The two foundational concepts in financial economics are: i) risk and return tend to go together, which we explore here; and ii) diversification is a good thing.
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The old European proverb, don’t put all your eggs in one basket, captures the benefits of diversification: if you’re collecting your eggs from the chickens in the morning, or if you’re carrying them to market, in either case, if they’re all in one basket and you trip, you risk all of them breaking. If you carry them in more than one basket, you reduce the risk that they all break.
This proverb is believed to have first been written down in the great Spanish novel Don Quixote, published in the year 1615, but it almost certainly was used in common speech long before that.
There is a similar proverb that is said to date back to Roman times: “venture not all in one ship”. “Venture” is used here in its old meaning of to take risk for a potential profit, a meaning that lives on in the term Venture Capital.
The timeless common sense captured by this proverb doubtless exists in other cultures too. In Chinese there is an expression 孤注一掷, gu1 zhu4 yi2 zhi4 which literally translates as to concentrate all on one throw, as in a throw of the dice, though it’s usually translated just as don’t put all your eggs in one basket (*).
So why is this good sense and what does finance have to say that improves on it?
If you have some resource, or wealth, or money, and if you care about losing it, that’s to say you care about risk, then it’s wise to divide it up into multiple investments, each of which is at least somewhat independent of the others. As we’ll see, finance makes this more precise in the notion of the correlation of risks between different investments.
Selling ice cream and umbrellas: perfectly negative correlation of risks
Here’s a well-worn example from finance textbooks, which we keep using because it makes clear the benefits of diversification, by taking an extreme case.
Imagine there are two companies, one of which makes ice cream, the other makes umbrellas. And further assume we live in a country where the weather is very changeable, indeed it is extreme to the point that every day is EITHER hot and sunny, OR cold and wet.
This is a simplification to make a point, which is what economic models are for.
In this world, on sunny days there is a high demand for ice cream, but no demand for umbrellas, and on wet days the opposite, no demand for ice cream and lots of demand for umbrellas.
You may of course object, “but some people like eating ice cream every day, regardless of the weather. And if I buy an umbrella once, I don’t need to buy another one.”
Fair enough, the point of this sort of idealised story is to illustrate something specific, rather than to be a realistic account of an actual economy. And personally, I have bought plenty of umbrellas but somehow never seem to have one when it actually starts raining (**), but that’s probably just me.
To keep things simple, let’s assume it’s sunny exactly half the days of the year and rainy exactly half the days of the year. So, the ice cream company makes a profit half the time and no profit, or even a loss, half the time. Its profit swings repeatedly between good and bad outcomes. The umbrella company has the same experience, but on the other days.
If you bought shares in just the ice cream company, you would get a return, a profit, averaged over the good and bad days, but you would have a lot of variation or risk in those returns, which depend entirely on the weather.
Equally if you bought shares only in the umbrella company, you would get a return averaged over the good and bad profit days, with a lot of volatility in those returns, swinging from high to low.
But if you bought shares in BOTH companies, you would be guaranteed a return every day, which would be the average of the good and bad state for each company, in other words the same return as if you owned either one of the companies. Every day we either sell ice cream (so ice cream profits are high, and umbrellas make losses) or we sell umbrellas (in which case we get exactly the opposite). So, if we own both companies, we are assured of a return every single day. If the two companies have the same rate of profit, then owning both means we reduce the volatility of profits to…. zero.
Diversification in this case eliminates risk completely.
Even imperfectly correlated returns can provide diversification benefits
Now I admit this is an extreme case, because it’s unlikely that we can find businesses with precisely offsetting business risk. But the good news from portfolio diversification theory is that we don’t need this unrealistically high level of offsetting riskiness. So long as we can find two businesses, or investments, with at least partly uncorrelated returns, we can improve our overall risk-return trade off.
More technically, the benefit of diversification arises from the covariance between two or more investments. Covariance is a statistical measure related to correlation. So long as the covariance between two assets or investments is less than perfect, that is less than 1, then there is some diversification benefit to holding both of them in a portfolio.
This is very helpful, because finding two companies whose risk is negatively correlated is quite difficult. This is because most businesses share some common influence from the general state of the economy, so their profits tend to rise and fall somewhat together. But so long as they’re not perfectly positively correlated, there is a diversification benefit to putting both of them in a portfolio of investments.
Imagine you own shares in both Apple and Walmart, two major US companies, both of which sell things to American consumers (among others). If there is a recession in the US, we might expect profits at both companies to fall, but to a different extent. If consumers feel less prosperous, they may decide that a new iPhone is something that can be postponed till the economy improves, so Apple profits may fall quite a lot. We therefore sometimes describe a good like an iPhone as a consumer discretionary item.
But Walmart, a low price, or value retailing company, might see sales fall proportionally rather less, because a lot of what they sell is everyday stuff that people still need to buy. These goods are described as consumer essentials or non-discretionary. Walmart profits will probably still fall, just not as much as Apple’s.
So although both companies are affected by the overall state of the economy, and therefore their share prices are somewhat correlated, there is a difference between them and that means their returns are imperfectly correlated. That in turn means that a portfolio that holds both companies’ shares or stocks will be less volatile, less risky, than one that holds only one of them.
The beneficial effect of adding imperfectly correlated investments to a portfolio continues as we add additional investments, but the effect gradually diminishes, as we add more and more investments. We eventually meet a limit where we cannot reduce risk any further, where we have eliminated all possible diversifiable risk. What remains is called undiversifiable risk, or what economists call systematic risk. That systematic risk, which can be thought of as macroeconomics risk, is the minimum risk that an investor must be willing to bear, if they want to invest in equities. The return that investors need to be compensated for bearing that systematic risk is called the cost of equity.
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(*) In 2023 there was a popular Chinese crime thriller film with the title 孤注一掷 but the English title is No More Debts. The film concerns Chinese people who are trafficked to a fictional South East Asian country and forced to commit internet fraud. The government of Cambodia banned the film.
(**) At this point I always have to point out, to a generally sceptical non-British audience, that Cambridge is one of the driest parts of the UK.
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