# When Does Volatility Equal Risk?

Volatility is one of the biggest risks in investing according to conventional financial wisdom.

A small minority of investors, mostly value investors — a group to which I belong — take a different view. We think it is the probability of permanent capital loss, not volatility, that constitutes the real risk.

Neither perspective is entirely correct. Nor are these the only two viewpoints — one in which volatility is *the* main investment risk and another wherein volatility is cast as unimportant. Rather, the right question to ask is: *When* does volatility equal risk?

Judging investment performance starts with the implicit assumption that the unit of risk is a measure of the portfolio’s volatility. Many metrics — the Sharpe ratio, tracking error, and information ratio, for example — compare a unit of return to a unit of portfolio volatility, measured either on an absolute basis or relative to a benchmark.

A generally accepted belief is that a below average rate of return achieved with low volatility can be considered an exceptionally good result, and most conventional investors avoid volatility at all costs, particularly given the pervasive short-termism of the investing industry.

### Why Value Investors Don’t Regard Volatility as Risk

Warren Buffett famously said that as a long-term investor he would “much rather earn a lumpy 15% over time than a smooth 12%.”

Following his logic, many modern value investors aren’t concerned with volatility. Instead, they focus their risk management efforts on decreasing the probability of permanent capital loss. After all, these investors believe they have the emotional fortitude to ride out the short-term ups and downs as long as the strategy and long-term results are sound.

### Volatility as a Source of Risk Is Not Absolute, But a Function of the Investor’s Circumstances

Consider the following four investor profiles and how volatility is likely to affect their long-term investment results:

**Long-Term Investors with Strong “Stomachs”:**Such investors have a 10-year or longer time horizon as they save for goals like retirement or college tuition for their children. Furthermore, these investors are behaviorally unaffected by volatility — they stick to the investment plan regardless of how bumpy the ride. For such investors, volatility is not a risk. Their main consideration is the long-term annualized rate of return and the probability of permanent capital loss along the way.**Short-Term Investors:**This cohort plans to use a major portion of their portfolios within the next three years. Volatility is a primary risk since the near-term withdrawal of capital will lock in short-term results. So volatility is a primary concern, because as it increases, so too does the potential for forced sales at disadvantageous prices.**Long-Term Investors with Weak “Stomachs”:**These investors are*behaviorally*affected by volatility. Many investors saving for long-term goals end up taking investment actions counter to their interests because of price volatility, market news, or other short-term developments. Ideally, these investors*should not*act in this manner given their goals, but they can’t stay rational and so frequently sell at low points. This type of investor should treat volatility as a risk since a more volatile return stream is likely to create worse financial outcomes.**Long-Term Investors Who Consistently Spend Small Portions of Their Portfolios:**This variety of investors could include institutions, such as an endowment that spends approximately 5% of its portfolio to support its organization, or an individual using a small portion of the portfolio to cover annual expenses. Volatility matters to some degree, but it is not the main risk.

Here are two Monte Carlo simulations of a scenario similar to those facing many endowments today:

**Scenario 1**

**Expected Return = 8%, Standard Deviation = 15%,**

**Annual Withdrawal ****Rate = 5%, Number of Years = 30**

**Scenario 2**

**Expected Return = 8%, Standard Deviation = 10%, **

**Annual Withdrawal ****Rate = 5%, Number of Years = 30**

The above analysis demonstrates that when the volatility of returns, as measured by the standard deviation, falls from 15% annually to 10%, the probability of the portfolio failing to last the full 30 years drops significantly — from 14% to 3%.

There are two lessons here: First, know your client’s situation so you can determine how important a risk portfolio volatility is in *their specific case.*

Second, do your best to condition clients to be long-term investors with strong “stomachs”** **for a substantial part of their portfolio. For more on this, please see “How and Why to Be a Long-Term Investor.” This will give you and them the freedom to maximize long-term returns without worrying about short-term volatility and will put them at an advantage over many other market participants.

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*All posts are the opinion of the author. As such, they should not be construed as investment advice, nor do the opinions expressed necessarily reflect the views of CFA Institute or the author’s employer.*

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Gary:

Thank you for posting your thoughts on risk vs. volatility. This discussion seems to be the focal point of active investing these days.

