Monday, October 27, 2008

Investment Risk vs. Volatility


Financial Advisor Magazine October, 2007

By Patrick R. Chitwood
A definition of risk must include an investor’s own perception of it.
    It is common today to find that investment risk is frequently expressed in terms of the annualized standard deviation (SD). Because the consequences of such usage are significant to portfolio construction and investment decision-making, we must carefully examine our premises and our definitions.

    In his landmark text A Random Walk Down Wall Street (1973), Burton Malkiel defines risk as follows: “Investment risk, then, is the chance that expected security returns will not materialize and, in particular, that the securities you hold will fall in price. … Thus, financial risk has generally been defined as the variance or standard deviation of returns.” 

    In two short sentences this groundbreaking publication has transferred the concept of risk to a number. It is interesting to note that even Markowitz (1953), dodged defining measures of volatility as risk.

    From Malkiel, Fama and French, Treynor, Black and Sholes, Sharpe, etc., the study of portfolio construction centered around enhancing return while decreasing “risk” as defined by SD. “Risk” by this definition is completely dependent on SD values. Uncertainty is only a byproduct of the dispersion around a mean. 

    Unfortunately, investment risk requires a decision maker—a human, in the case of investing. To the extent that events are important to the decision maker, one could posit that those events may impact the likelihood of making an undesirable decision. Because these events may be entirely unrelated to the underlying investment, risk is clearly much more than the volatility component of an investment.

    Addressing FAME in February 2002, Peter Bernstein stated: “What do we mean by risk? It’s a very messy four -letter word. Volatility is the most popular proxy for risk. It’s a good one. First of all, intuitively, it makes sense. When something is jumping around, it hits you in the gut, you’re not comfortable, none of us is comfortable with volatility. If we have a sense something is going on we don’t understand, we don’t know where the limits are. There are plenty of intuitive reasons for using volatility as a proxy for risk. Volatility is also nice because it’s a number, standard deviation or variance, it’s a number, and that means we can manipulate it mathematically. All those beautiful equations wouldn’t be there unless we had a mathematical concept for risk. But volatility cannot deal with fat tails, with non-normal distributions, with nonlinear relationships, with nonstationarity, with multiperiod analysis, and there’s more. It gets messed up, it doesn’t hold together. So we have to think about different kinds of risk models, and more elaborate kinds of risk models, and the more elaborate they get, maybe the further away we get from the basic ideas. And for long-term, buy-and-hold investors, volatility is essentially irrelevant. So our definition of risk, the thing that we use the most, is in a sense a floating crap game. Uncertainty means—this is what Keynes and Frank Knight were very clear to explain—uncertainty is something we cannot quantify, we do not know what is going to happen, we don’t know what the probabilities are.” And later in the same speech: “How well do we really understand investor responses and how they weigh the trade-offs between risk and return? How do we define risk aversion? How variable and how stable are utility functions? These are very important in making policy decisions for long-term asset allocation. We need some sense of this, and it’s very slippery because it is so intuitive and so internalized.”

    If the standard deviation does not represent risk but rather is simply a measure of volatility, what then is risk and how do we define it, or do we even need to do so? A critical part any risk definition necessitates that we understand that investment risk requires human behavior. That behavior is unique to the investor. 

    Put much more eloquently in the words of Glyn Holton (Financial Analyst Journal, Vol. 6, 2004): “The definition (of risk) depends on the notions of exposure and uncertainty, neither of which can be defined operationally. … All we can hope to define operationally is our perception of uncertainty. Consequently, it is impossible to operationally define risk. At best, we can operationally define our perception of risk. There is no true risk.”

    So then, we are left with the factors that influence an investor’s perception of his investment risk. This is the embryonic domain of behavioral finance. As professionals we must strengthen our ability to determine the risk for each individual, recognizing that the same investment has different risks in the hands of different investors. Because of the extensive dynamics of an individual life, risk determination is dynamic and potentially complex. Perhaps it is for this reason that there is such unfounded allegiance to quantifying risk with the proxy of a standard deviation. 

    As a point of discussion I would like to propose the following operational definition. Investment risk can be defined as the exposure of capital to a future decision based on the perceived value of an investment at the time of that decision.

   Notice that the exposure of capital is to a future decision, not to an investment. Also, that the decision is based on perceived value, and that perception is based on several factors such as observation frequency, deviation from expectation, volatility and current life factors, to name a few.

    It is not the purpose of this article to propose a strategy for assessing risk and recommending investments as a result of that assessment. Nor is its purpose to address the components associated with risk and how those components can be impacted by investment work.  What I do hope to accomplish is to further motivate a dialogue for investment professionals to open their thinking to other ideas of assessing risk and to question, (in the words of Ken Fisher), “What is it that I believe that is wrong?” 

    To quote Bertrand Russell, “In all affairs it’s a healthy thing now and then to hang a question mark on the things you have long taken for granted.”

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