The asset that (almost) doesn't shake
Most assets have some σ. Stocks, bonds, real estate, commodities — they all wiggle. But one class of asset is treated as almost risk-free: short-term government debt of stable countries (US Treasury bills, Korean treasury bills, German Bunds at the short end, etc.).
Why "almost"? Two reasons. First, even a 3-month T-bill has a tiny σ — interest rates can move during those 3 months. Second, governments can default in theory (rare for major economies, common for some emerging markets). The "risk-free" label is shorthand, not literal.
For practical finance math, though, we treat short-term high-quality government debt as having σ ≈ 0 and zero default risk. Its return is the risk-free rate, written r_f.
Why the risk-free rate matters
r_f shows up everywhere. It's the foundation that everything else gets compared to:
- Discount rate. The
rin TVM equations starts fromr_fand adds a "risk premium" for non-risk-free cash flows. Sor = r_f + premium. - Excess return. When measuring how a stock or fund did, you usually subtract
r_ffirst. "5% return on a stock when T-bills paid 4%" is only 1% of excess return — that 1% is what the risk earned you, not the 5%. - Sharpe ratio. Track 9 — return per unit of risk, computed using excess returns over
r_f. - CAPM. Track 9's foundational equation:
E(R) = r_f + β × (E(R_m) − r_f). Right there,r_fshows up twice. - Risk-free portfolio anchor. Track 9 again — the efficient frontier extends through any tangent line drawn from
r_f, opening up the "capital allocation line" idea.
Real numbers, real ranges
r_f isn't a fixed number — it changes with monetary policy. Some recent benchmarks (US 3-month T-bill, approximate):
- 2010-2015: 0.0-0.1% — near zero, post-financial-crisis
- 2018-2019: 2.0-2.4% — Fed normalization
- 2020 (COVID): 0.1% — emergency easing
- 2023-2024: 4.5-5.5% — Fed tightening cycle
- 2025-2026: started declining as Fed eased — varies by month
So when finance models use r_f = 4% in 2024 and r_f = 0.1% in 2020, they're both right for their period. The number changes; the role of r_f in the math doesn't.
Why a higher r_f is bad for risky assets
This is one of the most important consequences of r_f being part of the discount rate. When r_f rises, r in equations like P = FCF / (r − g) rises too. Bigger denominator → smaller P. Higher r_f → lower asset prices, all else equal.
This is why the 2022 Fed rate-hike cycle crushed stocks and bonds simultaneously. r_f went from near-zero to 4-5% in 18 months. The discount rate on every future cash flow rose. Bond prices dropped (math is direct — Track 7). Growth stocks dropped harder than value stocks (high-growth → cash flows are way in the future → discounting hits them more). Track 7 covers the 2022 carnage in detail; this lesson is the seed.
The takeaway
r_f = the return on short-term high-quality government debt. Treated as σ ≈ 0 by convention. Foundation of every other rate (r = r_f + premium), of excess returns, of Sharpe and CAPM. Changes with central bank policy. When r_f rises, prices of everything else fall (because the denominator in valuation grows). When r_f falls, the reverse. Almost every market move has r_f doing something quietly in the background.