# Defining Risk

**"If names be not correct, language is not in accordance with the truth of things." Confucius**

A study of ancient Chinese sayings isn't required to grasp the wisdom that the use of misguided definitions often leads to misguided decisions. The concept of risk is tremendously important to investment decision making. How we define that concept, then, is also paramount.

The academic definition of risk as it relates to investment is variance. The issue with this definition is not that price variance is an illegitimate definition of risk, it's that it is not the only legitimate definition. Since there is more than one rational definition of risk then it's possible to mislabel, and therefore misunderstand, risk.

Let's look at the fundamental assertion of the academic definition, that is, higher variability equals higher risk and, of course, the opposite, lower variability equals lower risk.

I've structured private investment offerings. These types of ventures are illiquid typically with no secondary market to sell your shares into. In putting together private placements I struggle to justify the thought that these investment are less risky simply because there is no variability in the price of the ownership interest during the hold time. I, and those who chose to invest in these ventures, did so on the basis of the prospects of the underlying assets. Had we been receiving appraisals of the assets every week it would not have affected the income generating capacity of those investments. Does the fact that there is no market to receive frequent price quotes make these private investments less risky? Conversely, does the presence of a daily quote on liquid investments increase their risk? Price variability bestows on the owner the option, not the obligation, of making a transaction. While selling numerous properties I occasionally would receive terrible offers. Not once did I feel compelled to sell a property during those times. Nor did these unattractive offers affect my conviction of the value of the asset we owned.

Having options with no attached obligations is generally viewed as a positive. However, in publicly traded securities, depending on your definition of risk, this non-obligatory discretion can be inverted into a negative.

Betas are a form of relative variance and are commonly used to express the risk of a stock. Although I disagree with the use of betas to identify the level of risk an investment carries, it is understandable. At bottom using betas as a gauge of risk says your definition of risk is volatility. This fits with the reasoning that the more uncertain a future benefit is the more risk it carries and the more it should be discounted today, which is correct. The issue becomes whether variance or volatility and uncertainty are the same thing. The answer is inseparable from your investment time horizon. If, for example, you had a strong conviction that the competitive strengths of an investment would produce a very good return over the next 5 years, but there could very well be a terrible year during that time (and maybe that's the case at time of purchase which makes the price appealing), if your horizon was 5 years, you don't care about the volatility because you feel there is a high degree of certainty that it will perform well over your ownership period. If, however, your time window was 3 months, volatility would more equate to uncertainty. This concept has similarities to the concept of "probability as a limit" or "relative frequency". The probability of rolling a 3 on a six-sided die is 1 in 6 or 16.67%. It is possible, however, to roll a die 20 times and not get a single 3. But eventually as more and more rolls are made the probability of 1 in 6 will take effect. If the time horizon was 3 rolls, the variance of outcomes would dictate your level of certainty. If the time horizon was 200 rolls, your degree of certainty would be less concerned with variance.

**Loss of Purchasing Power as Definition of Risk**

Under the view that variance equals risk the asset that becomes the least risky is generally fixed income. However, based on a different definition of risk -the loss of purchasing power- there are times (occasionally long periods of time), that bonds can be very risky yet still have low variability. Simply characterizing entire asset classes by their variability and resulting "risk" can be risky. To illustrate let's look at how a "variance adverse" investor would have fared in terms of purchasing power over the 20th century.

**Real Returns on U.S Asset Classes 1900-2011**

Three different investors each invest $1 in 1900. Each one chooses a different asset class. Investor A places his dollar into T-bills, Investor B into Bonds, and Investor C into Equities. A,B, and C are all exposed to continual offers from the market for their holdings. "A" had the least variance in those offers and "C" had to tolerate the most. Checking in with them 112 years later in 2011 it was found that A's $1 had become $2.80, B's was worth $9.30, and C's was $834 (all in real terms). All three of them managed not to succumb to the temptation to ditch their holdings despite the many offers received, some at very unattractive prices. Who was most successful out of the group depends again on definition. "A" achieved the lowest variance. Nevertheless, he will probably be calling on C for some help paying the bills.

The definition of risk that Ideal Capital Investments uses is the permanent loss of money. More specifically, the loss of purchasing power. The problem with this definition is that it cannot easily be mathematically summarized.

A minimum variance portfolio graph or an efficient frontier graph will have a Y (vertical) axis of expected return and an X (horizontal) axis of standard deviation (the square root of variance) as the measure of risk. Using instead the loss of purchasing power as the measure of risk would create an X axis of "probability of loss of purchasing power". This would factor things such as current price relative to value and the qualitative aspects of the business (e.g. its competitive shelters). This would be immensely more difficult to neatly quantify than variance. There isn't a readily available distribution for loss of purchasing power like there is for variance in asset prices. If prices fully reflected the earning power of the asset then variance would be a good proxy for purchasing power. Since this is not the case, variance becomes less of a usable measure of purchasing power risk with longer time frames. Because an investor's purchasing power is tethered to the assets earning power over reasonable lengths of time, and because variance isn't always reflective of an asset's long term earning power, variance can be a good thing. Just as variance creates negative possibilities to sell an asset at a lower price it also creates positive opportunities to buy at lower prices.

The longer an investor's time horizon the less meaningful variance is as a measure of risk. What will cause an investment's eventual return to not equal its expected return over a sufficiently long time period is not its volatility but the fundamental aspects of its business- its competitive position, management, operating efficiency, etc. Since time neutralizes the negative effects of variance, this implies that the longer term investor can benefit from the higher return offered to compensate for higher variance- you might have the opportunity to choose between a lumpy 15% return or a steady 12%.

**Summary**

Despite the position of this essay, I stated early on that variance is not an illegitimate definition of risk. A rational perspective on this topic is that for different investment motives, variability may justifiable amount to risk. For instance, a defined benefit pension fund, property/casualty insurance company, or a mother investing a sum which needs to grow to a specific amount in order to cover a child's college tuition cost are examples of investing what equates to a liability of theirs. They will definitely and knowingly be a seller of their investment position at a time when those liabilities come due. This reality means the presence of variability increases the possibility of a shortfall in paying their liability. This is a valid definition of risk. However, given a suitable time frame If you are confident of the final destination of the train you're on, unless you're a forced or compulsive exiter, you likely won't get off at the wrong stop. In fact, these extra "stops" actually provide more opportunities to get on.

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