If you have followed my writing for any length of time you surely know that I hate the concept of volatility in investing. It is used as a proxy for risk and honestly that is a disaster for our industry, and for our end clients. Though I have covered this ground previously, I do not think I have covered it in as detailed a fashion as I do below. First, though, here are the other editions of this series on The Most Misunderstood Investing Concepts:

• Fair value and its evil twin, target price;
• Time horizon and its subterranean influence on investors’ thinking;
• PEG ratios and the ignorance of the math underlying them; and,
• When valuing a business, growth is not free!

Risk = Volatility Only in Finance

The concept of volatility as risk rests on a critical assumption that is overlooked by most of the industry: Only in finance is risk defined as volatility. Dictionary definitions of risk have as their center of gravity, something like the “chance of loss.” For example:

1. Noun: exposure to the chance of injury or loss; a hazard or dangerous chance.
2. Insurance: the degree of probability of such loss.
3. Verb: to expose to the chance of injury or loss; hazard.

Surely you notice that not a single definition includes volatility as a part of the meaning of risk. You might say, “Yeah, that’s great but dictionary definitions and popular understandings of risk might differ from a business definition.” But a popular business dictionary from Barron’s describes over a dozen different forms of risk, ranging from exchange rate risk to unsystematic risk, all of which focus on the chance of permanent loss. Where’s volatility? Nowhere to be found.

Risk is central to the concerns of investors, but not the way it is in the very business whose entire operations are obsessed with it, the insurance business. These are some of the oldest enterprises on the planet and they are worth hundreds of billions of dollars. They must have a hyper-refined understanding of risk in order to be a going concern, and for several centuries. Yet, an insurance licensing tutorial says that “Risk means the same thing in insurance that it does in everyday language. Risk is the chance or uncertainty of loss.”

Only finance equates risk with volatility. Isn’t this peculiar? Why? How?

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Risk = Volatility Origin Story

In 1952, Harry Markowitz argued that investment portfolios should optimize expected return relative to volatility. In “Portfolio Selection” risk is directly associated with volatility and as measured by the variance of return. Markowitz states, “V (variance) is the average squared deviation of Y from its expected value. V is a commonly used measure of dispersion.” He then continues to say:

We next consider the rule that the investor does (or should) consider expected return a desirable thing and variance of return an undesirable thing. . . We illustrate geometrically relations between beliefs and choice of portfolio according to the ‘expected returns — variance of returns’ rule.

Whoa, did you catch what just happened there? Investors do want variance of return, and to the upside. Right? Yet, Markowitz states, “the rule that the investor does consider…variance of return an undesirable thing.” Not only that, how did a blithe proposition regarding a statistical calculation when he was discussing “V (variance)” turn into a “rule” in less than a paragraph? Markowitz then states, again a bit blithely, “[This rule] assumes that there is a portfolio which gives both maximum expected return and minimum variance, and it commends this portfolio to the investor.”

Sadly, this sentence is the source of tremendous misunderstanding: risk ≠ volatility. Ugh!

We Live in a CAPM World

This philosophical screwup creates a major problem for how investment managers are currently evaluated. Markowitz is the basis for the belief asset allocation is the most important consideration when seeking the maximum return for a given amount of volatility. Because his work was seen not just as a philosophical treatise, but also as a tool, the investment industry still seeks efficient frontiers made up of “a portfolio which gives maximum expected return and minimum variance.”

It is not minimum variance that investors want! It should go without saying they want maximum upside relative to downside, or in other words, large outperformance that offsets smaller underperformance. Sadly, though, mean-variance frontiers became the first pillar of modern portfolio theory (Capital Asset Pricing Model and Efficient Market Hypothesis being the other two). In fact, the positive correlation of risk and return is a paramount assumption in CAPM.

In other words, this idea lies at the heart of two of three pillars of a modern portfolio theory. Thus, if it is demonstrated that the risk = volatility connection is spurious then we should also have confidence in rejecting MPT.

