Risk and Return — Turning Fear into Numbers¶
For / Key Points
For: Anyone interested in investing but stuck at "I'm afraid of losing money." Anyone who understands risk only as a gut feeling.
Key Points:
- Risk is not danger — it is dispersion. Two investments with the same expected return can have wildly different ranges of outcomes
- Risk premium is compensation for patience — only those who accept uncertainty receive the extra return above the risk-free rate
- The Sharpe ratio measures return per unit of risk, letting you compare options without relying on emotion
You have one million yen. Put it in a fixed deposit and in one year you will have 1,000,500 yen. Almost certainly. Alternatively, invest it in an equity fund and in one year you might have 1,200,000 yen — or 800,000 yen.
Which is the "right" choice? To answer that, you need tools that convert "scary" into numbers. Those tools are risk-return quantification, and the three concepts covered in this article — risk premium, Sharpe ratio, and maximum drawdown — form the basic toolkit.
What Risk Actually Means — Not Danger, but Dispersion¶
In everyday language, "risk" means danger. In investing, the definition is different. Risk is the dispersion of possible outcomes — uncertainty.
A fixed deposit yields 0.05% per year with near certainty. The dispersion of outcomes is close to zero, so risk is low. An equity fund might return +20% one year and -20% the next. Even if the average return is +7%, individual years swing widely. The size of that swing is risk.
In statistics, dispersion is measured by standard deviation (volatility) — see the volatility article for a deeper dive. A larger standard deviation means returns are more likely to land far from the average — in other words, risk is higher.
The crucial point: dispersion goes both ways, up and down. High risk does not mean "high probability of loss." It means "outcomes are harder to predict."
Risk Premium — The Compensation Only Risk-Takers Receive¶
Fixed deposits return 0.05% per year. Equities are expected to return roughly 7%. What explains the 6.95% gap?
That gap is the risk premium — the reward for holding an asset whose value is uncertain. Think of it as "compensation for enduring unpredictability."
Why does it exist? Simple. If equities returned the same as deposits, no one would accept the possibility of losing money. To attract investors, equities must be expected to deliver more than the risk-free alternative.
| Asset class | Expected return (approx.) | Risk (std. dev.) | Risk premium |
|---|---|---|---|
| Savings deposit | ~0.05% | ~0% | — (baseline) |
| Government bond (10Y) | ~1% | Low | ~1% |
| Equity index | ~5–7% | ~15–20% | ~5–7% |
| Emerging-market equities | ~7–10% | ~20–25% | ~7–10% |
One critical caveat: the risk premium is not a guaranteed bonus. It is a long-run expectation. In any given year, equities can underperform deposits. Yet over long horizons, those who accepted risk have historically been compensated — that is the empirical track record.
Sharpe Ratio — Return per Unit of Risk¶
Two funds. Fund A: 10% return, 20% standard deviation. Fund B: 6% return, 8% standard deviation. Which is "better"?
By return alone, A wins. But A takes 2.5 times more risk. The Sharpe ratio answers whether the return justifies the risk.
Assuming a risk-free rate of 1%:
- Fund A: (10\% - 1\%) / 20\% = 0.45
- Fund B: (6\% - 1\%) / 8\% = 0.63
Fund B earns return more efficiently. For the same amount of risk, B delivers more.
Rules of thumb: 0.5 and above is "decent," 1.0 and above is "excellent." These are backward-looking calculations and guarantee nothing about the future. Still, the ability to compare "return earned per unit of risk" provides a foundation for decisions that transcend emotion.
Maximum Drawdown — Knowing the Deepest Valley¶
The Sharpe ratio measures average risk efficiency. But what investors truly fear is not the average — it is the worst case.
Maximum drawdown is the largest peak-to-trough decline an asset has experienced.
Example: 1,000,000 yen grows to 1,200,000 yen, then falls to 780,000 yen. The maximum drawdown is (1{,}200{,}000 - 780{,}000) / 1{,}200{,}000 = 35\%.
Why does this metric matter? The reason is psychological. Humans feel the pain of a loss roughly twice as strongly as the pleasure of an equivalent gain (prospect theory). When your portfolio is down 35%, can you stay the course? This is where theory diverges from reality.
Two funds with identical Sharpe ratios of 0.7 can feel entirely different if one has a maximum drawdown of -20% and the other -50%. A 50% drawdown means your assets are cut in half. To recover, you need a +100% return.
The Risk-Free Rate — The Starting Point for Everything¶
The Sharpe ratio formula includes the "risk-free rate." This is the minimum return you earn by taking zero risk — typically approximated by government bond yields.
Why is it the starting point? Because every investment decision is implicitly a comparison against "buy government bonds and do nothing." If equities are expected to return 7% but the risk-free rate is 5%, the extra return for bearing risk is only 2%. The same 7% equity return means something very different when the risk-free rate is 0.05% versus 5%.
The Fundamental Tradeoff — No Risk, No Return¶
Bring all these concepts together and a single principle emerges.
Eliminate risk entirely and you eliminate return. A fixed deposit yields 0.05% precisely because that is the price of near-zero uncertainty. Conversely, seeking higher returns means accepting commensurate risk.
The question is not whether to take risk. It is how much risk to take. Risk premium, Sharpe ratio, and maximum drawdown exist to answer that question with numbers instead of feelings.
There is no universal answer to this question. It depends on your age, income, total assets, investment horizon, and the very personal test of whether you can sleep at night.
Summary¶
- Risk is not danger — it is dispersion of outcomes, measured by standard deviation
- The risk premium compensates for uncertainty; historically, it has rewarded patient investors
- The Sharpe ratio lets you compare return per unit of risk across assets
- Maximum drawdown reveals the deepest valley — check it against your psychological endurance
- The risk-free rate is the baseline; the same return carries different meaning depending on the rate environment
As long as risk remains just "scary," your decision-making framework is emotion. The moment you convert fear into numbers, you can compare, debate, and automate. Every topic in this series — volatility, market structure, valuation — builds on this foundation of quantifying risk.