What it means
Plot risk on one axis and expected return on the other, and different investments sit at different points. Cash and short-term government bonds sit at the low end, with little risk and a modest return.
Shares, small companies and emerging markets sit further along, with higher risk and a higher expected return. Joining the points creates a curve, usually rising from left to right.
The slope tells you how much extra return the market pays for each extra unit of risk. A steep curve means investors are well rewarded for taking risk, and a flat curve means the reward is thin.
The idea sits behind modern portfolio theory, which uses a similar picture called the efficient frontier. A portfolio on the frontier gives the highest return available for its level of risk, and anything below it is inefficient.
Risk is often measured by standard deviation, a statistical measure of how widely returns vary. The phrase is also used in other ways.
In some texts, a risk curve plots the probability of different outcomes or losses, so that a manager can see how likely a loss of a given size is. This version is common in insurance and risk management, where it helps set limits and buy cover.
Both uses help people think clearly about trade-offs. A risk curve can reveal an investment that offers too little return for its risk, or one that fits an investor's comfort level.
It can also warn that an investment far out on the curve could lose a lot of money. The curve is a model, not a promise.
Risk and return are estimated from past data and forecasts, and they can change when markets change. In real life, higher-risk assets sometimes deliver lower returns, especially over short periods.
In practice
Real-world examples.
Example
A financial adviser draws a risk curve for a client, with bonds at the lower left and shares at the upper right. She uses it to show why the client's request for high returns with no risk is unrealistic. The client agrees to discuss a more balanced target.
Example
A fund manager plots the risk and return of several funds. One fund sits well below the curve, offering a low return for its risk, and she recommends selling it. She explains that a better fund could deliver the same return with less risk.
Example
An insurance risk manager draws a curve showing the probability of losses of different sizes. She uses it to decide how much cover to buy against a major flood. The board approves the cover and reviews the curve each year.
Formula
Calculation
Slope = (Return at high risk - Return at low risk) / (Risk at high risk - Risk at low risk)
Expected return at a given risk = Low-risk return + Slope x (Chosen risk - Low risk)
Suppose bonds offer a 4% expected return with 4% risk, and shares offer 10% with 16% risk.
Slope: (10% - 4%) / (16% - 4%) = 6% / 12% = 0.5
Expected return at 10% risk: 4% + 0.5 x (10% - 4%) = 4% + 3% = 7%
This straight line is a simplification. It suggests that for each extra 1% of risk, an investor expects about 0.5% of extra return.Case study
Seen in the real world.
Brightcove Wealth is a fictional adviser used in an illustrative scenario. A client wants a 12% annual return and says he cannot accept a loss of more than 5%.
The adviser draws a risk curve using her firm's estimates: cash earns 3% with almost no risk, bonds earn 4% with 4% risk, and shares earn 10% with 16% risk. A 12% return would require risk well beyond the share portfolio, and the client's loss limit would only allow a mix with a return of around 5%.
She explains the trade-off and the client revises his expectations, targeting a 7% return with a risk level of 10%. The case shows how a simple curve can turn a vague wish into a realistic plan.
Watch out
Common mistakes.
- Believing higher risk always brings higher return. The curve shows expected rewards, not guaranteed ones.
- Using the curve without checking the data. Risk and return estimates depend on assumptions that can be wrong.
- Confusing different meanings. Some risk curves plot return against risk, while others plot the probability of losses.
Questions
People also ask.
What does the slope of a risk curve show?
It shows the extra return expected for each extra unit of risk. A steeper slope means investors are paid more for taking risk.
How is risk usually measured?
Often by standard deviation, which measures how widely returns vary around the average. Other measures include the probability of loss and the largest fall seen in the past.
How is a risk curve different from the efficient frontier?
The efficient frontier is a specific curve showing the best return for each level of risk among portfolios.
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