April 17, 2017: Risk vs. Volatility: Long Term Stock Market Returns

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Risk vs. Volatility: Long Term Stock Market Returns

Recently, we received the following email from a user:

This is not really a support question, but rather a general observation. First, I should say that I am a subscriber, and I find the service to be useful, and the observations to be astute. Nevertheless, I have the same comment on your service that I have about most of the financial industry, and that is this: you treat the words “risk” and “volatility” as though they were synonyms. But they are not. The only relevant “risk” for a retirement investor is that he (or she, of course) runs out of money before he dies. Volatility is only risky, in the long run, if you chicken out in a bear market and sell. By choosing assets during the accrual years that are uncorrelated, you absolutely guarantee yourself a lower return than you would have gotten by simply holding the asset class with the highest rate of return. This is a mathematical certainty. As you approach retirement, you do, of course, need sufficient liquidity to ensure that you will not need to sell assets at depressed prices. However, for younger investors, why should there be any allocation at all to less volatile investments, if their return is lower? Certainly, this calls for a level of investor education which is sorely lacking – but shouldn’t that be the job of an investor service such as yours? By conflating the terms “volatility” and “risk”, you play into the fears of uneducated investors, who should be embracing volatility as the best friend of the long term investor at a young age.

Just a thought.

The user’s comment is right on. In this newsletter, we will look at the notions of risk and volatility in more details and also clarify the concepts.

Common sense on risk

Let’s first look at the notion of risk in common sense. There are many ways to define investment risk:

Permanent loss of capital: this is the one used by Warren Buffett in some occasions. Basically, in Buffett’s framework, an investment incurs risk when one can not recoup his capital permanently. Several assumptions are embedded in this notion: the investment horizon is indefinite (or you have long enough time or patience to wait it out to need the investment capital again); the loss of capital should include the inflation risk, i.e. even if you get your money back 20 years later, but if at that time, inflation has reduced the purchasing power of a dollar by half, then you still lose half of your capital. The key here is that this notion assumes a long enough period of time.
Run out of money in your retirement: just as what the user stated in his email, for retirement investments, the most common sense of risk is that one runs out of money to support his/her retirement.
However, there are more investment objectives to consider. The most important one is that one needs the capital (or part of the capital) in various time horizons. Practically, you might need to spend some money in 10 years for kids’ college or you might even need to withdraw money periodically when you are in retirement or when you are out of job or just to supplement or need to support others.

In essence, investment risk should be looked at from the need of (part of ) the capital in various horizons.

Other risk factors including the behavior risk stated in the user’s email: investors can behave in appropriately because of the mismatch of expectation (or lack of) with the actual investment fluctuation (such as the stock market loss in a bear market).

Volatility and risk in various investment horizons

Volatility is more a mathematical metric that’s used to gauge the fluctuation of investments (or an overall portfolio) in a period of time. This is just an attempt to approximate (or model) the risk mathematically. From the above discussions, one can see that such an approximation has to be defined in a certain investment horizon (or time interval).

Common volatility measures are often defined in one to three years and they can be as fine grained as daily to weekly to monthly.

Once volatility is defined with respect to a specific time horizon, it becomes more relevant to the notion of risk. For example, if you want to spend some of your capital in five years, you would want to understand how the investments would fluctuate in five years. If the nature of the investments fluctuates a lot even after five years and it’s possible to even incur a loss (inflation adjusted), then we would say these investments are risky in five years.

Notice however, here we are not talking about the daily fluctuation in the five years, but instead the fluctuation after five years. This brings us to the notion of rolling years returns. In this case, what one wants to understand is how volatile the investments are on a rolling 5 year basis. Supposed we look at historical data on a rolling 5 year basis and we find the returns of investments are less volatile, we would say they are less risky. Again, there are many scenarios where one can find such a model is inaccurate.

Risk in long term stock market returns

Let’s look at the US stock market returns, especially in a long period of time.

First of all, as stated previously, assuming one is in a fair market, investing in a stock market aggregate (index) for a long period of time virtually guarantee you an inflation beating return. We again cite what’s stated in a previous article,

regardless of the macro economic situation, company stocks should give investors (their owners) a better return. since a company owner would demand higher returns compared with just simply putting money into a bank: otherwise, the owner would just simply closes the company and get similar or better returns in a bank without much risk and work, for example. In aggregate, equities in general should return more than cash or even safer fixed income.

