# 30-Year Treasury
**Summary:** A 30-year Treasury is a long-term U.S. government bond that pays semiannual coupons and returns principal at 30 years. Historically a market bellwether, it remains a key indicator of long-term interest rates, inflation expectations and portfolio duration risk.
## Definition & Key Takeaways
## Why It Matters
## Formula & Variables
## Worked Example
## Practical Use
## Comparisons
## Limits & Misconceptions
## Research Notes
## Definition & Key Takeaways
– A 30-Year Treasury is a U.S. Treasury bond with a nominal maturity of 30 years from issuance and semiannual coupon payments.
– It is a marketable, liquid debt instrument backed by the full faith and credit of the U.S. government and typically offers higher yields than shorter Treasuries to compensate for term risk.
– Pricing is driven by prevailing yields (yield to maturity, or YTM); a bond can trade at par, premium, or discount depending on the relationship between coupon and YTM.
– The 30-year rate is a widely watched indicator of long-term borrowing costs, inflation expectations, mortgage rates, and the long end of the yield curve.
– While once considered the bellwether U.S. bond, the 10-year Treasury is now often treated as the benchmark; the 30-year remains crucial for duration exposure and pension/insurance valuation.
## Why It Matters
The 30-Year Treasury occupies a central role in fixed-income markets and the broader economy. Because it provides a long, safe cash flow stream, market participants use its yield to:
– Gauge long-term interest-rate expectations and the term premium investors demand for holding duration risk.
– Price long-dated liabilities and assets, including pension obligations, life-insurance reserves, and long-term corporate debt.
– Inform mortgage-rate formation and the pricing of mortgage-backed securities; longer-term mortgage rates move with the longer portion of the Treasury yield curve.
– Serve as a low-risk allocation in portfolios seeking steady income and duration exposure as a hedge against deflation or economic stress.
Movements in the 30-year yield reflect shifts in monetary policy expectations, inflation forecasts, global demand for safe assets, and changes in fiscal issuance.
## Formula & Variables
A Treasury bond’s price can be calculated as the present value of its future coupon payments plus the present value of the repayment of face (par) value at maturity. The standard formula for price P of a fixed-rate bond is:
P = C * (1 – (1 + r)^-n)/r + F / (1 + r)^n
Where:
– P = price of the bond (dollars)
– C = coupon payment per period (dollars). For a 30-year Treasury with annual coupon rate R% and face value F, if coupons are semiannual: C = F * (R/100) / 2
– r = yield per period (decimal). If quoted YTM is annual compounded semiannually, r = (YTM/100) / 2
– n = total number of coupon periods (for 30 years with semiannual coupons, n = 30 * 2 = 60)
– F = face (par) value of the bond, typically $100 or $1,000 depending on pricing convention
Units and scales:
– Rates (R, YTM) are expressed in percent per annum and converted to decimal per coupon period for calculations.
– Periods use the coupon frequency (semiannual for nominal Treasury bonds).
Other related measures:
– Current yield = annual coupon payments / market price
– Yield to maturity (YTM) = discount rate that equates present value of cash flows to current price
– Duration (Macaulay or modified) measures weighted-average time to cash flows and sensitivity of price to yield changes
## Worked Example
Calculate the market price of a 30-year Treasury bond with these features:
– Face value (F): $1,000
– Coupon rate (annual): 3.00% (paid semiannually)
– Quoted YTM (annual): 3.50% (compounded semiannually)
Step 1: Convert to coupon per period and yield per period
– Annual coupon payment = 3.00% * $1,000 = $30
– Semiannual coupon C = $30 / 2 = $15
– Semiannual yield r = 3.50% / 2 = 1.75% = 0.0175
– Total periods n = 30 years * 2 = 60
Step 2: Compute present value of coupons
– PV(coupons) = C * [1 – (1 + r)^-n] / r
– = 15 * [1 – (1 + 0.0175)^-60] / 0.0175
– Compute (1 + r)^-n = (1.0175)^-60 ≈ 0.3499 (calculator)
– Then bracket = 1 – 0.3499 = 0.6501
– PV(coupons) ≈ 15 * 0.6501 / 0.0175 ≈ 15 * 37.1486 ≈ $557.23
Step 3: Compute present value of face value
– PV(face) = F / (1 + r)^n = 1,000 * (1.0175)^-60 ≈ 1,000 * 0.3499 ≈ $349.90
Step 4: Add components for price
– P = PV(coupons) + PV(face) ≈ 557.23 + 349.90 = $907.13
Interpretation: With a coupon (3.00%) below the market yield (3.50%), the bond trades at a discount (below $1,000). This price reflects the higher yield investors require relative to the coupon.
