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Risk versus Reward Explained


Richard Suvak, MSF, CFA


Financial academia and market practitioners spend an inordinate amount of time talking about risk versus reward. To be fair, I have added my own two cents on the subject as well. However, portfolio risk versus reward is seldom described beyond a distribution of returns. This article hopes to change that.

The distribution of market returns is often referred to as steep, fat-tailed with a positive mean. That is, the distribution is higher at the peak than normal, has more events in the lowest and highest bins than normal and has an average greater than zero. Consider the charts below. The left chart shows the full distribution of S&P 500 returns over a 1-year period while the right chart shows the same over a 3-year period. Both distributions have positive means (6.1% and 5.9% annualized respectively) – which is, by the way, why we invest in the equity market. What’s also noticeable about the distributions is the steepness and the percentage of observations in the extreme bins.


S&P 500 Returns Distributions


Circling back to our purpose, these charts demonstrate risk versus reward. The reward is the return we hope to achieve. Since 1871, the average annual return of the S&P 500 has been 6.1%. Over a three-year period, the annualized return has been 5.9%. Over the same period, the 1-year standard deviation has been 19.0%, while the annualized standard deviation over a 3-year period has been 10.5%.


S&P 500 Returns Return Table


Given these statistics, it is reasonable to expect that 68% of the time (1 standard deviation), we can expect annual returns to be somewhere between -12.9% and +25.0%, or -4.6% and 16.4% annualized over a three-year period. Our risk therefore is the possibility that returns are less than expected, potentially significantly so.

Most discussions of risk stop here. Long-term market averages are used to demonstrate the return expectations long-term investors should hope to achieve. However, this is not always the case. The start and end-points are important. For example, if you invested just prior to the 2008 financial collapse, you have yet to achieve the historic 6% annualized return, despite some fantastic returns recently. To make matters worse, you’ve suffered through some pretty difficult years along the way.

While start and end times matter in determining risk versus reward, hopefully my cherry-picked example demonstrates that market environment is the true determinant of long-term returns. For example, had I chosen a “normal” period to start (one with no major market disruptions, normal valuations, normal economic growth, etc.) and ended during a similarly “normal” period, one would expect the average returns achieved to fall close to our long-term historical average. While that may be true, it’s also true that we’re not in this “normal” period now. As a result, our risk versus return calculations must take the current situation into account when making investment decisions. Currently, we are in the 93rd percentile based on Price-to-Earnings and the 97th percentile based on Robert Shiller’s Price-to-Earnings ratios. Meaning, we have only been more expensive 7% and 3% in the entire history of the S&P 500 using these two measures. While nearing an extreme, expensiveness does not always determine future market direction. Interest rates, economic growth and ultimately corporate earnings play a significant part as well. As such, President Trump’s proposed tax policy and Fed Chair Yellen’s interest rate decisions will each play a part in future returns, and why I have devoted so much time writing about these two items of interest. Both, in different ways, impact corporate earnings and by extension market valuation and expected returns.  More simply, market valuation, interest rates, corporate earnings, tax and interest rate policies affect risk versus return calculations.

Since corporate earnings (level and growth rate) combined with the level of the market determine valuation, it is reasonable to conclude that market valuation influences market returns. The evidence proves that, on average, the more expensive the market, the lower the returns. However, that is not true for all periods. Sometimes, the market does quite well when it is expensive. The internet bubble of the late 1990’s is an easy example. It was quite expensive for a very long period of time, and only got more expensive as the market continued to grow. In hindsight, most blame Alan Greenspan for over-reacting to the potential consequences of the year-2000 bug by flooding the market with easy monetary policy. Similarly, other periods of extreme valuation can be understood in the context of the environment at the time. Many believe today’s current market valuation can be explained by a combination of low interest rates and high expectations of economic growth and corporate earnings growth due to Trump’s tax reduction and lower regulatory proposals.

Using history, we can see the paths the S&P 500 took when expensive to know that not all markets are the same. The charts below examine the 1-year and 3-year returns every time markets entered the 90th percentile based on Price-to-Earnings and Shiller’s Price-to-Earnings ratio. We can see that there were some very good returns (in excess of +40% over 1-year and nearing +100% over a 3-year period), while there were also some quite poor returns (-40% and -80% respectively).


S&P 500 Returns Return Paths


Adding this data to our previous distribution charts from above, we can see a leftward shift in returns, particularly over the 3-year period. We also see significant returns at the upper end of our distribution – there were times when expensive markets just got more so!


