Many investors just don’t understand the risk/reward trade-off


Confusion but there is hope

Almost everyone thinks that to earn a higher reward you have to incur a higher risk. It’s just not so. Also, many investors think that by incurring a higher risk you will earn a higher reward. Again, not so. This is a tricky subject.

To get our minds around it, think about the following:-  Incurring additional risk does not earn you a better return unless the likely reward more than justifies the additional risk.

What I have introduced the reader to is the investment concept of ‘expected return’. This is the notion that you can figure out the expected return on an investment by multiplying potential outcomes by the chances of them occurring and then totaling these results.

If this makes your head spin, we can let Warren Buffett explain it to us. Here’s what he said at the Berkshire Hathaway Annual Meeting in 1989: “Take the probability of loss times the amount of possible loss from the probability of gain times the amount of possible gain. That is what we’re trying to do. It’s imperfect, but that’s what it’s all about.”

Howard Marks weighs in on the same subject: “While in investing we generally aren’t offered explicit odds, the attractiveness of the proposition is established by the price of the asset, the ratio of the potential payoff to the amount risked, and what we perceive to be the chance of winning versus losing.” Memo to Oaktree Clients, 2020

Having got this far, many thoughtful investors would still stoutly insist that getting a higher reward necessarily means incurring a higher risk.

But, here’s the key idea: An investment with a lower risk may have a lower expected return than an investment with a higher risk. And, a higher risk investment may have a higher expected return than another equally high risk investment that has a lower expected return.

Let’s try it this way. Suppose I invite you to play two games. In the first I have created a card game in which the odds of winning are one in three. To make it fair you bet one dollar on each turn of the game and if you win you get three dollars. If you lose on any turn you forfeit your bet. So, you play and win three times in a row and receive nine dollars. If you play a thousand times you will almost certainly end up essentially even. That’s because your return expectation is zero and we have allowed the law of large numbers to take hold.

Now I offer you a different game. This time I have created a card game in which the odds of winning are one in ten. To make it fair, if you bet a dollar and win you get ten dollars and if you lose, you forfeit your bet. If you play this game a thousand times you will also end up with zero net loss and zero net gain. Your return expectation in the second game is the same as the first.

So here’s the question; which game is more risky? Is it the game with 1:3 odds or 1:10 odds? Your chances of winning on any turn in the second game are less than the first. I think most people would say the second game is more risky. You are betting the same amount of money, but, you are likely to lose nine out of ten turns.

Let’s switch the example: is it more risky to invest in blue chip stocks or penny mining stocks? Penny mining stocks are more risky for sure. But, with penny mining stocks if the potential reward is high enough the ‘expected return’ is the same. This is all premised on allowing the law of large numbers to work its magic. In investing, this means diversification and the long haul.

We can ask the question again with reference to the risk/reward trade-off. If we claim that to get a higher reward we have to take more risks, our claim is wrong without more information. It is wrong because it depends on the size of the reward and the chances of winning. And, it depends on the number of turns in the game. A short game can have any outcome. You can lose your dollar at the first turn of either game. We could bet even money on each of a series of fair flips of a coin. The coins could quite easily come up heads ten times in a row. It would be bad luck but it’s possible. The return expectation is really only practically valid if the game is played a large number of times.

We can change the game to tilt the return expectations. Let’s continue with our card game rigged so that the odds of winning are 1 in 10. However, if you win you get $10.05. If you lose you forfeit your dollar. In this game you might lose several turns in a row. That would be bad luck. But, over the long haul, you will win. That is because you have an edge. The risks of the game are tilted in your favor. If you play the game for a thousand turns you can be sure you will, for all intents and purposes, come out ahead. In this game you have a positive return expectation.

We have have just looked at a case where a higher risk bet/investment may have a higher expected return than another equally high risk bet/investment that has a lower expected return. It depended on what you stood to win on a successful turn.

Before playing any game you will want to look at the expected return offered in the game. You will also want to look at whether the game contains an edge in your favor. And, you will want to look at how much bad luck could hurt you in the short term before the long haul carries you to success. Are you betting a dollar or are your life savings on the line?


So, is it true that you cannot earn a “greater return unless one incurs additional risk”? The answer is that you earn a greater return by investing with an edge over the long haul. Incurring additional risk does not earn you a better return unless the reward more than justifies the additional risk. That is, the higher risk investment with the higher return must carry with it an additional return, thought of as an edge.

For readers wanting to dig deeper into the subject of risk take a look at Chapter 4. Risk and Uncertainty

Specifically on risk reward see Section 4.14 Risk/reward trade-off assumption

In the future, I plan to do a post on earning a higher return at less risk. But in the meantime you can take a look at Section 4.16 Are higher rewards from lower risk possible? And sections that follow;

Want to dig deeper into the principles behind successful investing?

Click here for the Motherlode – introduction.

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