Optional: Current yield = annual coupon / price = 30 / 907.13 ≈ 3.31% (less than YTM because price is below par and capital gain is realized over time).
## Practical Use
Checklist for investors and analysts before using 30-year Treasuries:
– Confirm coupon frequency (semiannual) and settlement conventions used for pricing.
– Convert quoted yields to per-period rates consistent with coupon frequency.
– Check for callable features (most nominal Treasury bonds are noncallable; verify instrument type).
– Evaluate inflation expectations and real yields (consider TIPS or breakeven inflation rates).
– Assess portfolio duration exposure and the impact of price sensitivity to yield changes.
Common pitfalls and how to avoid them:
– Misconverting yields: Always match compounding frequency. Don’t compare nominal annual coupon to semiannual-per-period yields without conversion.
– Ignoring inflation: Nominal yields incorporate expected inflation; compare to TIPS breakevens for real return insights.
– Overweighting duration: Long Treasuries have high duration; small yield changes produce large price swings—use duration hedges if necessary.
– Assuming Treasury yields equal risk-free rate for all horizons: Different investors may use different proxies (e.g., OIS rates for risk-free short-term funding). Use the appropriate benchmark for valuation.
## Comparisons
– 10-Year Treasury: Often treated as the benchmark for general market interest rates and economic expectations. Prefer the 10-year when tracking near-term economic signals or when referencing the conventional benchmark for mortgage rates and equity discount rates.
– Treasury Inflation-Protected Securities (TIPS): Provide inflation-adjusted principal. Prefer TIPS when you need explicit inflation protection and to measure real yields and breakeven inflation.
– Treasury Bills & Notes: Bills (short-term) are used for cash and liquidity; notes (2–10 years) for medium-term rate exposure. Choose notes or bills for lower duration and less sensitivity to long-run rate changes.
– Corporate Bonds: Offer higher yields due to credit risk. Use corporates when seeking credit spread income and accept elevated default risk relative to Treasuries.
When to prefer the 30-year Treasury:
– Hedging long-term liabilities (pensions, insurance).
– Expressing views on long-run inflation or long-term real rates.
– Matching cash flows for long-dated fixed-income portfolios.
## Limits & Misconceptions
– Misconception: The 30-year Treasury is always the market benchmark. Reality: The 10-year Treasury has assumed that role in many markets, though the 30-year remains important for long-duration pricing.
– Misconception: Treasuries guarantee positive real returns. Reality: Nominal Treasuries can deliver negative real returns if inflation exceeds the nominal yield; TIPS protect against this risk.
– Limit: Liquidity vs. tenor trade-off. While the 30-year is liquid relative to many corporate bonds, it is less liquid than the 10-year and may have wider bid-ask spreads during stress.
– Limit: Yield reflects many factors. A move in the 30-year yield conflates expected policy path, inflation expectations, term premium and global safe-asset demand; disentangling causes requires supplementary data.
## Research Notes
Data sources commonly used to analyze the 30-year Treasury:
– U.S. Department of the Treasury (TreasuryDirect) for auction results, issue details, and official yield curves: https://www.treasurydirect.gov
– Federal Reserve Economic Data (FRED, St. Louis Fed) for historical yields, yield curves, and macro time series: https://fred.stlouisfed.org
– Bureau of Labor Statistics (BLS) CPI series for constructing breakeven inflation rates when paired with TIPS: https://www.bls.gov
Methodology notes:
– Yields are often quoted on a bond-equivalent basis and need conversion for per-period discounting (semiannual compounding for nominal bonds).
– Breakeven inflation = Nominal Treasury yield – TIPS yield (same maturity) and approximates market-implied inflation expectations.
– Duration and convexity calculations require per-period cash flows and market YTM as the discounting rate; use a spreadsheet or fixed-income library for precise analytics.
Citations:
– U.S. Department of the Treasury — TreasuryDirect: https://www.treasurydirect.gov
– Federal Reserve Bank of St. Louis — FRED: https://fred.stlouisfed.org
– Bureau of Labor Statistics — CPI: https://www.bls.gov/cpi
– Investopedia — 30-Year Treasury: https://www.investopedia.com/terms/1/30-yeartreasury.asp
Educational disclaimer: This article provides informational content and not personalized investment advice; consult a qualified professional before acting.
### FAQ
### See also
– 10-Year Treasury
– Treasury Inflation-Protected Securities (TIPS)
– Yield Curve
– Duration
– Treasury Bill