This page is educational content, not investment advice. It does not recommend buying or selling any particular security.
Who this is for / Key points
For: Readers interested in investing who feel held back by the fear of loss, or who understand “risk” only as a vague feeling.
- Risk means variation in possible outcomes. With the same expected return, the investment with a wider range of outcomes carries more risk.
- Risk premium is compensation for bearing uncertainty.
- The Sharpe ratio compares return per unit of risk, while maximum drawdown shows the worst historical fall from a peak.
Suppose you have ¥1 million. A time deposit might turn it into ¥1,000,500 after one year with near certainty. A stock fund, by contrast, might leave you with ¥1.2 million—or ¥800,000.
Which choice is right? To answer, you need a way to turn the feeling of fear into numbers. Risk premium, the Sharpe ratio, and maximum drawdown are three basic tools for doing that.
What risk means: variation, not just danger
In everyday speech, risk usually means danger. In investing, it has a more precise meaning: risk is the dispersion, or uncertainty, of outcomes.
A deposit with a fixed 0.05% rate has almost no variation in its result, so its risk is low. A stock fund may return +20% one year and −20% the next. Even if its average return is +7%, the result can vary widely from year to year. That variation is risk.
Statistics commonly measures this dispersion with standard deviation, also called volatility. The larger the standard deviation, the farther returns tend to spread from their average. See our guide to volatility for a detailed explanation.
Variation can occur upward as well as downward. A high-risk investment does not necessarily have a higher probability of losing money; it means the outcome is harder to predict.
Risk premium: compensation for bearing uncertainty
Suppose a deposit returns 0.05% a year while stocks have an expected annual return of 7%. What accounts for the 6.95 percentage-point difference?
That difference is the risk premium: the expected compensation for holding a risky asset and tolerating uncertainty.
If stocks offered the same return as a deposit, few people would accept the chance of a large price decline. Investors need to expect a higher return before taking that extra risk.
| Asset class | Illustrative expected return | Risk (standard deviation) | Illustrative risk premium |
|---|---|---|---|
| Bank deposit | About 0.05% | Near 0% | — (baseline) |
| 10-year government bonds | About 1% | Low | About 1% |
| Equity index | About 5–7% | About 15–20% | About 5–7% |
| Emerging-market equities | About 7–10% | About 20–25% | About 7–10% |
These figures are illustrations, not forecasts. A risk premium is not a guaranteed bonus; it is a long-run expected value. Risky assets can underperform deposits for extended periods.
The Sharpe ratio: return per unit of risk
Fund A returns 10% with a 20% standard deviation. Fund B returns 6% with an 8% standard deviation. A has the higher return, but it takes 2.5 times as much measured risk. The Sharpe ratio compares whether return was proportionate to that risk.
$$ \text{Sharpe ratio} = \frac{\text{return} - \text{risk-free rate}}{\text{standard deviation}} $$
Assuming a 1% risk-free rate:
- Fund A: $(10\% - 1\%) / 20\% = 0.45$
- Fund B: $(6\% - 1\%) / 8\% = 0.63$
Fund B earned return more efficiently relative to its measured risk. The calculation is backward-looking and does not guarantee future performance, but it gives you a consistent comparison.
Maximum drawdown: measuring the deepest fall
The Sharpe ratio describes average risk efficiency. Investors, however, often care most about the worst period.
Maximum drawdown is the largest percentage decline from a portfolio's previous peak. If ¥1 million rises to ¥1.2 million and then falls to ¥780,000, the drawdown is $(120 - 78) / 120 = 35\%$.
Why does that matter? Because your ability to remain invested is psychological as well as mathematical. Could you continue following the plan after a 35% loss from the peak?
Two funds can have the same Sharpe ratio but maximum drawdowns of 20% and 50%. The lived experience is completely different. A 50% decline cuts capital in half and requires a 100% gain merely to recover.
The risk-free rate: the starting point
The Sharpe ratio includes the risk-free rate: the baseline return available without taking meaningful investment risk. Government-bond yields are commonly used as a proxy.
Every investment competes with the option of holding a low-risk asset. If stocks are expected to return 7% while the risk-free rate is 5%, the expected compensation for taking equity risk is only 2%. A 7% return means something very different when the baseline is 0.05%.
The fundamental trade-off
Remove risk entirely and expected return generally falls with it. Seek a higher return and you must accept some form of uncertainty.
The useful question is not simply “Should I take risk?” It is “How much risk can I take?” The answer depends on your age, income, assets, time horizon, liabilities, and ability to sleep through losses.
Summary
- Risk is variation in outcomes, which can be quantified with standard deviation.
- Risk premium is the expected compensation for bearing uncertainty, not a guaranteed payment.
- The Sharpe ratio compares excess return per unit of measured risk.
- Maximum drawdown shows the worst fall from a previous peak and should be compared with your real loss tolerance.
- The risk-free rate is the baseline against which risky returns should be judged.
When risk remains only a feeling, emotion drives the decision. Once you translate it into numbers, you can compare alternatives, discuss assumptions, and design rules.