Investment Risk in Greater Detail

On 05/11/2010, in Investment Concepts, by Jordan Wilson

Today we look at investment risk in greater detail.

This expands on our preliminary discussion in Defining Investment Risk.

Investment Risk Revisited

Previously we defined investment risk as a speculative risk. As such, investment risks provide the possibility of incurring a loss, breaking even, or profiting.

I stated that investment risk is the probability that the actual returns on an investment will differ from the expected returns. The higher the probability of a different result, the greater the risk. The lower the probability of a different result (or the greater the certainty of the same result), the lower the risk.

For those of you poor souls who have taken statistics courses, investment risk is typically viewed from a normal distribution perspective. The graph below is an example of a normal distribution curve.

Normal Distribution Curve

Normal Distribution Curve

Not the easiest concept to explain in a blog post (augmented by the fact that I am not a statistics professor), so we shall try and keep this basic.

Like head-ache medication though, I caution you not to read this post while driving or operating heavy equipment. The following may just put you to sleep.

Normal Distribution

You may also recognize the graph above as a Bell curve, so named for its shape. Or you may have heard it called a Gaussian distribution; named after Carl Friedrich Gauss.

Within a normal distribution, historic outcomes are placed on the graph and a distribution similar to the one above typically results.

It is called normal because the potential outcomes are symmetric in nature. You can see this by the equal spread of outcomes on both sides of the curve. Notice how the tails on both the left and right sides of the curve are similar in distribution.

If the distribution was not normal, but rather skewed, one end of the curve would be longer and more pronounced than the other end.

The important thing to note with a normal distribution is the way the Bell curve looks. As you can see, most of the actual results cluster relatively close to the middle of graph. The higher the curve, the more results are at that level. As you move farther from the middle, the number of results decreases. This creates the diminishing tails at either end.


In investing, the mean is the expected return on the investment. This is represented by the average result on the above normal distribution curve, located at position 0.

The expected return may be calculated based on historical data, theoretical probability models, experience, and professional judgement.

Because most investments have some risk, actual results may differ from the expected outcome. Actual results will usually lie somewhere to the left or right of the expected return. That said, there is no reason that they cannot fall exactly on the mean.

Investment Risk

So we know that the expected return of an investment is the mean, or average, in a normal distribution. We also know that the actual results will fall on either side of the mean.

But what does that tell us about the investment risk?

The investment risk is the variability of the actual returns around the mean.

As you can see above, actual results may be both greater or less than the expected return. So investment risk applies to the possibility of higher than expected returns, not simply lower than expected ones. However, investors are usually more concerned with results to the left of the curve. That is, where the actual performance is less than the expected returns.

The risk of an investment is determined by the variability, also known as volatility, of the actual returns around the expected return. Volatility is the amount of fluctuation in the actual returns from the expected returns. The greater the degree of volatility, the greater the risk of the investment.

The tighter the probability distribution of the expected future returns around the mean, the greater the certainty of the returns. As the certainty of the return increases (i.e. the less potential difference between the actual and expected result), the smaller the amount of uncertainty or risk.  In a normal distribution curve, the vast majority of actual results would amass extremely close to the mean. The bell would be quite high and narrow in width.

For results with high variability, the actual returns would be disbursed much farther from the mean. This would cause the bell shape to be shorter in height and much wider in width.

For example, investment “A” has an expected return of 5% and the actual returns over the last 6 years were 4%, 6%, 5%, 5%, 6%, 4%. The distribution around the 5% mean is quite tight. You would be right to expect the return over the next year to be close to the expected outcome.

Investment “B” also has an expected return of 5%. However, its performance for the last 6 years was 2%, 12%, -4%, 15%, -3%, 8%. The actual results are significantly different from the expected result. You may be concerned that the actual result for the upcoming year will not be close to the expected return of 5%.

Here you have two investments with the same expected return. Yet the certainty of earning 5% on A is pretty high for next year while there is very little guarantee as to what B returns. It may be 5%. Or it may be significantly different than 5%. Even experiencing a loss.

That is investment risk.

So how does one differentiate between the two investments?

Standard Deviation

In comparing two investments with the same expected return, it is extremely useful to quantify the investment risk.

To be of any practical use, a measure of risk must have a definitive value that may be analyzed by investors. The 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 any 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. And 98% of all returns will occur within 3 standard deviations of the mean.

This is consistent in any normal distribution scenario.

So if you are concerned about negative returns, under 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. Choice A offers an expected return of 10% over a one year period. Option B offers an expected return of 13% over the same period.

Ceteris paribus (all else equal), investment B should be your choice as it offers a 30% higher expected return for the year.

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. Investment A has a standard deviation of 2. Investment 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.

Investment A has an expected return of 10% and a standard deviation of 2. That means that 68% of all possible returns you may actually achieve are between 8% and 12%. It also means that 95% of the time you will experience returns between 6% and 14%.

For investors worried about experiencing a loss or lower than desired returns, 95% of the time they will, at worst, earn a 6% return.

Investment B has an expected return of 13% but a standard deviation of 9. So 68% of the results will lie between 4% and 22%. And 95% of the returns will be between -5% and 31%.

Very nice upside potential. But if you are concerned about lower potential returns or even losses, investment B might be too risky.

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 risk).

Other investors might be lured by the potentially high returns of investment B. Option A should rise no higher than 14% (97.5% of the time), whereas investment 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, whom we will discuss later) tend to be risk averse. That is, when faced with two investment choices of similar return, 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 looking back at the example above, I would suggest that investment A is the better choice based solely on the information given. I say that because the relatively greater expected return of investment B is not great 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.

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.

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