flows

This doesn’t look like a safe company. But if you know the probabilities and magnitudes of the cash flows, you could potentially purchase many of these companies. The distribution of the company valuations will look like a bell curve; the variance being driven by the timing of the cash flows. The median (and average) will equal exactly as if the cash flow was a constant $0.166 per year (with $0.166 being the average expected payout of a dice throw), and would effectively diversify the “risk”. In this sense, even volatility in cash flows (or revenue or earnings) isn’t risk.

In fact, in the example above, the investment would be risk-less, and you’d use the risk-free rate as your discount rate.

If you know the probabilities for certain, then there is no risk - even though the outcome is uncertain.

So I ask again, what is risk? We know that it’s not price volatility. And now we know it’s not even permanent loss of capital (if you know the probabilities). Even volatility in earnings isn’t risk.

As far as I can tell, risk is just an estimation of the “unknown unknowns”. We can’t measure what’s unknowable, but we can measure how the collective market prices the unknowable - this is the risk premium. Aswath Damodaran estimates where the market prices this risk premium every month on his website.

A natural follow up is “what is price volatility then?” I think I might have an answer for that as well.

Price volatility is a measure of the change in risk. It can also be as a result of the change in future cash flow expectations, but this post has been focused on risk so I’ll keep the focus there for now.

Every day, investors collectively are estimating how risky the market is. This is simply the market sentiment. Over the course of days or weeks, this sentiment might not move much; maybe moderate oscillations from investors reacting to inflation readings or economic news and indicators. If the market experiences an event of consequence, like Covid for instance, the pricing of risk can change drastically, which will in-turn cause large swings in the market.

A great way to think about this is to imagine the YTM on a bond changing over time. If this risk estimation never changed (constant value for YTM), then returns would be smooth, and volatility would be diminished to zero.

The absolute value of the risk is the measure of market sentiment. The change in the risk is volatility.

I’m working on a follow up post that further explores my thoughts on risk and volatility. Stay tuned.