Chapter 20
COMING TO GRIPS WITH THE MANY DIMENSIONS OF RISK
We begin with a definition of investment risk, illustrated with an example. Then we explain the key concept of market risk and some of the ways it is measured. Next, we offer an overview of some of the other kinds of risks faced by investors, ranging from those that can be quantified to those that are more subjective. Finally, we present a perspective on risk that strives to balance complementary risks against each other.
A Definition of Investment Risk
If there are many ways to measure an investment’s rate of return, there are even more measures of investment risk. The complexity embodied in the idea of risk means that it cannot be adequately captured by any single measurement or number. Nevertheless, there is an underlying unity that links the different kinds of investment risk:
Risk is the chance that your investment goals will not be realized in the time frame you specify.
Notice that the definition says
goals, and not merely
results. Unfortunately, investors are not always clear on what their goals are. Furthermore, an investor’s goals can, and frequently do, change in response to the following:
• Changes in the investor’s financial situation
• Changes in the investment climate
• Changes in the economy
The Relativity of Risk
Recognition that risk is relative to an investor’s goals, time horizon, and other constraints helps avoid confusion in thinking about risk. An example further illustrates the point. Let’s say you are deciding how to invest $100,000. You have the following three goals:
A1 To at least double your money in the next six years
A2 To keep up with a broad market index, like the S&P 500, never falling below its rate of return as measured quarterly
A3 To never be down more than 10 percent in any given calendar year
What’s missing from this example? An explicit statement of the investor’s time horizon and other constraints. The first goal suggests that the horizon is six years, perhaps the date of some anticipated future liability such as a child’s education or expenses associated with retirement. The other goals are shorter term, reflecting the investor’s desire not to fall behind a broad measure of average stock market performance and also not to lose a significant amount of money in a short time frame.
How achievable these goals are, singly or in combination, is not certain. From our definition of risk, it is apparent that there are three separate risk factors:
• Your average annual rate of return may be inadequate to double your money in six years. (Recalling the rule of 72, you would need to average about 12 percent.)
• Quarterly rate of return might fall below the benchmark in one or more of the 24 quarters of the investment period.
• Calendar year return could be worse than -10 percent at some point during one of the calendar years of the investment period.
To illustrate the dependency of risk on the investor’s goals, we now consider an alternative set of goals for the same $100,000 investment, this time with an investment horizon of 18 years:
B1. To grow to a minimum value of $800,000 by the end of the 18th year
B2. To grow at least 6 percent per year, net, after taxes, expenses, and consumer price inflation
B3. No calendar year return worse than -15 percent in inflation-adjusted dollars
It should be apparent that the risks associated with this second set of goals are different from the risks associated with the first set of goals. Some observations:
• Goals A1 and B1 each establish a minimum average rate of return for the investment, calculated from the end of the period. In fact, each works out to the same target return number, except that goal B is for a more distant time horizon.
• Goals A2 and B2 each establish an intermediate benchmark, but on very different terms. While A focuses on tracking an investment index, B selects a measure of potential future liabilities against which to measure success or failure.
• Finally, A3 and B3 each establish absolute worst-case limits, figured annually, but they differ in the way they establish a standard of value over time.
In the preceding examples, we gave no indication of the relative importance of the separate goals, lending credence to the assumption that they should be given equal weight. In general, different investors may give more or less importance to particular goals. Different weightings of, for example, short-term versus long-term goals, may have important consequences for the design of an investment strategy.
Having established a working definition of risk and illustrated the relativity of risk to an investor’s goals, we are now in a position to analyze one of the most fundamental investment risks: market risk.
What Is Market Risk?
Some measures of investment risk define it in terms of any deviation from an anticipated result, whether positive or negative. For example, volatility, the most frequently used measurement of market risk, counts positive deviations as well as negative deviations in attempting to quantify the riskiness of an investment. A stock that moved up faster than anticipated would have a higher risk rating than a stock that performed poorly but closer to expectation. This may seem like an odd way to define risk, but it is probably the single most widely accepted measure of market risk, and it works well under many circumstances. It is widely used because it is (relatively) easy to calculate, and the problem cited doesn’t arise too often. Investments that are volatile to the upside are volatile to the downside as well—for the most part.