I can’t help but notice that the discrete risk factors mentioned in your article, are already embedded in the standard individual IPS framework as time horizon, liquidity needs and the willingness to take risk. Maybe we all need to re-frame these every now and then to understand the nature of risk…

Much like you, I do not think that volatility should be used as the sole measure of risk. Volatility or any derivation thereof has some utility as a concept, but I don’t accept it as a valid measure of risk. Doing so would assume that (i) markets always efficient and that (ii) correlations between asset classes are stable. This may be a convenient assumption for a mathematical model to work, but it is not necessarily true, especially when panic/euphoria drive the market sentiment and when the contagion breaks correlation barriers.

Under these conditions, being tied to volatility, creates a host of problems, not the least of which is excessive trading to stay within the portfolio mix and risk constraints.

While I see how using individualized risk measures (as opposed to volatility) can help individual portfolios, I think the greater danger of equating risk to volatility is in the institutional portfolio side.

In the institutional portfolios the constraining factors that affect individuals are less pronounced: time horizons are usually long, willingness to take risk (or having a “stomach”) isn’t usually a factor. Liquidity may be the only factor that may affect both individual and institutional portfolios somewhat equally.

In the individual portfolios, behavioral constraints provide some form of protection (albeit imperfect) against the tendency to using volatility as a sole risk factor. In contrast, within institutional investment mandates, it is not unusual to see portfolio risk coded as some quantifiable measure such as standard deviation.

Re-defining risk as the probability of loss (an intellectually honest thing to do) is the first step in the process of finding the next risk framework. The challenge is finding risk factors that works across all asset classes.

Gary,

I couldn’t agree more with your statement that “We think it is the probability of permanent capital loss, not volatility, that constitutes the real risk.”

However, I would like to provide some details about the math that is driving the results in your simulation experiment. I see this argument used a lot when discussing volatility but the results are actually driven by the mathematical relationship between normal distributions and log normal distributions, and you aren’t comparing apples to apples here.

1. First, when does volatility equal risk. Basic economic theory says this occurs when an investor has either a quadratic utility function or negative exponential utility function and returns are normally distributed.

2. For the experiment you ran — First according to basic economic theory, no rational investor would ever choose scenario 1 over scenario 2 as scenario 2 completely dominates scenario 1. Second, the geometric return, i.e. annualized total return of scenario 2 equal 7.5%/year whereas the geometric return of scenario 1 equals 6.875% / year. So if you invested $100 in scenario 2 and scenario 1, on average you would always have more money at the end with scenario 2 — That is exactly why it works better in the experiment. This is due entirely to the relationship between a normal distribution and log-normal distribution, the concept called “volatility drag” which is really just a mathematical statement of this relationship:

Geometric Avg. = Arithmetic Avg. – (Variance^2)/2

I hope this explanation helps shed some light on the math behind your conclusions.

Thanks,

Just checking notation, should the last term be (variance/2) instead of (variance^2)/2?

Hi Gary,

thanks for this interesting note on risk and volatility. This clearly references decision taking questions of investors and I would agree that in order to clearly advice on the “right” decision / investment you need to identify your client’s / investor’s preferences in terms of risk. Depending on the situation the investor is in and the actual goals he pursues volatility may not play such an important role at all.

Nevertheless, standard valuation approaches do focus a lot on volatility to measure risk and to identify the required rates of return by the investor. Mos commonly accepted approaches to determine the “fair value” will still and likely in the future use these methods and strongly base calculations on volatility as the measure of risk.

Once we move away from “fair value” ideas and clearly look at what’s best for the investor and consider his view, this will clearly change the view on required returns and the “true” value from the point of view of the investor. So volatility then changes from being bad to being neutral or being good … and the idea of permanent loss of capital will become a stronger measure of the risk perceived by the investor.

so again, thanks for providing these thoughts – they clearly overlap with what we have developed at KPMG, an approach that focuses on risk from a more subjective view of the investor, we call this “Corporate Economic Decision Assessment” (CEDA). happy to discuss, if you would like to learn more on this!