Risk and Uncertainty

Risk and uncertainty are often used as synonyms; however, it is important to distinguish the difference between the two. For reasons I will hopefully make clear, a current lack of distinguishment regarding risk and uncertainty is a serious problem in the financial industry in my opinion.

Risk is calculable. It is a known unknown. It is a casino. A roll of the dice. A computer can calculate risk.

Uncertainty is not calculable. It is an unknown unknown. It is life. A black swan event. A computer can’t calculate uncertainty.

Nassim Taleb tells a story about the turkey illusion:

One day a turkey is approached by a man. The turkey is nervous, but the man feeds him. Each day the man returns, and each day the man feeds the turkey. The risk that the man will not feed the turkey decreases each day and is calculable. It is called the rule of succession and was created by Pierre-Simon Laplace- in the turkey illusion it equals (n+1)/(n+2) where n is the number of days the man has fed the turkey. If you plug in a few numbers, you can see that each day the man feeds the turkey the chance he will continue to do so increases (and, conversely, the risk he will not feed the turkey decreases). Everything is great for the turkey until the day before Thanksgiving when the man does something drastically different. 

The turkey illusion illustrates the difference between risk, calculable by the formula (n+1)/(n+2), and uncertainty, that the man will one day do something unrelated to the feed-or-not-feed options to the turkey. A computer can calculate risk. A computer can’t calculate uncertainty. 

The differences between calculating a problem using a computer versus a more qualitative approach is best explained by an example: In the book Risk Savvy the author, Gerd Gigerenzer, discusses how an outfielder catches a fly ball. Essentially, he or she subconsciously uses a rule of thumb. The individual runs towards the spot that keeps the angle of their view on the ball constant. A computer can’t calculate this trajectory as it is occurring. However, if you need to calculate the square root of a twenty digit number, a computer is your go-to choice. Point being, calculations are useful (and better) for some problems but not others.

There are many ways to make money investing; however, there is no “right” way in my view. It all depends on the individual, and some strategies are more responsible than others. In my opinion, quantitative investing can be a successful strategy. Despite this, as demonstrated by the fall of Long Term Capital Management in the late 1990s, models are great for calculating risk but not uncertainty. It is like the Ancient Egyptians who would build flood control systems to protect their villages based on the worst flood that occurred during the last 100 years. That is fine until something new happens in the next 100 years that is worse than before. There is an inherent flaw in creating control systems, such as financial models, based on the worst event in the past. This is because, as I have written before, black swan events are by definition unpredictable. They represent uncertainty and occur in the world we live in. To ignore uncertainty and only focus on risk, or even worse, think you are calculating both uncertainty and risk due to either a lack of understanding or mixing up the two, would be a drastic error.

Loss Aversion

Think about the following scenario - Your friend will flip a coin. If it is tails, you lose $100. How much do you need to win if it is heads to take the bet?

Most people say somewhere between $180 to $220. In a perfectly logical world, you should accept the bet if heads results in you receiving $100.01; however, this is not the case for most people. This is because the pain caused from a loss is greater than the happiness caused from a gain.

In The Art of Thinking Clearly the author, Rolf Dobelli, writes the following:
Losing $100 costs you a greater amount of happiness than the delight you would feel if I gave you $100. In fact, it has been proven that, emotionally, a loss “weighs” about twice that of a similar gain. Social scientist call this loss aversion.

In the investing world, risk and potential return go hand-in-hand. There is no “limited downside with huge upside” investment. Return is not a possibility without taking risk. Due to loss aversion, each person usually has a slightly different answer to what risk-return tradeoff they can handle. Furthermore, this is effected by risk capacity. That is, the amount of risk one can actually afford to take. (The risk capacity of a single 20 year old with zero debt is much different than the risk capacity of a 40 year old with four infant children regardless of their risk tolerance.)

The best investment strategy is one that is specific to the individual. This has to take into account a person’s individual outlook on the risk-return tradeoff, which will almost certainly be affected by loss aversion. 