There is No Evidence

The powerful prediction that beta, as a measure of risk, has a positive relationship with expected returns was challenged by Irwin Friend and Marshall Blume just a few years after the CAPM was first proposed. Based on a sample of 200 portfolios using monthly returns from 1960-1968, they conclude:

While rate of return is normally found to be positively related to risk, the adjustment of the rate of return for risk which would be expected to eliminate this relationship actually reverses it [emphasis mine].

Figure 1: Beta versus Expected Return from Friend and Bloom (1970)

The original graph from Friend and Bloom showing beta versus performance (expected return) is displayed up above. In one of the great understatements in the history of financial research, they conclude “The results are striking”! The graph clearly shows a negative slope rather than the positive one predicted by the CAPM. This means that the portfolio with supposedly the highest level of risk (i.e. highest beta) generated the lowest return. To this day, this is a gob smacking result. Wow!

Furthermore, the intercept, which is supposed to be zero based on how the test variables are constructed, was positive, meaning the intercept of the security market line is greater than the risk-free rate intercept predicted by the model. [The regression variables are constructed by subtracting the risk-free rate from both sides, so if the CAPM is correct, the intercept should be equal to zero.] Their results not only are visually convincing but are also highly statistically significant.

Friend and Bloom set off a scramble among academics to explain why the empirical results did not match theoretical predictions. Dozens of explanations have been proposed and tested over the decades, but none have salvaged beta as the exclusive measure of risk in financial markets. Similar research condemns other measures of volatility standing in as “risk.”

Frankenstein Lives On

Despite, Friend and Bloom delivering an unmistakable “dead on arrival” message to the academic finance community, volatility = risk lives on like an over-electrified Frankenstein’s monster. The theory goes that if you want more return, you must take on more risk. Not only that, but a pernicious corollary is that if you have more return, it necessarily must be because you took on more risk as an investment manager. The framework provided by Markowitz is still with us after almost 70 years. This return for risk trade-off is used to explain investment manager outcomes almost daily, despite its lack of support. <sigh!>

Our industry forgets that implicit in Markowitz’s work is a framework for improving investment management. He attempted to improve active investment management returns, not to worsen them. Yea! Markowitz’s overriding point is about the wisdom of “don’t put all of your eggs in one basket,” and how to manufacture the best basket for your eggs. In doing so, he is not primarily concerned with what constitutes the soundest measure of risk. Instead, he is applying statistical concepts to make an important point: proper diversification can lead to better outcomes in investing.

Making the leap to volatility and its close cousin, beta, as risk measures, as much of the industry has done, is an egregious mistake. Sadly, this legacy is still with us. Most investment managers are still evaluated as to their skill based on their Sharpe ratio (and very rarely on their Treynor ratio). Both put volatility right at the heart of their calculations. Another legacy of this misunderstanding is that old alpha-destroyer “tracking error.” Its theoretical justification is that an active manager must match the volatility of her index, otherwise they are necessarily more risky. Said another way, it is a form of an insult that says you are not good selectors of securities, just buyers of risks.

Fortunately, folks have pointed out the spurious nature of standard deviation and beta as risk measures and proposed alternatives like semi-standard deviation (thanks, Frank Sortino). But the “volatility = risk” and “returns only happen by taking on risk” misunderstanding still steers the manager selection ship captained by many folks in investment management. Mostly it punishes active investment managers because in the Treynor ratio the risk measure of the market is given as 1.0, by definition. In other words, the “market” gets to keep all of its return. The Sharpe ratio makes a similar tilted assumption in its use of standard deviation, where investment managers with high amounts of outperformance are considered more risky. How exactly?

In summary, if you are a rational investment manager and you understand that large outperformance hurts your Sharpe ratio, and that the measure of your Sharpe ratio may be the reason why you receive in excess of $1 billion in additional assets under management, and that these additional assets are the difference from just getting by and large profits for your firm, then you look for ways to “toe the line” and reduce your volatility. But wait, what about end clients? Didn’t they just lose out? Yes.

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