The Divorce of the Risk/Return Relationship

They are always seen together, hand in hand going in the same direction. When return rises, so does risk. When risk is lower, so is return. A marriage that seems to enjoy a cohesive and consistent relationship. Inseparable, really. Could it be that they are not? Is it allowable that they might move in opposite directions- meaning that it would be possible to have both lower risk and higher return on a single investment? Yes.

The ability for this to happen rests on a different definition of risk than the one typically used in finance. The definition of risk that has become the traditional one is volatility. Our definition, instead, is the probability of permanent loss. That's ultimately what we want to avoid.

Let's take a look at volatility as the measure of risk, but first it's a good time to clearly acknowledge that there are indeed situations where these two differing definitions equate to the same thing. The situations that give rise to this caveat have to do with inflexible and generally short investment horizons. For example, a very specific and rigid investment horizon could result for an endowment that must fund a construction project at a known point in time in the near future or a pension fund that has offered a buyout option in a year. These types of scenarios can mean that near term price variance does indeed equate to probability of permanent loss, but suffice it to say for now that these two definitions have large and very different implications for investing.

Volatility as the source of risk

The idea of volatility, or more precisely variance, describing risk in stock markets was introduced by Harry Markowitz in his 1952 paper "Portfolio Selection". Up until that time most of the investment community's attention was solely on return and Markowitz shifted the focus (although his ideas were not widely accepted immediately) to also include the risk that came along with return. He never used the word "risk" in describing his investment strategy of minimizing variance but only identified variance as the "undesirable thing". A couple of decades after "Portfolio Selection" was published, risk and variance became synonymous. But is variance in prices always an "undesirable" thing? To answer this question I need to make another distinction. This time it is between price and value. (Click here for a short speech I gave on this topic-- albeit using a microphone with a dead battery).

About 10 years after Markowitz's paper something called the efficient market hypothesis gained momentum. Essentially the hypothesis says that asset prices fully reflect all available information and therefore prices equal values- they are one and the same. Some of the base assumptions under-girding this line of reasoning are problematic in real life, the most notable being the assumption of rationality. It is my opinion, formed from observing human behavior laced with biases and the resulting evidence littered throughout finance, that this is simply not true.* Ironically, it might be at least somewhat irrational to think it is. If that's the case, it holds large and important consequences for investors. It means that price and value are distinguishable from each other and that's a big deal.

Let me be clear that I'm not proposing markets are wildly inefficient with dumb decisions consistently leaving the door wide open for bargains to be had. Market participants, by and large, are smart and ambitious people. Yet even smart, ambitious people are not perfectly efficient. Perhaps the most reliable and pesky human inefficiency is the focus on the near term. The emphasis on tomorrow's gratification to the neglect of a more distant future.

In 1985, economists Richard Thaler and Werner DeBondt released their paper titled "Does the Stock Market Overreact?" They studied the 3 year returns of a group of more than 1,000 stocks for the period of 1926-1982 to see if stock prices with extreme movements in one direction would be followed by extreme movements in the opposite direction. They found clear evidence that it does- during that period loser portfolios went on to beat the market by an average of 19.6% over the 3 years after those portfolios were formed and winner portfolios lagged the market on average about 5%. These findings were confirmed through other researchers using different methods as well. This demonstrated that investors have a penchant for taking a very near term perspective on earnings releases and other short term news, failing to see that excessive earnings in any given quarter may not be sustainable and, conversely, that near term missteps in a fundamentally good business may carry within them the seeds of correction and even improvement, making the company stronger than before.

Price is what you pay, value is what you get.

The fact that price and value exist independently of each other, not being one and the same thing, opens up a much different perspective on variance. If there can be separation between price and value, there can be exploitation. Variance, then, might equal valuable space between an asset's price and its intrinsic value and thereby represents not risk, but potential for gain. I say "might" because it's entirely possible that when a price falls it did so justifiably- value also fell. For the price decline, or variance, to be a benefit, the anchor of value must hold.

Let's take an illustrative look at this idea. Reluctantly I'll introduce a bit of technicality as it might help visualize the concept of how, given our definition of risk being the probability of permanent loss, a greater return can be achieve while simultaneously having lower risk. The "normal" distribution, or bell curve, captures and describes a great host of details in our world and our everyday lives. If you graph the statistics of human heights, daily temperatures for any given place over time, age of death among house cats, or how long brake pads last under similar driving conditions, to name just a few, you'll see the data begin to distribute over the familiar bell curve. This also holds true for returns on stocks. Here's what a normal distribution looks like:


This phenomenon is important as it enables us to calculate probabilities. As you can quickly see when looking at the bell curve, most of the occurrences happen in the middle with a decreasing amount happening at the outsides. As you move further away from the middle you have less likelihood of experiencing those values. For instance, if the average height of a man in the U.S. is 5'10" (the middle of the curve) and 1 standard deviation from that average is 3", the distribution confirms what you already know from experience- that it is very unlikely you'll meet a man that is 6'7" and taller or 5'1" and shorter.

Now, stock returns may be normally distributed, but stock prices are not because they are bound on the left side at zero. Stock prices are what's called log-normally distributed. Nevertheless, the concept that I'm communicating is that as you move to the left within the distribution, there is less probability of seeing values further left and increased probability of seeing values to the right of that point. Although the probabilities are different in a log-normal distribution, this concept holds true for stock prices as well as returns.

When we can confidently estimate the intrinsic value of a stock and establish this value as the average value in its price distribution, then if price falls yet the value remains unchanged a situation is created where we can experience greater return yet have lower risk. To put some flesh on these bones, let's say that the intrinsic value of a stock is $50/share and it's currently trading at $55. A disappointing earnings statement is released which is significantly below expectations and the price falls to $40. Assuming value remains anchored at $50 for the long term, according to our definition of risk being the probability of permanent loss, there is now less risk; less probability of loss at $40 then there was at $55. This continues the further the price falls while the return potential does just the opposite: we stand to make a 25% return from a $40 price but a 43% return from a $35 price.

According to traditional definitions, the stock just described would have experienced greater variance, have an increased beta, and have become riskier. Yet from our standpoint that stock is less risky and now possesses potential for an enlarged return. Let's graphically look at the return/risk relationship under both definitions.

The first graph demonstrates the wedded nature of risk and return in the academic viewpoint- you don't have a movement in one without a same direction movement in the other. The second graph depicts just the opposite given that you're getting better value.

When value remains constant, or at least moves lower less than price does, variance may just be the desirable thing. Saying this so effortlessly reminds me of a Mickey Mantle quote: "You don't know how easy this game is until you get into that broadcasting booth." Unfortunately, it isn't emotionally easy to master this concept, particularly if you already own the investment before the "variance event". Buying low and selling high is a classic case of 'easy to exclaim and hard to execute'. When we experience prices declines our supposedly efficient, utility-maximizing rationality is tried and often found lacking. The fact is people emotionally like to buy high and sell low, it's a natural inclination. When prices (and therefore returns) are rising and you're watching a competing endowment, or fund, or whomever, make large gains it's not easy to standby and do nothing (or sell). Even for smart, presumably rational investors that are aware prices exceed values, participation is a difficult temptation to resist in this environment. When things collapse and all the news is terrible, buying (or not selling) feels like running into a burning building. It's simply hard to be disinterested when you're tempted and brave when you're scared. Yet, the knowledge that price and value are two different things affords some help.

When assets fall (vary) you must be able to discern what you're really looking at- is it price or value. If it's variance in value, be afraid; if it's price only, be happy- what was difficult to buy has gone on sale.

*For much more fascinating research on this point of view read Kahneman and Tversky.

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