S&P 500 Returns Distributions


Viewed differently, we can see that when markets were expensive, they generally fell more often than average (33% and 31% versus 27% over a 1-year period and 23% and 47% versus 25% versus a 3-year period).


S&P 500 Percent of Time


More than that, when markets were expensive, the magnitude of any rise (on average) was smaller while the magnitude of any fall (on average) was bigger than the long-term average. The charts below combine the percentage of time rising, remaining flat or falling (represented by the size of the circle) with the magnitude of each. These charts tell us that when the market is expensive and falls, it falls by 18.7% (based on P/E) and 18.8% (based on Shiller’s P/E) while the history of S&P falls is 16.6%. In contrast, when the market rises, it rises by 16.7% (based on P/E), 16.5% (based on Shiller’s P/E) and 20.1% on average. The annualized 3-year numbers are even more damaging to return expectations in an expensive market (see table).


Time vs Return


Up Flat Table


Despite this data, one could fairly conclude that the risks of an expensive market are not materially worse than those of all markets. After all, the market falls 27% of the time regardless of valuation, adding another 4-6% additional probability that the market will fall isn’t that much worse despite the fact that the average fall is more than 2% greater.

However, combining the three scenarios by summing the returns multiplied by the percent of time the market rises, remains flat or falls provides weighted average return expectations for our two versions of an expensive market combined with the market ignoring valuation. In the 1-year case, we can see the lower expectations given the lower up- and down-market returns while the 3-year weighted return expectations are a bit mixed based on which valuation measure you choose for your focus.


Wgtd Avg Return


But, is this enough to change your risk and return inputs? Perhaps not.

Let’s return to my cherry-picked year-2000 internet bubble example. I chose this example because of its abnormality. The market was expensive because Alan Greenspan set the monetary conditions such that there was virtually no risk in the market. By his actions, and his words, he removed the possibility that the economy and the market would be adversely affected by a computer glitch. His thinking was, if something when wrong, there would be enough money sloshing around the economy that we could muddle through until the necessary fixes were made.  Recognizing the opportunity, investors flocked to the market in such a way as to push prices beyond reasonable valuations. Quite frankly, valuation didn’t matter during this period. The only thing that mattered was click-through rate (something my colleagues and I used to laugh about). In the end, reality caught up with investors and the bottom fell out of the market. There are other, albeit opposite, times in the history of the market where valuations were at extremes yet didn’t matter. After the 1929 crash and the beginning of the Great Depression, valuations were also at extremes. In this case, earnings were the issue and not prices. Prices had fallen 80% peak-to-tough. During the same period, earnings had fallen 66%. However, as the country began to work through these difficult economic times, the market saw the light ahead and drove forward. As a result, market prices recovered quicker than earnings, leading to a period of 90th percentile valuations. As earnings eventually materialized, valuations normalized. Similarly, the period following the Financial Crisis of 2008 saw similarly high valuations as the market recovered quicker than earnings. These two periods, along with the internet bubble were quite abnormal in that market valuations reflected events beyond what would be considered reasonable. In the internet bubble, Greenspan underwrote risk. In the aftermath of the two big financial crises, investors pushed markets ahead in expectations of future earnings.

If it’s true that these three events are abnormal, they have skewed our view of risks versus reward during moments of high valuation. Removing these events from the analysis provides a “cleaner” insight into the expectations we should have during these periods. The revised Percentage of Time charts below show that expensive markets rise less often and fall more often than the average market once these three abnormal events are removed.


Percent of Time


Not only that, expensive markets rise less and fall more as well.


Time vs Return


Leading to the inevitable conclusion that the weighted average expectation of expensive markets is exceedingly worse than that of the average market.


Wgtd Avg Regurn


Revising the table from above, we now see marked reductions in return expectations (both in up and down markets) as well as marked reductions in the percent if times the market rises and a marked increase in the percent of time the market falls.


Up Flat Table


The conclusion (I hope) is self-evident. When markets are expensive (as they are now), it is only the special circumstance which allows the continuation of “normal” market returns. In other words, return expectations based on the full history of market returns during an expensive market is a fool’s game. Similarly, the downside risk of an expensive market is significantly more likely and significantly more damaging than that of the full history of the market.

Determining risk versus reward is a key component in investor decision-making. However, analysis of risk and reward can be obscured and difficult to measure due to the smoothing effect of history and the confusing effect of significant historical events. One must look through the data to determine the real risks and rewards of the current market environment.  Today, despite what you may hear, risks are high and rewards are low.  Eunoia Financial hopes you are taking the necessary steps to protect your hard earned assets.