There are two basic, common-sense principles at the heart of finance theory. The first is that risk and return tend to go together, in other words, if somebody offers you an investment which promises to be both low risk and high return there’s probably something wrong with it. And the second principle is the benefit of diversification, which is captured in the old European proverb, don’t put all your eggs in one basket.
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We’ll return to diversification another day. Today we’re going to talk about risk and return.
The basic idea here comes from economics, of which finance is a part. Economists’ view of how humans behave is that people in general like higher returns, but they dislike risk.
On the whole, this is probably not a controversial way of thinking about people. But you might object, there are times when people like risk. When they go to Las Vegas or Macau to go gambling they’re presumably going there to enjoy taking risks, assuming they’re attracted by the gambling casinos. That’s true, but it’s risk as entertainment, which if they keep it under control and only let themselves spend a limited amount of money is rational, whatever your ethical view of gambling.
But we assume that when people are thinking about more serious aspects of their life, such as investments, pensions and how to protect their family, that on the whole they don’t like risk. We often say that people are in general risk-averse, though like every economic generalization, you may find exceptional cases.
When we talk of return, what do we mean?
For any particular asset or investment, the return can potentially come in two ways.
First, it can generate an income. So for example if you own an apartment and you rent it out, you receive rent; if you own a bond issued by the government or a company you receive interest; and if you own a share in a company you may receive a dividend, although it’s not guaranteed.
Secondly the value of the asset can go up: if you bought shares in Apple many years ago you would have achieved a very high increase in the value of the shares: that’s a capital gain; on top of that, from 2012 you would also have received a dividend, but in the previous seventeen years it didn’t pay a dividend.
What we call the total return is the combination of these two ways of getting a financial benefit from owning an investment, the income plus the capital gain. Of course, you may also make capital losses – not every company share does as well as Apple, and many become worthless.
You will sometimes see total return indices for the stock market which capture both the dividend income and the capital gain on the shares in that stock market index. Apart from tax considerations, which in practice can be quite important, we don’t distinguish whether the return comes in the form of income or capital gain. The important thing is that we assume that people like returns.
Financial economics thinks of risk as volatility of returns
Now what can we say about risk? There are lots of ways of thinking about risk and the way that finance tends to think about it is the variability or volatility of the returns.
So, if we’re thinking about a particular investment possibility like buying shares in Apple, the risk involved is how far the returns vary over time, usually measured on an annual basis. If we plotted on a chart the annual returns on Apple shares over the last 25 years or so we would see that in some (indeed most) years they go up, but in some years they might go down. The range of variation between the ups and downs is essentially the riskiness of that investment. We can measure that variation statistically by using a measure known as the standard deviation which is a measure of variability of those returns around their mean or average return.
This is only one way of measuring risk, which treats losses and gains equivalently. There is a lot of evidence that ordinary people treat losses as disproportionately worse than the benefits of gains – this theory is called loss aversion. It is considered a deviation from the conventional corporate finance theory, but there is strong evidence for it being valid. Richard Thaler and Alex Imas make a convincing case for this being a more accurate way of thinking about how real human beings think of risk in the revised 2025 edition of the book The Winner’s Curse, which contains a wealth of fascinating research on behavioural economics anomalies.
They do recommend that we keep teaching the conventional theory, as outlined above, as a guide to how we should think about risk. Professional investors, whose behaviour is (mostly) more important for financial markets than retail investor behaviour, might plausibly thought as being closer to the textbook rational model, but even they have their behavioural biases.
But nobody disputes that people typically dislike risk, even if they do disagree about how to measure it.
So, to conclude, the two variables that conventional finance theory assumes that people care about when they look at an investment opportunity are the average or mean expected return, it can only be an expectation, we don’t know what it will actually be; and the average expected variability of that return, stated as the standard deviation of the returns. History gives us a basis for estimating both the expected return and the expected risk, but, as financial advertising always reminds us, the past is not necessarily a guide to the future.
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