Why Does Risk Demand a Higher Return?

Every extra unit of risk must be compensated by extra expected return. Understanding this trade-off is the basis of every discount rate.

Risk PremiumRisk-free RateExpected ReturnVolatility

Live Result

10.00%

ƒ: rf + risk_premiumraw: 0.100000

ƒ(x)

Use variable names from the panel above (e.g. FV, r, n) — or type numbers directly: 10000 / (1 + 0.08)^10

rf% as decimal

Risk-free rate — return on safest investment (e.g. government bond)

rf = 0.04

risk_premium% as decimal

Extra return demanded for taking on risk

risk_premium = 0.06

beta% as decimal

Measure of systematic risk (1 = market average)

beta = 1.2

erp% as decimal

Equity Risk Premium — market return above risk-free

erp = 0.05

💡 You can also enter values directly in the formula: 10000 / (1 + 0.08)^10

⬇ Export Calculation

Exports a plain .txt file with your expression, formula, all variable values, result, and educational notes — ready to paste into any report, Word doc, Notion, or Google Docs.

The exported file includes the formula in standard mathematical notation — you can paste it directly into Excel, Google Sheets, or back into FinanceSheep.

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Learn: Why Does Risk Demand a Higher Return?

Time Value of Money · Educational Guide

The Core Idea

If a friend asked you to lend $1,000 — would you charge the same interest to your most reliable friend as to a stranger with a history of not repaying? Of course not. This is risk-return: more risk demands more reward.

How It Works

The higher the risk, the higher the return investors demand. Risk-free investments (government bonds) earn the lowest return. Equities earn more. Emerging market equities even more. The "risk premium" is the extra return above risk-free that compensates for uncertainty.

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Real-World Example: US 10-year Treasury (risk-free): 4%. S&P 500 long-run return: ~10%. Equity Risk Premium = 10% − 4% = 6%. A stock with beta=1.2 requires: 4% + 1.2 × 6% = 11.2%.

Why Does Risk Demand a Higher Return?

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