When most people think about market risk, they think about stock market crashes, like the infamous Black Monday crash that sent the Dow Jones Industrial Average down by over 20 percent in a single day. Others, taking a longer-term view, think of market risk as the chance of encountering a bear market, which by one definition is a decline of at least 20 percent from a market’s high (see Chapter Five, “Of Bulls and Bears”). At this point, you might be tempted to ask, “Whose perspective on market risk is valid?” The answer, as we have already seen, is that they both are. Market risk, like all forms of investment risk, is relative to the investor’s time horizon, goals, and constraints. An investor who plans to be in the market for 12 months will tend to have a very different idea of market risk than an investor who is in for 20 years.
modern portfolio theory (MPT)
The standard theory for building an optimally efficient market portfolio. Alternative theories are sometimes referred to as post-modern portfolio theory (PMPT)
Not only is market risk linked to the investor’s time frame, goals, and limits, the very concept of market risk has evolved in response to changes in the markets themselves and to changing risk measurement techniques. As recently as the 1950s, stocks were deemed risky investments by the majority of institutional investors, who largely avoided them in favor of bonds. Only gradually did new ideas, notably the modern portfolio theory (MPT) of Harry Markowitz and the Capital Asset Pricing Model of William Sharpe, combined with the fading memory of the Great Depression and the great postwar boom of the 1950s and 1960s, convince professional money managers that stocks were an appropriate part of an institutional portfolio.
Part of the justification for investing in stocks came from Markowitz’s and Sharpe’s mathematical analysis of the role of diversification in building long-term returns. In addition, it was argued that the greater potential returns of stocks justified their greater risk. Many analysts began looking at individual stocks in terms of their beta coefficient, a number indicating the degree to which a stock’s price moves in relation to changes in the overall market. Though beta still has its adherents, it has gradually surrendered pride of place to volatility, a measure of a stock’s (or other security’s) tendency to undergo fluctuations in its rate of return.
beta (beta coefficient)
Correlation of a stock with an index such as the S&P 500.
“It Will Fluctuate”
J.P. Morgan’s fabled three-word answer to the anxious investor who wanted to know what the market would do next contains within it a hint of the importance of volatility to markets. Market price levels fluctuate. The price of individual securities that comprise markets fluctuate. We have already seen, in Chapter Sixteen, the importance of the volatility of prices to the valuation of options.
Now we are learning about the importance of another related fluctuation. Rates of return, which are calculated at least in part from price movements, also fluctuate. It is the fluctuation in rates of return, not in prices alone, that is the primary means used to define volatility. It is not the only means, however. The concept of volatility actually shows up in at least three ways in the markets: as historical volatility, as forecasted future volatility, and as implied volatility.
These three faces of volatility reflect three different ways in which market risk is measured and used. The first, historical volatility, is the most fundamental. For any particular time frame and group of investments, a unique historical volatility can be calculated. For example, you can calculate the 200-day historical volatility of IBM common stock based on daily return data (derived from closing prices, adjusted for dividends, splits, etc.). This is a well-defined number. So, however, is the 10-year historical volatility of IBM common stock based on monthly return data (derived from month-end prices with the same adjustments). These numbers would be useful in studies of the historical relationship between risk and return for large-cap stocks.
A problem with historical return volatility arises when someone attempts to use it to forecast future return volatility. We have already encountered this problem with price volatility: How do you go about figuring out which historical volatility, if any, is a useful predictor for the forecast period? The solution requires a model of the relationship between historical and future volatility. This model can be so simple that the person using it isn’t even aware of the model’s existence, or it can be an elaborate mathematical/ statistical construct implemented on a computer. Either approach may yield good results; neither can be guaranteed to work. This is an example of model risk, which will be discussed later in this chapter.
model
Set of mathematical formulas or computer programs representing a part of the world; a set of computer programs designed to simulate some aspect of the financial markets.
