SERIES 65 | FINANCIAL REGULATION COURSES
Yield to maturity — abbreviated YTM — is the total annualised return an investor would receive if a bond is purchased at its current market price, all coupon payments are received as scheduled throughout the bond's remaining life, each coupon is reinvested at the same rate as the yield to maturity itself, and the bond is held to its stated maturity date at which the full face value is returned. Yield to maturity is the bond equivalent of the internal rate of return — mathematically, it is the single discount rate that makes the present value of all future cash flows from the bond — the coupon payments and the par value at maturity — exactly equal to the bond's current market price.
YTM is the most comprehensive and most widely used measure of bond return — unlike the nominal yield which measures income as a percentage of face value and unlike the current yield which measures income as a percentage of current price, the yield to maturity incorporates all three components of bond return simultaneously — the coupon income stream, the capital gain or loss from purchasing at a price different from par, and the time value of money through the discounting framework that converts all future cash flows to present value equivalents.
Yield to maturity is the foundational yield measure of fixed income analysis — every bond pricing calculation, yield spread comparison, and bond valuation model uses yield to maturity as its primary analytical input — and is directly and extensively tested on the Series 65 examination in the context of bond pricing, the price-yield relationship, and the comparison among the multiple yield measures.
The Three Assumptions of Yield to Maturity
The precision of yield to maturity as a return measure depends critically on three assumptions that are explicitly embedded in its definition and that investors must understand to correctly interpret the YTM figure.
The first assumption is that the investor holds the bond to maturity — if the bond is sold before the stated maturity date, the actual realised return will differ from the YTM because the sale price may be above or below the purchase price depending on how interest rates have changed since purchase. YTM is a hold-to-maturity return measure — it is the return only for investors who genuinely intend to hold the bond until it matures and receives par.
The second assumption is that all coupon payments are received as scheduled — there is no default by the issuer. For investment-grade corporate bonds and Treasury securities this assumption is generally reasonable. For high-yield bonds with meaningful default probability, the YTM overstates the expected return because it does not account for the possibility that some coupons will not be received or that the par value will not be repaid in full.
The third assumption — and the most significant practical limitation of YTM — is that all coupon payments received are reinvested at the same rate as the yield to maturity itself throughout the bond's remaining life. In practice, the reinvestment rate will change as market interest rates change over the bond's life — when interest rates fall below the YTM, reinvested coupons earn less than assumed, and the realised return falls below the YTM. When interest rates rise above the YTM, reinvested coupons earn more than assumed, and the realised return exceeds the YTM. Only zero coupon bonds — which pay no interim coupon and therefore have no reinvestment rate assumption — actually deliver the YTM with mathematical certainty if held to maturity.
The Price-Yield Relationship — The Foundational Bond Theorem
The relationship between a bond's market price and its yield to maturity is the most fundamental theorem in all of fixed income analysis — an inverse relationship whose mathematical certainty derives directly from the discounted cash flow framework through which bond prices are determined.
When interest rates rise — meaning the market requires a higher yield to maturity on bonds of a given credit quality and maturity — the current cash flows of existing bonds become less valuable because they must be discounted at a higher rate. The bond's price must fall until its yield to maturity — the discount rate that equates its future cash flows to its price — equals the new higher market yield. The mathematical consequence is that bond prices fall when interest rates rise.
When interest rates fall — meaning the market is satisfied with a lower yield to maturity — existing bonds with above-market coupons become more valuable. The bond's price must rise until its yield to maturity equals the new lower market yield. Bond prices rise when interest rates fall.
This inverse relationship — bond prices move opposite to interest rates — is the most critical single fact in fixed income investing and is tested on virtually every fixed income question in the Series 65 curriculum. Every bond question about price movements in response to interest rate changes is answered by this inverse relationship.
The magnitude of the price change for a given yield change depends on the bond's duration — the weighted average time to receipt of all cash flows. Longer duration bonds have greater price sensitivity to interest rate changes — a thirty-year bond changes in price far more than a two-year bond for the same one percentage point change in yield. Duration is covered in the Duration entry of this dictionary.
The YTM and the Three-Way Yield Relationship
As established in the Yield entry of this dictionary, yield to maturity participates in a precise three-way relationship with nominal yield and current yield depending on whether the bond trades at par, at a discount, or at a premium.
