FI 7 Yield and Yield Spread Measures for Fixed-Rate Bonds

A yield-to-maturity (YTM) collapses everything about a bond, its coupon, its price, and its remaining life, into one number, which is why analysts lean on it to compare instruments with different maturities and coupons. Two features complicate that single number, and this lesson works through both. The first is how often interest is assumed to compound within a year, a property called periodicity. The second is the presence of embedded options, such as a call feature, that can change the amount or the timing of the promised cash flows.

A third idea runs through the second half of the lesson: any yield can be split into two parts. One part is a benchmark rate, usually a government yield, that reflects broad top-down forces affecting every bond in a market. The other part is a spread over that benchmark, which captures bottom-up factors specific to the issuer and the security, such as credit risk, liquidity, and taxation. Separating the two lets an analyst judge whether a bond looks cheap or rich once the general level of interest rates is stripped away.

All else equal, compounding more often produces a larger future value. That single fact drives much of the periodicity mathematics: a lower stated rate compounded frequently can deliver the same total return as a higher stated rate compounded less often, because the extra compounding compensates for the lower rate.

Investors want an annualized, compounded yield so that bonds with different cash flow patterns can be lined up directly. For a security maturing in more than a year, that annualized yield hinges on how many interest periods the year is assumed to contain, a count named the periodicity of the annual rate. Periodicity usually matches coupon frequency. A bond paying semiannual coupons with a stated annual YTM of 3.2% has a periodicity of 2, which is 1.6% per half-year doubled. A bond paying quarterly coupons carries a periodicity of 4, found by taking the quarterly rate and multiplying by four.

An annual rate with a periodicity of 2 is called a semiannual bond basis yield, also termed a semiannual bond equivalent yield. It is the dominant convention across markets like the United States and the United Kingdom, where semiannual coupons prevail. Keep two phrases distinct: a yield of 2% per semiannual period corresponds to an annual yield of 4% on a semiannual bond basis.

Effective annual rates and the effect of frequency

The interest a 5% stated annual YTM actually generates over one year depends on how often it compounds. Assuming each coupon is reinvested at the periodic rate for the rest of the year, a par bond priced at 100 produces the following year-end amounts.

Expressed as percentages, those year-end percentages are the effective annual rates. Such a rate has a periodicity of 1, because only one compounding period fits in the year. The quarterly example is instructive: paying 1.25% four times a year, with each coupon reinvested at 1.25% until year end, produces the same 5.0945 of interest as an annual coupon bond stated at 5.0945%. So more frequent compounding at 5% is equivalent to less frequent compounding at a higher stated rate.

Converting one periodicity to another

A core skill is restating an annualized yield from one periodicity to another, a periodicity or compounding conversion. The general rule links an annual percentage rate for m periods per year to one for n periods per year.

Take a three-year, 5% semiannual coupon bond priced at 104 per 100 of par. Solving the pricing equation gives a periodic rate of 0.01791, so the YTM is 3.582% on a semiannual bond basis (0.01791 times 2). Converting that to quarterly and monthly compounding gives quarterly and monthly annual yields that are slightly lower.

A yield of 3.582% for semiannual compounding therefore gives the same return as 3.566% for quarterly and 3.556% for monthly compounding. The rule worth memorizing, and a handy check on any conversion, is that a lower annual rate compounded more often lands at the same place as a higher annual rate compounded less often. It follows that, holding the cash flows fixed, a higher periodicity always pairs with a lower stated annual rate, and the reverse.

Beyond the yield-to-maturity, several simpler or convention-driven measures appear in quotes and price screens. The current yield is a bond’s annual coupon divided by its flat price.

If a 3.2% semiannual coupon five-year bond trades at 98.7 per 100 of face value, its current yield is 3.2% divided by 0.987, or 3.242%. The measure is crude: it looks only at interest income and ignores coupon frequency, the reinvestment of coupons (interest on interest), accrued interest, and any gain or loss from buying below or above par and redeeming at par.

Street convention, true yield, and government equivalent yield

The exact timing of cash flows matters for a precise yield. Take a Romania eurobond, 30 years in length with a 4.625% annual coupon and maturity on 3 April 2049, priced at 97.3684 for settlement on 3 April 2026 to yield 4.75% on an annual, actual/actual basis. The yield math assumes coupons land on 3 April each year, yet several of those dates fall on weekends: 3 April 2027 and 3 April 2032 are both Saturdays, so investors are actually paid on the following Mondays. A yield that ignores weekends and holidays and treats cash flows as arriving on their scheduled dates is quoted on street convention, and it is the common practice. A true yield uses the actual payment dates. Because weekends and holidays only delay payment, the true yield is never above the street convention yield, and the gap is usually a basis point or two, so the true yield is rarely quoted.

