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The fundamentals of risk to reward in investing

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Understanding Risk and Reward in Investing: Practical Insights

Many people believe that to earn higher rewards, you have to take on higher risks. This isn't always true. Similarly, some think taking on higher risks will automatically lead to higher rewards. Again, this is a misconception. Let's break it down with some simple examples.

Expected Return: What It Means

To understand risk and reward, we need to talk about "expected return." This is the idea that you can estimate the return on an investment by looking at all possible outcomes and their probabilities.

Here's how Warren Buffett explained it: "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."

A Simple Dice Game Example

Imagine two dice games.

Game 1:

  • Odds of winning: 1 in 6
  • Bet: $1
  • Win: $5

If you play this game 1,000 times, you can calculate the expected return like this:

  • Expected gain per game: 16×5=5=0.8361​×5=5=0.83
  • Expected loss per game: 56×(-1)=−1)=-0.8365​×(-1)=−1)=-0.83

So, the expected return is 0.83−0.83-0.83=000.83-0.83=0.83=0. Over many plays, you'll likely break even.

Game 2:

  • Odds of winning: 1 in 20
  • Bet: $1
  • Win: $19

For this game, the expected return calculation is:

  • Expected gain per game: 120×19=19=0.95201​×19=19=0.95
  • Expected loss per game: 1920×(-1)=−1)=-0.952019​×(-1)=−1)=-0.95

So, the expected return is 0.95−0.95-0.95=000.95-0.95=0.95=0. Here, too, over many plays, you'll likely break even.

So, which game is riskier? Most would say Game 2 because you lose 19 out of 20 times, even though both games have the same expected return.

Real-World Investing Example

Let's compare two types of stocks:

  • Blue-chip stocks: Generally considered safer but with lower returns.
  • Penny mining stocks: Riskier but with the potential for higher returns.

Penny stocks might offer the same expected return as blue-chip stocks if the potential reward justifies the risk. This works over the long term with many investments, thanks to diversification.

The Role of Luck and Time

Short-term outcomes can be unpredictable. For instance, flipping a fair coin could result in heads ten times in a row, purely by chance. But over many flips, the results will balance out.

Now, suppose we tweak Game 2:

  • Odds of winning: 1 in 20
  • Win: $20.10

In this version, you have a slight edge. Over many plays, you will likely come out ahead because the game's expected return is positive.

Here's the calculation:

  • Expected gain per game: 120×20.10=20.10=1.005201​×20.10=20.10=1.005
  • Expected loss per game: 1920×(-1)=−1)=-0.952019​×(-1)=−1)=-0.95

So, the expected return is 1.005−1.005-0.95=0.0550.0551.005-0.95=0.95=0.055. Over many plays, you can expect to win.

Key Takeaways for Investors

  1. Look at Expected Return: Before investing, understand the expected return based on possible outcomes and their probabilities.
  2. Find Your Edge: Invest in opportunities where you have a favorable edge.
  3. Think Long-Term: Short-term bad luck can happen, but over the long haul, a positive expected return can lead to success.

In Conclusion

Higher rewards don't automatically come from taking higher risks. Instead, focus on investments where the rewards justify the risks and play the long game. The key is to find investments with a positive expected return and an edge in your favor.

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