Yield to Maturity
Yield to Maturity (YTM) is the total annualized return that an investor earns on a bond if it is purchased at the current market price and held until maturity, assuming all coupon payments are received as scheduled and reinvested at the same yield. It is the internal rate of return (IRR) of the bond's cash flows.
Key takeaways
- YTM equates the present value of all future coupon payments and the principal repayment to the bond's current market price.
- YTM captures both the coupon income and the capital gain (for discount bonds) or capital loss (for premium bonds) experienced over the holding period.
- The reinvestment assumption—that coupons are reinvested at the same YTM—is a simplification; actual realized yield depends on prevailing rates when coupons are received.
- YTM is the standard benchmark for comparing bonds of different maturities, coupon rates, and credit qualities.
- For bonds with embedded options, YTM is supplemented or replaced by yield to call, yield to put, yield to worst, or option-adjusted spread.
Explanation
Yield to maturity is the foundational fixed income metric, translating a bond's complex stream of cash flows into a single comparable number that enables investors to evaluate bonds across maturities and coupon rates. It answers the question: 'If I buy this bond today at the current market price and hold it to maturity, what compound annual return will I earn?' The answer requires solving for the discount rate (YTM) that makes the present value of all future cash flows equal to the current price—a calculation that requires iterative numerical methods (Newton-Raphson or similar) because the equation has no closed-form solution.
The YTM formula embeds three return components. First is the current yield (annual coupon divided by price), which represents the income return. Second is the capital gain or loss effect: a bond purchased at a discount to par will accrete toward par as maturity approaches, providing additional return; a premium bond will amortize its premium, eroding return. Third is the reinvestment return: coupons received over the holding period can be reinvested, and YTM assumes this occurs at the YTM rate itself. The reinvestment assumption is the critical weakness of YTM as a measure of realized return; in practice, reinvestment rates depend on the interest rate environment when coupons are received, not on the initial YTM.
The relationship between YTM and bond price is foundational: when market interest rates rise (new bonds offer higher yields), existing bonds with lower fixed coupons become less attractive and their prices fall until their YTMs rise to match market rates. When rates fall, existing bonds with higher coupons become more valuable and prices rise, compressing YTMs toward prevailing lower market rates. Duration quantifies this price sensitivity: a bond with a modified duration of 7 years will lose approximately 7% of its price for every 100-basis-point rise in yield.
In practice, YTM is quoted in bond markets on a semi-annual bond equivalent yield basis (BEY) for U.S. fixed income instruments, reflecting the convention that most U.S. corporate and Treasury bonds pay coupons semi-annually. The nominal YTM so quoted must be divided by 2 to compute the semi-annual periodic rate, which when compounded gives the effective annual yield (EAY): EAY = (1 + YTM/2)² − 1. This distinction becomes important when comparing U.S. bonds (semi-annual BEY) with European bonds that quote yield on an annual basis or money market instruments quoted on discount or add-on bases.
Formula
P = \sum_{t=1}^{2n} \frac{C/2}{(1+YTM/2)^t} + \frac{FV}{(1+YTM/2)^{2n}}
Example
Consider a 5-year corporate bond with a face value of $1,000, a coupon rate of 6% (paying $30 every six months), currently priced at $970. To compute YTM, we solve for r in: $970 = $30/(1+r) + $30/(1+r)² + ... + $30/(1+r)^10 + $1,000/(1+r)^10. Using numerical iteration, the semi-annual rate r ≈ 3.31%, implying an annual BEY YTM of 6.62%. This 6.62% YTM consists of approximately 6.19% current yield ($60/$970) plus approximately 0.43% from the annual accretion of the $30 discount ($30 discount / 5 years / $970 price ≈ 0.62% annual accrual on a simple basis, somewhat lower on a present value basis). If a benchmark 5-year Treasury yields 5.40%, the credit spread is 6.62% − 5.40% = 122 basis points, reflecting the market's assessment of this issuer's credit risk.
Related terms
Basis Bond Bond Covenant Corporate Bond Coupon Rate Credit Risk Credit Spread Current Yield Discount Rate Duration Face Value Interest Rate