What Is the Risk and Return Relationship?
The risk-return relationship states that higher-risk investments typically offer higher expected returns to compensate investors for taking on that risk. This fundamental principle guides how investors choose between safe bonds and volatile stocks.
The risk-return relationship shows that an investment's expected return is proportional to the risk it carries—higher risk demands higher compensation (return).
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Step-by-step worked examples
Risk-free rate = 3%, Market return = 11%, Stock beta = 1.5. What is expected return?
E(R) = Rf + β(Rm − Rf) = 3% + 1.5(11% − 3%) = 3% + 1.5(8%) = 3% + 12% = 15% The stock's higher beta (1.5) justifies 15% expected return.
Treasury bond (Rf = 2%), Tech stock (β = 2.5, market return = 10%). Compare expected returns.
Bond return = 2% (certain, low risk) Stock E(R) = 2% + 2.5(10% − 2%) = 2% + 20% = 22% The 20% risk premium compensates for the stock's higher volatility.
Two stocks: A (β=0.8) and B (β=1.3). Risk-free = 4%, Market = 9%. Which has higher expected return?
Stock A: E(R) = 4% + 0.8(9%−4%) = 4% + 4% = 8% Stock B: E(R) = 4% + 1.3(9%−4%) = 4% + 6.5% = 10.5% Stock B has higher risk (β=1.3) and higher expected return.
Flashcards
Quick quiz
Q1.The risk-return relationship means…
Q2.What does beta = 2 mean?
Q3.The Security Market Line (SML) shows…
Q4.If a stock has β=0.7, it is…
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Common mistakes
Confusing beta with total risk. — Correct: Beta measures only systematic risk; diversifiable risk is not in beta.
Assuming past high returns predict future high returns. — Correct: The relationship is about expected returns, not historical performance.
Thinking all high-risk investments will earn high returns. — Correct: The relationship shows expected returns; actual outcomes vary due to luck.
Ignoring that risk-free rate changes with market conditions. — Correct: The risk-free rate (Rf) fluctuates; it's not static.
FAQ
What is the risk-return relationship?
The principle that higher-risk investments have higher expected returns as compensation for investors bearing additional volatility and potential losses.
How is expected return calculated?
Using CAPM: E(R) = Rf + β(Rm − Rf), where risk premium is β times the market risk premium.
Can a low-beta stock outperform a high-beta stock?
Yes — actual returns vary, and other factors (management, innovation) matter. But expected return favors higher-beta stocks.
Is the risk-return relationship always true?
For expected returns, yes — it's the foundation of modern finance. But actual returns depend on many factors and market conditions.