Return is the reward for risk
Investors expect a higher return for accepting more uncertainty. Risk-free assets offer a low return precisely because there is no uncertainty to compensate for. Everything above that rate is a risk premium.
Risk in finance is not only the chance of loss. It is the spread of possible outcomes around what you expect.
Key points
- Expected return is a probability-weighted average.
- Higher expected return comes with wider outcomes.
- Risk-free return plus a risk premium sets the required return.
Measuring expected return
E(R) = Σ (pᵢ × Rᵢ)
The probability-weighted average of each possible outcome.
E(R) = Rf + β × (Rm − Rf)
Estimates the return required for holding a risky asset relative to the market.
- Rf
- Risk-free rate
- β
- Sensitivity to the market
- Rm
- Expected market return
Real return = (1 + nominal) ÷ (1 + inflation) − 1
The return after removing the effect of inflation.
Subtracting inflation from a nominal return is a quick approximation. The Fisher relationship is the precise version when inflation is high.
A worked example
An investment returns 20% in a good year and 0% in a poor year, each with a 50% chance. Expected return is 0.5 × 20% + 0.5 × 0% = 10%. The outcomes still range from 0% to 20%, which is the risk.
If a bond pays a 12% nominal return and inflation is 4%, the real return is 1.12 ÷ 1.04 − 1 = 7.69%. That is the increase in buying power, not just in the balance.
Why diversification works
Some risk is specific to one company, and some is shared across the whole market. Holding many assets cancels much of the company-specific risk, because unrelated surprises tend to offset.
Market-wide risk cannot be diversified away. That is the risk the market rewards with a premium, and why the CAPM uses a market beta rather than total volatility.
Key points
- Company-specific risk can be diversified away.
- Market risk is unavoidable and is what earns the premium.
- Diversification reduces risk without requiring lower expected return.
02 / Calculate
Watch value compound.
Change the starting amount, the rate, or the horizon. A negative rate models inflation and shows the loss of buying power.
An annual ৳100,000 grows at 8% for 15 years with no extra contributions.
Future value
৳317,216.91
After 15 years the balance is ৳3.17 L. You contributed ৳100,000.00 and earned ৳217,216.91 in growth.
Total interest earned
৳217,216.91
Compounding vs simple interest
+৳97,216.91
Year by year
| Year | Opening | Added | Growth | Closing |
|---|---|---|---|---|
| 1 | ৳100,000.00 | ৳0.00 | ৳8,000.00 | ৳108,000.00 |
| 2 | ৳108,000.00 | ৳0.00 | ৳8,640.00 | ৳116,640.00 |
| 3 | ৳116,640.00 | ৳0.00 | ৳9,331.20 | ৳125,971.20 |
| 4 | ৳125,971.20 | ৳0.00 | ৳10,077.70 | ৳136,048.90 |
| 5 | ৳136,048.90 | ৳0.00 | ৳10,883.91 | ৳146,932.81 |
| 6 | ৳146,932.81 | ৳0.00 | ৳11,754.62 | ৳158,687.43 |
| 7 | ৳158,687.43 | ৳0.00 | ৳12,694.99 | ৳171,382.43 |
| 8 | ৳171,382.43 | ৳0.00 | ৳13,710.59 | ৳185,093.02 |
| 9 | ৳185,093.02 | ৳0.00 | ৳14,807.44 | ৳199,900.46 |
| 10 | ৳199,900.46 | ৳0.00 | ৳15,992.04 | ৳215,892.50 |
| 11 | ৳215,892.50 | ৳0.00 | ৳17,271.40 | ৳233,163.90 |
| 12 | ৳233,163.90 | ৳0.00 | ৳18,653.11 | ৳251,817.01 |
| 13 | ৳251,817.01 | ৳0.00 | ৳20,145.36 | ৳271,962.37 |
| 14 | ৳271,962.37 | ৳0.00 | ৳21,756.99 | ৳293,719.36 |
| 15 | ৳293,719.36 | ৳0.00 | ৳23,497.55 | ৳317,216.91 |
Test the assumption
What if the rate changes?
The same inputs, compared across nearby rates.
6.0% rate
৳239,655.82
Comparison scenario
8.0% rate
৳317,216.91
Your current assumption
10.0% rate
৳417,724.82
Comparison scenario
Growth uses a constant annual rate with interest added once a year. Contributions are added at each year-end. Real products compound more often and carry fees, taxes, and risk.
03 / Apply
Two portfolios, same expected return
One investor holds a single share with an expected return of 12%. Another holds a diversified index fund with the same expected return but far less company-specific risk.
The assumptions
- Both investments carry the same market exposure.
- No transaction costs or taxes are included.
- Expected returns are estimates, not promises.
What to take away
01
Diversification lowers avoidable risk.
02
Only market risk is rewarded with a premium.
03
Concentration can add risk without adding expected return.
Your turn
0 of 3 answered
01Question
An investment returns 20% with probability 0.5 and 0% with probability 0.5. What is the expected return as a percentage?
02Question
A bond returns 12% while inflation is 4%. Using the Fisher relationship, what is the real return as a percentage? Round to two decimals.
03Question
Diversification mainly removes which kind of risk?
Take it into the Lab
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What-if analysis
Change price, cost, and working capital. Watch margins, return, and risk move together.
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Open the playgroundSources & further reading
OpenStax · Principles of Finance (free textbook) ↗Educational sample content. Worked examples use hypothetical figures. Dates refer to the note's latest content update.