Finally, implied volatility is also a model-derived measure of the riskiness of an investment. In the case of price volatility, the model is an options pricing model. Here, however, implied volatility, like future volatility, may be derived from a theoretical model of the investment portfolio. It is subject to the same type of model risk already mentioned.
Other Kinds of Investment Risk: From the Quantifiable to the Subjective
Some market analysts reserve the use of the word risk for quantifiable uncertainties. For them, other uncertainties are just . . . uncertain. We understand their desire to emphasize quantifiable measures, but we take a broader view of risk that encompasses a whole spectrum of quantifiability and subjective judgment. We do this because it is apparent that any risk has a combination of quantifiable and subjective components. We do not think it wise to draw an arbitrary line, in the process increasing the risk that something difficult to quantify is overlooked.
That said, we begin our survey of other investment risks with those (relatively) easy to quantify. These include reinvestment risk/rollover risk, credit risk, inflation/deflation/currency/exchange rate risk, country/sector/ asset mix risk, catastrophic risk, and liquidity risk.
Reinvestment/rollover risk arises most obviously in the world of bonds and other fixed-income securities. Bonds are often chosen for the reliability of their payment of interest and principal. Reinvestment risk is the chance that you won’t be able to get a comparable interest rate when seeking to reinvest either interest and/or principal. The term rollover risk refers to the reinvestment of principal.
Of course, there are other risks that can affect bondholders. Bond issuers may suffer financial reverses, leading to credit downgrades or even default and bankruptcy. These possibilities make credit risk one of the great fears of bondholders.
For a long time, U.S. investors were most worried about inflation risk, as oil price shocks and expansive monetary policies combined to erode the purchasing power of the U.S. dollar.
More recently, deflation risk has become more of a concern to the public, as global labor markets and ever more powerful information technologies have combined to lower the cost of a broad spectrum of goods and services. The danger of deflation is its tendency to depress economic activity.
Each of the two preceding risks can be looked at as special cases of currency risk, another dimension of which is exchange rate risk. All of these involve the financial loss that can result when a currency deviates from its expected value. For bondholders and stockholders, changes in interest rates and currency exchange rates can have major impact on their portfolios.
Consideration of currency risk leads us naturally to the related concept of country risk, which arises when the economy of a particular country suffers a setback impacting its financial markets. Japan is a recent example of country risk. Sector risk is conceptually similar, except that industries instead of countries are affected. The gold mining industry can serve as an example of industry risk. Both of these risks can be thought of as special cases of asset-mix risk, which also includes decisions about which broad categories of assets to invest in (e.g., bonds versus stocks).
Catastrophic risk includes disasters of human origin (e.g., 9/11, Bhopal, and Three Mile Island) and natural disasters (e.g., Florida’s recurrent hurricanes and the episodic earthquakes of the Pacific Rim). Such catastrophes can have major economic fallout beyond the immediate damage and suffering they cause. Then there is the much less noted but cumulatively enormous damage of catastrophes whose effects are local: building fires, burst water pipes, and run-of-the-mill accidents that collectively far outweigh the headline-grabbing disasters in economic impact.
Liquidity risk is something of a misnomer—it should probably be called illiquidity risk—the hazard that demand for a company’s shares or other securities will dry up, leaving investors with no one to sell to.
Having briefly mentioned a number of moderately quantifiable risks, we now describe some that are more difficult to quantify. Ironically, several of these risks involve the potential misuse of mathematical models.
Model risk occurs whenever there is a discrepancy between how a model defines and/or measures a real-world phenomenon and the thing in itself. An example of model risk is the recent controversy over whether inflation is being measured correctly. There are two special subclasses of model risk. Extrapolation risk arises whenever we wrongly assume that the past can be reliably used as a guidepost to the future. Interpolation risk is a subtler, time-related risk, which comes from wrongly assuming that by drawing a straight line from the past to the present, we can accurately calculate intervening values. An obvious problem with this approach to data analysis is that it ignores cyclical phenomena like the weather. If it is dark outside now, and was dark outside 24 hours ago, it would not be advisable to assume that it was dark, say, 12 hours ago. And yet this is the equivalent of what many people do.