Frame-of-Reference Risk

The most ubiquitous challenge I have faced that I was not aware of during college is what Roger Gibson calls frame-of-reference risk. Essentially, frame-of-reference risk consists of individuals mistakenly comparing their globally diversified portfolios to the S&P 500. 

The value of holding a globally diversified portfolio is straightforward for most: in addition to the old adage of “not putting all your eggs in one basket,” it results in a more favorable risk-return tradeoff. However, Roger Gibson suggests that this often increases frame-of-reference risk. 

A table best illustrates the problem:

(this is a simplification. assume equal weighting)

In both scenarios the individual is comparing the return of the portfolio (8%) to U.S. Stocks return. In situation A they like what they see. In situation B they do not. (And in fact want to invest more in the best asset - the opposite of what rebalancing calls for.)

Considering the nature of the media in the United States, this is not surprising. Turn on CNBC and it is feast or famine with the Dow Jones Industrial Average and the S&P 500; either the sky is falling or we are all going to be rich. This has been particularly relevant the last several years as the United States stock market has performed well while most other countries have struggled.

Josh Brown wrote a post recently summing up frame-of-reference risk to a tee. Here it is verbatim:

I had dinner last weekend with a financial advisor friend who works on a large wirehouse team based here in New York. Last year “was a major pain in the ass” he told me. He had to remind his clients again and again about the wisdom of global asset allocation while the S&P gained 14% and the rest of the world slumped.

Convincing someone that there is a right way to invest for the long term is hard enough, “re-closing them on our approach every few months is nearly impossible,” he said. I agreed with him. I spent a lot of last year blogging about the frustration among professional wealth managers borne of the huge dispersion between US and foreign stocks. As James Osborne says, what works over most years doesn’t work during every year.

“All the data I could come up with to prove the truth wasn’t enough. People don’t want to see the data when there’s a party going on and they feel left out.”

This year is a different story, he tells me. He got an email the other day from a client to the effect of “Thanks for keeping my portfolio intact and not listening to me when I complained.” Supposedly he had kept the guy from an all-in bet on US stocks just before Christmas. The US stock market is now flat with where it was the first week of Thanksgiving. International stocks have gone berserk to the upside.

So far this year, the power of a global portfolio has reasserted itself, right on schedule – just at the moment where it looked like there was no reason to allocate outside the “best house” ever again:

table via Bank of America Merrill Lynch

The reality is that foreign stocks and US stocks take turns outperforming each other in roughly four year increments. The last such timeframe where foreign developed equities beat the S&P was from 2003 to 2007. There’s no way of seeing the next such streak coming. The first five months of 2015 could be a blip or the start of something bigger.

The point is that it’s likely a diversified portfolio, if history is worth anything at all, will ultimately reward the investors who can stick with it. Even through years like 2014. “They can judge me against the S&P 500 this year if they want,” he said with a laugh.

If you fired your advisor last year to run off and join the Circus of What’s Working Now, don’t be surprised if you find yourself making yet another change in the near future when the grass turns out not to have been greener.

Frame-of-reference risk is basically a simplified version of applying home-country bias to this asset quilt:

via J.P. Morgan Asset Management

When the green box (large cap, represented by the S&P 500) is below the asset allocation box, individuals love diversification. See 2008. When the green box is above the asset allocation box, as it has been the last six years, individuals question the allocation decisions, especially when all you hear from the television shows is “the Dow sets a new high!!”

With diversification, one will never have a portfolio equal to the worst performing asset class, which would have occurred in 2002 if one had held solely the S&P 500; however, one will never have a portfolio equal to the best performing asset class either. While “don’t put all your eggs in one basket” intuitively makes sense, it is easier said than done. When I was coming out of college I erroneously believed diversification was a no-brainer. It certainly is the top strategy in my opinion, but as the advisor in the Josh Brown article stated, “People don’t want to see the data when there’s a party going on and they feel left out.” This is the challenge for advisors: through communication and managing expectations, helping clients avoid improperly benchmarking themselves to their home country’s large cap stocks when they hold a more diversified portfolio.