🎓 Prepared by students from Boğaziçi University

What is Risk and Return?

Risk and return describes the fundamental trade-off in investing: to earn a higher expected return, investors generally must accept a higher chance their actual return will differ from what they expect. This relationship shapes how assets are priced and how portfolios are built.

Short answer

The risk-return trade-off says that higher potential returns come with higher risk (uncertainty of outcome); the Capital Asset Pricing Model (CAPM) quantifies this as E(R) = Rf + β(Rm − Rf).

Security Market Line (Risk vs Expected Return)

x: Beta (β) · y: Expected Return (%)

Try it: interactive calculator

Expected Return E(R)

= 2 + 1*(8-2)

Risk-free rate2 %Beta (β)1 Expected market return8 %

Step-by-step worked examples

A stock has a beta of 1.2. The risk-free rate is 3% and the expected market return is 9%. Find its expected return using CAPM.

E(R) = Rf + β(Rm − Rf)
E(R) = 3 + 1.2 × (9 − 3)
E(R) = 3 + 1.2 × 6 = 3 + 7.2 = 10.2%

A defensive stock has beta = 0.8, Rf = 2%, Rm = 7%. Find its expected return.

E(R) = 2 + 0.8 × (7 − 2)
E(R) = 2 + 0.8 × 5 = 2 + 4 = 6%

A high-growth stock has beta = 1.5, Rf = 4%, Rm = 10%. Find its expected return.

E(R) = 4 + 1.5 × (10 − 4)
E(R) = 4 + 1.5 × 6 = 4 + 9 = 13%

Flashcards

Quick quiz

Q1.Using CAPM with Rf = 2%, β = 1, Rm = 8%, what is the expected return?

Correct answer: A. E(R) = 2 + 1×(8−2) = 2 + 6 = 8%.

Q2.What does beta primarily measure?

Correct answer: A. Beta captures an asset's sensitivity to market-wide (systematic) movements.

Q3.If beta = 0, CAPM says the expected return equals…

Correct answer: A. When β = 0, β(Rm − Rf) = 0, so E(R) = Rf.

Q4.Why do investors generally demand a higher expected return for higher risk?

Correct answer: A. Higher risk means more uncertain outcomes, so investors require extra expected return as compensation.

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Common mistakes

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Higher risk guarantees higher return. — Correct: Higher risk means investors demand a higher expected return, but actual outcomes can still be worse — risk is uncertainty, not a promise.

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Beta measures a company's total risk. — Correct: Beta measures only systematic (market) risk; unsystematic, company-specific risk can be diversified away.

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The risk-free rate is truly zero-risk. — Correct: It's the closest proxy to risk-free (e.g. short-term government bonds), not literally free of all risk.

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Diversification eliminates all investment risk. — Correct: Diversification reduces unsystematic risk only; market-wide (systematic) risk remains no matter how diversified you are.

FAQ

What is the formula for risk and return (CAPM)?

E(R) = Rf + β(Rm − Rf) — expected return equals the risk-free rate plus beta times the market risk premium.

What is risk and return in finance?

It's the principle that expected investment returns rise with the level of risk (uncertainty) an investor accepts.

How to calculate expected return using risk and return concepts?

Use CAPM: take the risk-free rate, add beta multiplied by the market risk premium (market return minus risk-free rate).

What are examples of risk and return?

Government bonds offer low risk and low return; small-cap growth stocks carry higher risk and higher expected return.