Benchmark risk is another kind of model risk. It occurs when an incorrect index or other proxy is chosen as a reference point for a portfolio. Benchmarking compares the increase in a portfolio to an appropriate reference portfolio, or index. The index may or may not be an actual portfolio that is traded. If it is or can be traded, it is sometimes referred to as an investable index.
Tax risk can arise from a change in tax rates or a reclassification of the tax status of an investment (or an investor). The byzantine complexity of the tax code can make it much harder to compare the attractiveness of different investments. Consider, for example, a choice between two investments:
• Investment A is a high-quality corporate bond paying 7 percent.
• Investment B is a triple-tax-exempt municipal bond paying 4.5 percent.
Assume, for the sake of simplicity, that maturity, quality, and call provisions are equal. Which of these investments is better for you? Well, it depends on your current tax rate, and it may depend on your legal residence. But it also depends on your future marginal tax rate, which depends not only on your future earnings but on possible changes to state and national tax laws.
Tax risk can be seen as a special case of regulatory risk, which derives from changes in the regulatory environment that impact the profitability of a company or industry. Sometimes, it is the failure to change regulations to keep up with new economic or technological realities that leads to trouble (jobs moving overseas, capital flight, etc.).
Political risk develops when governments undergo change, whether evolutionary and peaceful or revolutionary and violent. Accounting risk refers to the possibility that the accounts of a company do not reflect its real business situation, whether by error (of omission or commission) or by design. Operational risk encompasses all the problems that can arise in the day-to-day operations of a business, including errors (of omission and commission) and malicious acts such as fraud and theft. Death of a key executive can be considered as an operational risk, although some would classify it as a catastrophic type of risk.
“Of Cotton Futures, Black Swans, and Uncertainty”: An Important Special Risk
In 1962, a then little-known (but now famous) mathematician named Benoit Mandelbrot discovered something funny about cotton futures prices. He realized that they were subject to more dramatic changes than would be expected by conventional finance theory. He proposed mathematical models for cotton and other markets in which such jumps would be expected, in contrast to the orthodox “Gaussian” view in which large moves should be extremely rare.
In 2004, he wrote (along with Richard Hudson) a book called The Misbehavior of Markets, in which he challenged regulators to devote 5 percent of the $400-plus million Wall Street settlement money to basic research in the structure of financial markets with a particular emphasis on understanding the dynamics of major financial disasters. His challenge was ignored.
It took Nassim Taleb’s talents as a writer and polemicist to bring Mandelbrot’s ideas the attention they deserved. In his book The Black Swan, Taleb forcefully argues that Wall Street habitually underestimates the likelihood of unexpected rare events, events that Taleb refers to as “Black Swans.”
This idea has caught the popular imagination, especially in the aftermath of 2008, even though many would argue that the collapse of the market was inevitable and that to label it a “Black Swan” is simplistic. An emerging view of financial markets begins by acknowledging the role of uncertainty in periodically upsetting our established view of things. Uncertainty can come from a “black swan”; it can also come from a bubble’s bursting; or from the actions of regulators trying to clean up the mess. It is a cardinal mistake to over-rely on “black swans” or any other “theory of everything.” It is better to admit that our knowledge is surrounded by a cloud of unknowing, which every so often descends on us like a thick London fog.
Balancing Risk and Return
Having provided some perspective on both risk and return, we are now in a better position to understand the interaction between these two concepts. A basic guidepost to the risk-return relationship states the greater the return an investment promises, the greater the risk it holds—and conversely, the riskier an investment is, the greater the return investors must be offered to compensate them for taking on that risk. While this principle holds good on average and in the long run, there are many important exceptions to consider. These exceptions arise from hidden assumptions about investor behavior, most notably, the assumptions that all investors have equal access to information and that all investors make rationally optimal decisions on the basis of the knowledge they do have. Both assumptions are clearly false at least some of the time. Investors do not always have equal access to information. Furthermore, different investors respond to new information in different ways and at different speeds. Finally, even when a given investor is in possession of all relevant information about a stock or other investment option, he or she may not act in a way that economists would consider rational or optimal.
