Risk and Return Part 1: The most important concept in finance and possibly in life

Is a crisis a bad thing or a good thing?

In 2003, I set up a new company, Expara. The new company needed a new logo, and I chose the Chinese character, “Wei Ji” which is most often translated into English as “crisis.”

You might wonder why I would want to make crisis the symbol of my venture capital company, given that crisis is generally considered to be a pretty bad thing. I chose it because “crisis is bad” is one of those things that seem so obvious, but when looked at more closely and carefully, doesn’t seem obvious at all.

Is a crisis truly a bad thing, or is it a good thing, or is it neither good nor bad?

If it is bad thing, how is a crisis different from a disaster? A situation that is a disaster is definitely a bad thing, so it seems there must be some additional aspect of a crisis that is not captured in the word disaster. If you are sick and your doctor tells you that your condition has reached a crisis, should you be happy or terrified?

You should probably be a little bit of both.

What exactly is a crisis?

A crisis is a situation that has reached a critical turning point . A crisis situation is characterized by uncertainty: it will either get much better or much worse in the near future, but we don’t know in which direction it will go or precisely when.

In 2020, we lived through the COVID pandemic, a global crisis of epic proportion. If you remember the degree of uncertainty we were living with back then, you know what makes a crisis special. Almost overnight, the world had completely changed. Normality was replaced by lockdowns, shortages, and empty cities that looked like scenes from a zombie apocalypse movie. We were constantly watching the number of cases, the mortality rates, and all the other COVID data, and wondering every day when the trend lines were going to turn up or down, whether the world was going to turn into Europe during the Black Death, or whether it was going to be over soon, and the world was going to go back to normal.

The one certainty we have about a crisis is that it is unstable. It is not going to remain the same for very much longer. A crisis is a duality.

Danger and opportunity

Wei Ji expresses the exact same essence of the duality of crisis. Like many Chinese characters, it is composed of two individual characters, each one with a different meaning. In this case, the first character means “danger” and the second means “opportunity.”

We can view the relationship between danger and opportunity from two different perspectives: 1) In every situation of danger there is opportunity or; 2) to reach the opportunity, we must first pass through danger.

When you hear danger and opportunity together, do they remind you of another pair of words that are central to our understanding of finance and investment (and many other things in life)?. Danger and opportunity sound a lot like risk and return.

What are risk and return?

Return is pretty straightforward – it is the gain or loss made on an investment (usually stated relative to the amount of money invested). If you invested $100 and received $110 your return would be $10 (or 10%). Return can be positive (you made money), zero (you broke even) or negative (you lost money). Return is fundamentally a duality; it will be either positive or negative (setting aside the neutral case).

Risk is not so straightforward – most people badly misunderstand financial risk and in a way that can cost them a lot of money and happiness. The common usage of “risk” is totally inconsistent with the financial definition of risk.

Dictionaries are not helpful here, as they reinforce the fundamental misunderstanding. Here are some examples of misleading dictionary definitions of risk:

“(Exposure to) the possibility of loss, injury, or other adverse or unwelcome circumstance” - OED

“Possibility of loss or injury” - Merriam Webster

Given these definitions of risk, would you say that risk is a good thing or a bad thing?

These definitions make it clear that risk is a bad thing. Losses, injuries, and adverse circumstances are all bad things, to be avoided at all costs. These definitions reinforce our intuitive understanding of risk.

Our intuitive understanding of risk is very useful in the physical world, where the potential returns to many types of risk are heavily shifted toward the downside, and were even more heavily shifted toward the downside in our evolutionary past.

The last definition below fails the worst, because it applies our intuitive understanding of risk to finance.

“The chance that an investment (such as a stock or commodity) will lose value" – Merriam Webster

What is financial risk?

In the financial world, intuitive definitions of risk not only cease to make sense, they lead to poor investment decision-making.

Financial risk is defined as the variance of the potential returns from an investment. In statistical terms, variance is the square of standard deviation. In ordinary terms, variance is the stability of the returns, except that low variance means highly stable and high variance means highly unstable.

The chart below shows the variance (volatility) of two investments, with variance on the y-axis and time on the x-axis, a no variance investment would show basically a straight horizontal line and a high variance would show a crazily zig-zagging line.

An investment with a low variance of its potential returns is a low-risk investment while an investment with a high variance of its potential returns is a high-risk investment.

This matches our intuition. An investment with a 100% guaranteed return would clearly be a very low-risk investment (or even a no-risk investment if the guarantee was strong enough) and would have a variance of zero. An investment with a 3% probability of returning $10 million and a 97% probability of returning $0 is a very high-risk investment and would have a correspondingly very high variance.

So far this seems completely obvious – so what is the key difference between our intuitive understanding of risk and financial risk?

Upside and downside risk

The key consequence of defining risk as the variance of potential returns is that a high variance of returns will create both high loss (downside risk) and high gain (upside risk) outcomes.

Financial risk is a duality; risk is no longer a bad thing.

Defining financial risk as the probability of loss is meaningless, because the common-sense association of risk with loss admits only downside risk while ignoring upside risk. In a world with only downside risk, rational people would be totally risk averse. In a world where there is both upside risk and downside risk, rational people can be risk averse, risk seeking or risk neutral.

What is the relationship between risk and return?

Now that we have clear definitions of risk and return, the next question is: What is the relationship between risk and return? When risk is defined as variance of return, risk and return are highly positively correlated. You have probably heard it expressed this way many times:

High risk, high return

And its inverse:

Low risk, low return

High risk, high return. Low risk, low return. Again, these seem completely obvious. Everyone knows about these correlations.

Although everyone has heard these before, many people seem to misunderstand what they mean, or if they do understand them, they act the same way they would if they didn’t understand them at all.

High risk/high return; low risk/low return

When you read these two statements together, they may appear to be making the same point in two different ways, but are they? Or are they each saying something completely different?

To answer this question, let’s transform the second statement into and If/Then proposition.

An If/Then proposition is a statement that if A is true then B is true 100% of the time. If A is true and then B is true 99.99% of the time, then the If/Then statement is false. In order to prove that an If/Then statement is false then, you just need to find one case in which A is true and B is false.

If we transform low risk/low return into an If/Then proposition it would now read:

If I take low risk then I will receive low return.

100% of the time.

True or false?

If you said that this statement is false, you are saying that there must be at least one case where you can take low risk and receive other than low return. There must exist at least one low risk/high return investment opportunity.

I am willing to bet you $100 that there is no such investment opportunity. If you can come up with one, you win and if you cannot come up with one, I win. To make sure we are clear on the terms of the bet, here are the rules. These rules are in place to make sure that your answer is a real investment. It must be:

1. A pure financial investment with a measurable financial return. It can’t be something like “my education is a low risk/high return investment.” It may well be, but this bet is just about financial returns.

2. A legal investment. Illegal investments come with additional non-financial risk, like the risk of imprisonment or death, which materially change the calculation.

3. A repeatable investment. It cannot be a one-time opportunity like you have some non-public (but legal) information about a potential investment that reduces the risk.

4. Accessible to an average investor. It cannot be an investment that is only available to certain investors, like government or government-linked investors or investors with huge amounts of capital to deploy.

5. An investment that generates higher than low return. It cannot be a low-risk investment that delivers less than low return or negative return.

Take some time to think about it and see if you can come up with one example of a low-risk, high-return investment.

OK, time’s up and you failed. I won our bet and you lost it. How do I know this?

Because there are no low real risk/high return investments that meet the criteria in my bet above. There are none, and there can never be one.

Find out why in Risk and Return – Part 2.