Let’s continue our look at Investment Risk in Detail.
In the last post, we ended with an example. Two investments with the same 5% annual expected return. “A” had a stable return history, so the probability of earning the 5% next year is high. However, “B” had a highly volatile return history, so the probability of earning exactly 5% next year is low.
Same expected annual return over time, but much different likelihoods of actually earning the 5% return in any one year.
As an investor, how does one differentiate between the two investments?
A very important question. Hint: it may involve investment risk.
Standard Deviation
In comparing two investments with the same expected return, it is extremely useful to quantify the investment risk.
And remember, investment risk is simply the volatility of an asset. High certainty of future returns as expected, low risk. Wide fluctuations in returns versus expected, high risk.
To be of any practical use, a measure of risk must have a definitive value that may be analyzed by investors. Standard deviation is the statistical measurement of the movement of returns around the mean.
In investing terms, the standard deviation is the measure of the total risk of the investment.
Under a normal distribution, the majority of actual returns will occur relatively close to the mean or expected return. This is good for predicting future results.
In a normal distribution, 68% of all returns will fall within 1 standard deviation of the mean. 95% of all returns will take place within 2 standard deviations of the mean. 98% of all returns will occur within 3 standard deviations of the mean.
Say the mean is 10 and standard deviation is 3. As 68% of results occur within 1 standard deviation from the mean, that equates to between 7 and 13. While 95% of the time, results will lie within 2 standard deviations. So, between 4 and 16.
This is consistent in any normal distribution.
Nice to know the range of possible results with 95% confidence. Makes investment analysis easier.
If you are concerned about negative returns, in a normal distribution, there is only a 2.5% probability that the next year’s actual return will be lower than 2 standard deviations from the mean. That is good to know.
Note that there is a 95% probability that a return will fall within 2 standard deviations of the mean. So there is a 2.5% probability that next year’s return will exceed 2 standard deviations (i.e. the far right tail of the curve) and a 2.5% chance that the return will be below 2 standard deviations from the mean.
Theory, theory, theory. Let us look at how this applies to real world investing.
An Example of Standard Deviation
Perhaps you have two investment choices. “A” offers an expected return of 10% over a one year period. “B” offers an expected return of 13% over the same period.
Ceteris paribus (all else equal), “B” should be your choice as it offers a higher expected return than “A”.
But all else is never equal, except in Latin phrases.
You notice during your research that each investment has a standard deviation assigned to it. “A” has a standard deviation of 2. “B” has a standard deviation of 9. You also note that both investments have normal distributions.
So how can standard deviations help your investment decision?
Remember that 68% of the time, actual returns will lie within 1 standard deviation of the expected return and within 2 standard deviations 95% of the time.
“A” has an expected return of 10% and a standard deviation of 2. That means 68% of all possible returns actually achieved will be between 8% and 12%. And that 95% of the time you will experience returns between 6% and 14%.
A fairly stable distribution of returns over time. Not a volatile asset, “A” has a relatively low standard distribution.
For investors worried about experiencing a loss or lower than desired returns, 95% of the time they will, at worst, earn a 6% return. Nice to know if you are worried about absolute losses.
“B” has an expected return of 13% but a standard deviation of 9. 68% of results will lie between 4% and 22%. And 95% of the returns will be between -5% and 31%.
“B” is much more volatile in its returns than “A”. This is reflected by the higher standard deviation value.
Very nice upside potential of 31% return. But if concerned about lower potential returns or even losses, “B” might be too risky with it’s potential -5% return.
Armed with this new standard deviation information, does your investment decision change?
It might, it might not.
Investment Risk is a Relative Concept
As we discussed previously, the concept of risk is different for every individual.
Risk is therefore a relative term, not an absolute.
Some investors want to limit their downside investment risk and any possibility of experiencing a loss. Widows and orphans are in this group. As are many other investors.
These individuals willingly accept a lower expected return in exchange for a greater certainty of that return being realized. Investments whose potential returns are less volatile or variable are desired. A less risky result is preferable to higher potential returns (and more downside risk).
Other investors might be lured by the potentially high returns of “B”. Option “A” should rise no higher than 14% (97.5% of the time), whereas “B” could beat that return easily (of course, it could also do significantly worse as well).
Risk Aversion Versus Risk Seeking
While each investor takes a different view of risk, most investors (as opposed to speculators, who we will discuss later) tend to be risk averse. That is, when faced with two investment choices of similar return, they select the less risky one.
In contrast, risk seekers will actively assume greater levels of risk in the hopes of achieving higher returns. Their risk tolerance is significantly higher than risk avoiders.
In the capital markets, you need some investors to be risk seekers and others to be risk avoiders. The system will not properly function if everyone is the same. As we will see later, hedgers actively attempt to reduce their risk exposure. But they need to transfer that risk somewhere. Without risk seekers, there would be no one to assume the hedger’s risk and the markets would be very inefficient.
In the example above, I would suggest “A” is the better choice based solely on the information given. I say that because the relatively greater expected return of “B” is not large enough to warrant the significantly higher level of risk you must assume. So while I have no problem with risk seekers as an investor class, risk should be assumed prudently.
A Rule to Remember
“When faced with two investments offering identical expected returns, investors will always choose the one with less risk.”
Or stated another way:
“When faced with two investments having identical risk, investors will always choose the one with the higher return.”
Of course, the issue is choosing between two investments when they have different expected returns and standard deviations. A more likely scenario in the real world. And the choice usually comes down to the individual investor’s risk tolerance and unique personal circumstances.
In the near future we will look at the risk-return relationship and the implications of risk aversion and risk seeking on investment decisions. After which, please revisit this example and see if your original opinion has changed at all.
Regardless of your personal risk profile, the standard deviation of an investment is a very useful piece of information to have at hand. But be aware that there are limitations to the use of standard deviations.
We will look at these limitations in my next post.
