Appendix C

The standard deviation

Table C.1 Losses according to standard deviation (SD)

So what does this mean for you?

Going back to Figure 6.1 you can get a decent picture of what risk you take by investing in the two markets (see Chapter 6). (Simplistically, I suggest using a 20% standard deviation.) You can then take this risk and use the standard deviation table (see Table C.1) to estimate how frequently you may expect to incur various levels of losses in the equity portion of the portfolio. While using the standard deviation is not an exact science in this context (we don’t know nearly enough about future risk to say that there is precisely a 15.9% or 2.3% chance of the loss), at a basic level the standard deviation can help us understand the probability of various things happening to our equity portfolio, and thus help us plan our finances.

This may seem like finance mumbo jumbo, but you should try to understand it because it gives you an idea of how much money you can make or lose from investing in equity markets.

The standard deviation is useful, but hard to predict and has some flaws

The large fluctuations in the risk of the equity markets shown in Figure 6.1 suggest that we should generally be cautious about claiming too much precision in estimating the risk of an investment portfolio.

Consider the increase in the market risk during the 2008–09 financial crisis. If you had allocated assets to equities because you thought they had a risk profile similar to the historical one, you would find yourself at the height of the crisis with an equity portfolio far riskier than that. Equities are more volatile in times of crisis, but this is also typically where you have already lost a lot of money investing in them. If you shied away from equities at the peak of the crisis because they were now riskier than before, you would be selling equities and probably lock in a big loss, perhaps at the bottom of the market. In order to avoid this, you must make a conservative enough allocation to equities so that you can afford both the occasional losses but also the increased risk that inevitably comes with that decline.

While the standard deviation is a useful concept it is certainly not a perfect measure of risk. One of its drawbacks is that it does not properly account for skew or ‘fat tails’. What this means is that outcomes that are considered highly unlikely if you look only at the standard deviation, in reality happen a lot more. This is very important as otherwise we would massively underestimate how frequently we can expect to incur very large losses from our equity portfolio. At the time of writing, the standard deviation of the S&P 500 is around 15%; if we assume an expected return of 5% a year we can see from above that a 40% loss would be a 3 standard deviation event (a 45% move from the 5% expected outcome). We can also see that if we blindly used the standard deviation we would expect this to happen every 741 years, when we know that in reality it happens every couple of decades.

Understanding that highly unlikely events happen more than suggested by the standard deviation is important when we consider the risk of our portfolio. Large losses can and probably will happen, and almost certainly happen more than the simple standard deviation will have us think. How much more is hard to predict, but be ready for the possibility, and avoid just blindly using the standard deviation to understand your risk, even if some textbooks and finance practitioners seem to think that this method is the answer. It’s not.

If you are confused about all this, don’t despair. You are not alone, and until a couple of decades ago this stuff was rarely mentioned even in academia. Just remember that the standard deviation gives you a reasonable idea of how much money you can make or lose and is therefore useful for planning the portfolio, but also remember that unlikely bad events with large losses happen far more than the standard deviation suggests, and be ready for surprises.