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TL;DR

The theoretical rate of return on an investment with zero risk. In practice, approximated by short-term government securities (T-bills). It is the discounting rate in risk-neutral pricing.

By Valenke Exam Prep Team·Last updated 2026-06-03

Risk-Free Rate

The theoretical rate of return on an investment with zero risk. In practice, approximated by short-term government securities (T-bills). It is the discounting rate in risk-neutral pricing.

Why it matters for interviews

The risk-free rate anchors all asset pricing: the CAPM, Black-Scholes, and bond pricing all depend on it. Understanding what constitutes 'risk-free' and how rates affect derivative prices is fundamental.

Definition and Mathematical Foundation

The theoretical rate of return on an investment with zero risk. In practice, approximated by short-term government securities (T-bills). It is the discounting rate in risk-neutral pricing.

Application in Quantitative Finance

The risk-free rate anchors all asset pricing: the CAPM, Black-Scholes, and bond pricing all depend on it. Understanding what constitutes 'risk-free' and how rates affect derivative prices is fundamental.

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Frequently Asked Questions

Is the risk-free rate truly risk-free?▼
No. Even T-bills have inflation risk, reinvestment risk, and (theoretically) sovereign default risk. The risk-free rate is a modeling convenience. In practice, the OIS (Overnight Index Swap) rate is often used as the closest proxy.
How does the risk-free rate affect option prices?▼
Higher rates increase call values and decrease put values (via put-call parity). The effect operates through the forward price: \( F = Se^{rT} \). This is captured by the Greek rho.
What is the natural rate of interest?▼
The rate consistent with full employment and stable inflation. It is unobservable and must be estimated. Central banks set policy rates relative to this neutral rate, affecting all financial asset prices.