Surprising Truth About Risk & Reward

Everyone knows risk and reward go together. No pain, no gain, no risk, no reward. But the relationship is not fixed, it’s not like one unit of risk must produce one unit of reward. That variability can produce surprising results.

Risk & return basics

Consider this simple example using the two portfolios shown in Table 1. “High Risk” has higher risk and “Low Risk” has lower risk. It doesn’t matter what’s in the portfolios, but “risk” is defined as the volatility of value. In other words, an investment that is more volatile in value has more risk, while an investment that is less volatile has less risk.

In Year 1, High (more risk) goes up +30% and in Year 2 it goes down -20%. The average return over the 2 years is +5% per year. Low (less risk) goes up +6% in Year 1 and +2% in Year 2. Its average return is +4% per year. The average returns are close, but clearly, High’s 5% is higher than Low’s 4%.

Table 1 : Risk & Return

Year	High Risk	Low Risk
1	+30%	+6%
2	-20%	+2%
Average	5% / Year	4% / Year

Risk & return surprise

The returns shown above are not suprising because we know High has more risk than Low. What may be surprising is how different the actual gains are. If we start with a $1 million investment, High produces a $40,000 gain by the end of Year 2. The same investment in Low produces an $81,200 gain.

So, the less risky portfolio produces over two times the gain of the more risky portfolio, and it does it with a lower average return! This is summarized in Table 2.

Table 2: Growth

Portfolio	Avg. Return	Beg. Value	End Value	Gain
High Risk	5%	$1,000,000	$1,040,000	$40,000
Low Risk	4%	$1,000,000	$1,081,200	$81,200

What? How does less-risk/less-return Low make so much more money than more-risk/more-return High? There’s no gimmick, that’s just how the math works. When it comes to investing and growth, the arithmetic average return is what we see, but the geometric average return is what we get.

When it comes to geometric returns avoiding big losses is more important than chasing big gains. High’s double-digit +30% gain was less consequential than its double-digit -20% loss.

The truth about risk & return

Volatility is crucial because big gains and big losses go hand in hand. If we want to chase big gains, we have to accept big losses (more volatility). Over time, volatility is like a hidden tax that drags on geometric returns. The difference in Table 2 happened after just two years, imagine what could happen after twenty?

Choosing the High portfolio based only on its higher risk-return profile is not always a good decision, but that’s how many people chose their investments –“I want high growth and I have high-risk tolerance, so I should choose the highest risk-return option.” Fortunately, you now know how detrimental that decision may be.

Professional investors use tools like mean-variance analysis and portfolio optimization to manage risk and return. It’s typically done with specialized software, but basic models can be built in common applications like Microsoft Excel.

That’s beyond the scope of this article, but the takeaway here is simple. When investing, we should not just focus on returns, that only tells half the story. To see the full picture, we should also consider the volatility of those returns and how that will affect investment results over time.

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HWL