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Risk Tolerance: This Time It Is Personal!

The most important role of any investment manager is to know their client well enough that they can align the client portfolio to their own individual risk tolerance. The advisor may ask: do you like to jump high, higher, or highest? It may not be until the client is fully off the ground before they realize that they may have misjudged their ability or their temperment for risk. The worst that can happen is a gnarly crash and burn while the best that can be expected is for them to retreat over to an easier trail the next time down the mountain.

One Size Does Not Fit All

Think about the last time you shopped for clothing. It is fairly easy to find a watch cap that fits your head. A winter coat is also a fairly generic fitting problem. Then we get into the pants department and things get more complicated. There are so many measurements and our "real" size may change over time - usually in one direction! The shoe department is perhaps the most challenging but then again the most rewarding. There is nothing like a good fitting, high quality pair of shoes. A tailored fit for our tired dogs is required for long days pounding the proverbial pavement. The same is true for matching our investment portfolio to our own individual risk tolerance.

Risk Capacity

The left side of our brain says that we have enough money to recover from our mistakes and enough time to reap the expected rewards of taking on risk. Our risk capacity is essentially a math problem summarizing our probability of success under different market scenarios. Banks have been the focus of many so-called stress tests over the past decade when we all thought the financial system was going to collapse back in 2008. Similar to these large institutions, we can stress test our own portfolios to determine what would have happened under certain historical market events. This gives us some sense (but no guarantee) over how the numbers on the lower right corner of our brokerage statement may change in the future. As the saying goes: knowledge is power; the power to make an objective decision with the data at hand to either take or not take investment actions in our portfolio.

Risk Tolerance

The right side of our brain says that we could get hurt. When people take a skiing or snowboarding lesson at an advanced age (above 13), their first question is usually something like: "How dangerous is this? I cannot break a leg and miss work on Monday." A second question that often closely follows is: "How do I stop?" Their 9-year old kid - on the other hand - asks: "Why do we have to go so slow?" or "When can we go off those jumps?" These are obviously stereotypes for a specific action sport, but the moral of the story is that everyone has their own personal preference for how high they jump or how fast they slide. This preference may or may not change with their age (I still go off some jumps). It also may not translate from the physical world into their financial life. Our risk tolerance is determined more by ou willingness to assume risk rather than our ability to take on the challenge.

Utility Theory

Part of what we struggle with is an emotional tug of war between our left brain and right brain. Research has shown that humans feel the magnitude of pain due to financial loss roughly 2.5 times [1] greater than the magnitude of the joy from financial gain. This may be one of the reasons that bad news "sells" better than good news when we consume headlines from current events. There is a solution to this problem suggested by utility theory. Thinking again about sliding down a mountain, the brain makes instantaneous calculations and judgements about the relative joy of an experience and the relative risk of that same experience. Our expectations are honed through past experiences and proprioceptive inputs from our eyes and ears. In the investing world, the joy comes from expected returns while the pain derives from expected risk.

E(Up) = E(Rp) - 0.05 * RA * E(Sp)2

RT = 0.05 * (100 - RA)

E(Up) = E(Rp) - 0.05 * (100 - RT) * E(Sp)2

The expected utility of our portfolio, E(Up), is equal to the expected return, E(Rp), minus what may be called a penalty function proportional to the risk aversion (RA) and the expected portfolio risk, E(Sp)2. The portfolio risk measure used here is the square of the expected standard deviation of returns - otherwise known as the variance of returns. If our risk tolerance spectrum ranges from 0 (very low) to 100 (very high), an average risk tolerance may land somewhere around 50. This suggests that an average investor feels the pain of loss 2.5 times greater (0.05 * (100 - 50)) than the joy of gain.

That is very nice, but what does it all mean? If we can maximize this expected portfolio utility, E(Up),  for each individual investor, they should be happy. It turns out that we are able to solve this type of optimization problem using a technique called calculus of variations. This process can be automated using expert spreadsheet skills or specialized software.

Animal Spirits

There is a nerve that connects our stomach with our brain. The signal traveling from the stomach to the brain seems to have a delay in alerting us that we have had enough to eat and that we should stop ingesting food. Our emotions play this same trick on us when we think about our investment portfolio. We humans tend to do the exact wrong thing at the exact right time when handling our own money. One of Warren Buffett's best quotes summarizes an antidote to this problem.

We simply attempt to be fearful when others are greedy and to be greedy only when others are fearful. - Warren Buffett

Economist John Maynard Keynes coined the term "Animal Spirits" [2] to describe the irrational herding mentality that surrounds the market making system. These emotions tend to oscillate between desperation and euphoria in somewhat predictable cycles. Part of the role of an investment advisor is to decouple the research process from the trading process so that emotions play no role and our risk tolerance converges with our risk capacity. This time it is personal!

References

[1] https://www.nber.org/system/files/working_papers/w18621/w18621.pdf

[2] https://www.economist.com/media/pdf/animal-spirits-akerloff-e.pdf

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