A view of your market risk, Riskgrades (
www.riskgrades.com), is a free service developed by RiskMetrics, a leading vendor of risk management systems.
How can an investor set about trying to balance risk and return? There is no universally accepted formula or simple rule for this. Instead, each investor needs to consider his or her unique financial situation. First, determine as best you can your present financial assets and liabilities. It is important to recognize that even at this stage—before looking to the future—there can be significant uncertainties about how to value your assets and liabilities.
What Is Alpha, and Would You Like Some?
Some investment professionals describe their work as a search for positive alpha. Alpha is defined as the difference between an investment’s actual expected return and the expected return that modern portfolio theory says it should have. Investments with positive alpha are said to be underpriced. Investments with negative alpha are said to be overpriced. Unfortunately, the search for alpha is complicated by three sources of noise that can lead the unwary astray: luck, hidden risk, and fraud. A manager who is lucky may appear to be a good source of alpha, but outperformance that arises from luck is likely to be fleeting. Worse are the instances where managers generate outperformance by (consciously or unconsciously) making risky bets that are likely to work for a while, until they fail dramatically. Short-term incentives at banks and hedge funds led to a dramatic increase in levels of hidden risk and are likely responsible for the financial crisis of the last few years. Finally, there are still too many bad actors in the investment business who try to get away with anything they can, and whose recent crimes are likely to keep the courts busy for years to come
Fortunately, finding real positive alpha, based on skill rather than luck, hidden risk, or fraud, though it may be rewarding for professionals who are judged against their peers, is neither necessary nor sufficient for most investors. Indeed, identifying small mispricings may be more effort than it is worth, especially after transaction costs are taken into account. What’s more, it can distract from the important task of estimating and planning for future liabilities.
In some cases, a range of values gives a more accurate depiction of reality than does a single number, which offers only the illusion of precision. For example, an inactively traded stock is hard to price accurately; its value is only an educated guess. In such cases, it may be prudent to set its value to a small fraction of what analysis says it should be worth. Sometimes, however, this approach can be costly. Biasing your estimates of value can distort the overall picture of your portfolio and lead to bad investment decisions. On the liability side, a mortgage that can be refinanced is not a simple investment: Its current value depends on future changes in interest rates and the availability of credit.
Shifting our focus from the present to the future, we are confronted with an exponential increase in possibilities. This complexity arises from the need for and interaction of three financial forecasts:
• Future personal earnings
• Future performance of investments
• Future liabilities
Let’s face it, even the most rigorous analysis of investment alternatives cannot guarantee a good result in the face of so much uncertainty. Why? Because of the uncertain relationship between future earnings, investments, and liabilities that each investor must try to understand. Risk is the dark side of opportunity. It is often said that there is no opportunity without risk. Even so, some opportunities are better than others. Some risks are more worth bearing than others.
An important consequence of the relativity of risk explained in the previous chapter is that performance standards do not attempt to compare unrelated investments by adjusting for risk. Instead, the standards limit themselves to comparing similar investments with each other, trying to ensure that comparisons are relevant, meaningful, and fair. Organizations that have created performance standards, such as the CFA Institute, tend to focus on the return component of performance.
This leaves investors with some difficult tasks—estimating their likely future assets and liabilities, developing a reasonable set of financial objectives, and trying to identify and avoid the risks that matter most to them. Good financial planners can help; unfortunately, all too many planners are narrowly trained in a particular product area. Furthermore, most planners do not have the proper degree of detachment from the products they are hired to evaluate. Finally, many lack an understanding of the risk/ return relationship. Fortunately, the increased sophistication and information access of individual investors is likely to force financial planners to better serve their clients.