Of course, the above claim is based on the assumption of investing in a fair market as well as in a long period of time. The question is how long. Let’s first look at the S&P 500 index total returns on a rolling 10, 15 and 20 year basis:

The above chart depicts the S&P 500 total return (annual dividend reinvested) using the rolling 10, 15 and 20 year annualized return from 1891 to 2016. The actual data start from 1871 to account for the first rolling 20 year period in 1891, a total of 145 years. For example, the annualized return of the rolling 10 years in 1891 is the annualized return from 1881 to 1891. Similarly, the rolling 20 years annualized return in 2016 is the one from 1996 to 2016 while in 2015 is from 1995 to 2015. The data are from Robert Shiller’s long term S&P 500 data. The chart only shows the data in a year end. However, the original data are monthly based.

On the rolling 10 year basis, S&P 500 had an annualized -0.55% return in 1938 (i.e. from 1928 to 1938, the great depression era). The other two instances of annualized loss are in 2008 (-1.4% from 1998 to 2008) and 2009(-0.73% from 1999 to 2009).

There are no negative rolling 15 and rolling 20 year annualized returns.

However, if we look at the monthly data, we see that if an investor would withdraw money in September 1944, he would incur an annualized loss of -0.38% from 1929 to 1994, a 15 year period. This is the only month that the rolling 15 year return was negative. For rolling 10 year return, all the months from November 2008 to December 2009 are negative, meaning if you would need money that was invested in 1998 in any of these months from 2008 to 2009, you would incur loss.

Now let’s look at the returns in some mathematical sense:

	Rolling 10 Years	Rolling 15 Years	Rolling 20 Years
Average Annualized Returns	9.2%	9.2%	9.3%
Standard Deviation (using Monthly Data)	5.0%	4.1%	3.3%
Minimum Annualized Return	-4.0%	-0.3%	2.1%
Maximum Annualized Return	21.1%	19.3%	17.9%

It’s interesting to see that the average annualized returns for the 3 rolling periods are very similar: around 9.2%-9.3%. However, the standard deviation and Min/Max of the returns can further tell us how risky S&P 500 index is:

There was a month when S&P 500 rolling 10 year annualized return was -4% — remember that is the annualized negative return. This would translate to -33% compound return in that 10 year period, without counting the inflation effect! That’s certainly very risky!
Assuming a normal distribution (an assumption), there is a 2.5% ((100-95)/2) chance that the rolling 10 year return would fall below 9.2%-(2*5% (2 standard deviation)) = -0.8%. This again says investing in a 10 year period is risky.
However, if you would extend the investment horizon to 20 years, it’s almost impossible to incur loss. But still, there is a 2.5% probability to incur 9.3%-2*3.3%=2.7% low return! The above does not take inflation into account. We suspect that it will incur a loss on the inflation adjusted basis.

What the above exercise shows us is that

Investing in a long enough period becomes much less risky. In S&P 500 index case, it would mean 20 years.
However, low returns can still happen even for 20 years.

Summary

We can draw some conclusions from the above discussion and exercise :

Risk and volatility are not the same.
Both should be on a specific period of time horizon.
Volatility is an approximation of risk. It should be with respect to a specific time horizon. To be more precise, one should look at returns in a rolling period.

Though we are also guilty of speaking too loosely on risk and volatility, just like many other financial sites, we want to emphasize that it’s important for investors to understand the real risk of investments. In a long time horizon, interim market fluctuation, if understood properly, can be your friends instead: utilizing lower prices or lower valuation to invest (additional) capital. On the other hand, market fluctuation can be your enemy when you need the capital in a short term. That’s why one should review your financial situation periodically and pinpoint possible risk and opportunity within a time horizon.

Market Overview

Even though we observed some volatility in US stocks last week, in general, we see markets are still priced optimistically. For now, stocks, risky bonds (high yield bonds and emerging market bonds) are still in favor. However, we do see that the yield curve (i.e. the yield difference between long term bonds and short term bonds) has flattened, indicating a more cautious stance on long term market perspective. As stated, stay on course and manage risk properly.

For more detailed asset trend scores, please refer to 360° Market Overview.

Now that the Trump administration is officially sworn in, the new president is facing the reality to deliver his many promises to make substantial changes. As the nation is posed to invest, the most important factor to watch is how productive the investments will be. Simply put, productive investments will result in better return on investment (ROI), tangibly or intangibly. They should also increase productivity that in turns will improve our standard of living. Capital misallocation can result in a higher growth but might not improve the real standard of living, which is the ultimate goal of economic activities. Whether the new president can truly achieve this goal is still yet to be seen. One thing is certain: we will see more market volatilities.

In terms of investments, U.S. stock valuation is at a historically high level. It is thus not a good time to take excessive risk. However, we remain optimistic on U.S. economy in the long term and believe much better investment opportunities will arise in the future.

We again would like to stress for any new investor and new money, the best way to step into this kind of markets is through dollar cost average (DCA), i.e. invest and/or follow a model portfolio in several phases (such as 2 or 3 months) instead of the whole sum at one shot.

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