At par — when market price equals face value — all three yields are equal. YTM equals current yield equals nominal yield. The coupon rate precisely equals the market required return — no capital gain or loss occurs at maturity.
At a discount — when market price is below face value — YTM exceeds current yield which exceeds nominal yield. The below-market coupon income is supplemented by a capital gain at maturity — the bond purchased below par will appreciate to par — adding to the total annualised return above what the current yield alone would suggest.
At a premium — when market price is above face value — YTM is below current yield which is below nominal yield. The above-market coupon income is reduced by a capital loss at maturity — the bond purchased above par will decline to par — reducing the total annualised return below what the current yield alone would suggest.
Calculating YTM — The Approximation Formula
The exact yield to maturity can only be calculated through iterative numerical methods — trial and error using a financial calculator or spreadsheet — because there is no closed-form algebraic solution for the YTM of a coupon-bearing bond. For examination purposes, the approximation formula provides a reasonably accurate estimate.
The approximate YTM formula — sometimes called the street method — equals the annual coupon payment plus the quantity face value minus market price divided by years to maturity — all divided by the quantity face value plus market price divided by two.
Approximate YTM equals coupon plus the quantity par minus price divided by years — divided by the quantity par plus price divided by two.
A ten-year bond with a face value of one thousand dollars, a five percent annual coupon paying fifty dollars annually, currently trading at nine hundred dollars. Approximate YTM equals fifty plus the quantity one thousand minus nine hundred divided by ten — equalling fifty plus ten — equalling sixty — divided by the quantity one thousand plus nine hundred divided by two — equalling nine hundred and fifty — equalling six point three two percent. The bond's yield to maturity of approximately six point three two percent exceeds both the nominal yield of five percent and the current yield of approximately five point five six percent — confirming the discount bond relationship.
The Reinvestment Risk Limitation and Zero Coupon Bonds
The reinvestment rate assumption is the most significant practical limitation of YTM as a return predictor — and the zero coupon bond is the instrument that eliminates this limitation entirely.
A coupon-bearing bond that matures in twenty years and pays six percent semi-annual coupons will only actually deliver a six percent YTM if each of the forty coupon payments received over twenty years is reinvested at exactly six percent for its remaining period. If interest rates fall to three percent after five years, the subsequent coupons are reinvested at three percent — producing a realised return below the six percent YTM. If rates rise to nine percent, the subsequent coupons are reinvested at nine percent — producing a realised return above the YTM.
A zero coupon bond with a twenty-year maturity and a six percent YTM purchased at the discounted price — approximately three hundred and five dollars for a one thousand dollar face value — will deliver exactly six percent annualised return if held to maturity regardless of what happens to interest rates during the twenty-year period, because there are no interim coupons to reinvest. Zero coupon bonds are the only fixed income instruments that guarantee the yield to maturity with mathematical certainty — making them ideal for liability-driven investing strategies where a specific dollar amount must be available at a specific future date.
Examination Relevance and Key Takeaways
Yield to maturity is tested on the Series 65 examination as the primary bond yield measure — in the context of the price-yield relationship, the three-way yield comparison, the YTM approximation calculation, the three embedded assumptions, and the comparison with current yield and yield to call.
The key points to retain are these.
Yield to maturity is the total annualised return on a bond assuming purchase at the current market price, all coupons received as scheduled, coupons reinvested at the YTM rate, and the bond held to maturity. YTM is the bond's internal rate of return — the discount rate making the present value of all future cash flows equal to the current market price — incorporating coupon income, capital gain or loss, and the time value of money simultaneously. The three YTM assumptions are hold to maturity, no default, and coupon reinvestment at the YTM rate — the reinvestment assumption is the most significant practical limitation.
The foundational inverse price-yield relationship — bond prices fall when interest rates rise and bond prices rise when interest rates fall — is the most critical fact in fixed income analysis. The three-way relationship — at discount YTM exceeds current yield exceeds nominal yield; at par all three are equal; at premium nominal yield exceeds current yield exceeds YTM. The approximate YTM formula equals coupon plus the quantity par minus price divided by years — divided by the quantity par plus price divided by two. Only zero coupon bonds guarantee the YTM with mathematical certainty — because there are no interim coupons to reinvest, realised return equals YTM regardless of interest rate movements during the holding period.