Corporate bond yields typically use a 30/360 day count. Restating such a yield on an actual/actual basis produces a government equivalent yield, which is useful for measuring the spread of a corporate bond over a government yield computed on the actual/actual basis.

A simple yield shows up in some markets too: it adds the coupon payments to the straight-line amortized part of any gain or loss and divides the total by the flat price. It is used mainly to quote Japanese government bonds (JGBs).

An embedded option cannot be stripped out and traded on its own, so it changes how the bond’s yield should be measured. A callable bond hands the issuer a right to repurchase it at preset prices on preset dates, though only once a call protection period, during which no call is permitted, has passed. Because the issuer may redeem early, a plain yield-to-maturity, which assumes every promised cash flow arrives on schedule, is not enough.

Consider a 6.5% seven-year callable note with US$400 million principal, paying semiannual coupons. The issuer cannot redeem it during the opening three years. Afterward it may buy the bond back on any business day under a declining schedule of call prices.

To gauge the least favorable outcome, an analyst computes a yield to each call date. A yield-to-call modifies the standard pricing equation so that the final cash flow is the coupon plus the call price on that date, rather than the coupon plus par at maturity.

Here PV is the bond price, PMT is the coupon per period, N is the number of evenly spaced periods to the call date, and r is the periodic market discount rate.

Option-adjusted price and yield

The yield-to-worst is widely quoted by dealers and investors, but a more precise route uses an option-pricing model plus a view on future interest rate volatility to price the embedded call. The investor bears the call risk, since the issuer holds the option, so the call feature reduces the bond’s value from the investor’s viewpoint: a callable bond is bought at a lower price than an otherwise identical option-free bond. Adding the value of the embedded call option to the flat price gives the option-adjusted price, and the discount rate that equates that price to the cash flows is the option-adjusted yield. The call option is worth the option-free bond’s price less the callable bond’s price.

To understand why a bond’s price and yield move, it helps to break the yield-to-maturity into a base benchmark rate and an issuer-specific spread. The benchmark carries the top-down, macroeconomic influences, while the spread carries the bottom-up, issuer-level factors. A yield spread is simply the difference between a bond’s yield-to-maturity and the benchmark yield.

The usual benchmark is the newest government bond outstanding, known as an on-the-run security. Being the most actively traded, its coupon sits closest to the current market discount rate, so it prices near par. Older, seasoned issues are off-the-run. On-the-run bonds usually trade at slightly lower yields than off-the-run bonds of similar maturity, partly from stronger demand and sometimes from cheaper financing in the repo market. Isolating the spread lets an analyst strip out broad moves in benchmark rates and judge a bond’s relative value against its own history and against peers.

The G-spread

The G-spread is the number of basis points by which a bond’s yield exceeds the yield on a matching government bond, real or interpolated, and it rewards the risks borne relative to the sovereign. When no government bond matches the target maturity, the sovereign rate is approximated by linear interpolation between the two nearest maturities before taking the difference.

The I-spread

A bond’s yield measured against the standard swap rate matched to its currency and tenor gives the I-spread, or interpolated spread. It sets the bond against a short-term, market-referenced rate and is standard for quoting euro-denominated corporate bonds off a euro interest rate swap. One illustration is a Chinese government five-year euro zero-coupon bond that carried a negative yield and was quoted at mid-swaps plus 30 bps, with mid-swaps meaning the midpoint between the bid and ask swap quotes. Issuers rely on the I-spread to compare fixed-rate bonds with floating-rate funding options like a bank loan or short-term commercial paper, while investors treat it as a read on credit risk. In an asset swap, the bond’s fixed coupon is converted to a market reference rate plus or minus a spread; when the bond trades near par, that spread approximates the price of its credit risk over the reference index.

The Z-spread and the option-adjusted spread

The G-spread and I-spread each compare two single yield numbers, applying one discount rate to every cash flow. A more granular measure adds a constant spread to each point on a government (or swap) spot curve. This zero-volatility spread, or Z-spread, is the constant amount Z that, when added to every benchmark spot rate, makes the present value of the bond’s cash flows equal its price.

The spot rates z1 through zN come from the government yield curve or from swap fixed rates, and Z is the same in every period. Because it does not change, the Z-spread is also called the static spread, and in practice it is found with a spreadsheet solver on a coupon date, when accrued interest is zero. The Z-spread also underlies a callable bond’s option-adjusted spread (OAS): with an option-pricing model and a volatility assumption, the embedded call’s value, quoted in basis points per year, is deducted from the Z-spread.

A relative-value screen makes the ordering concrete. For a 3.75% corporate bond maturing in 2047, a market data function reported the spreads below. An I-spread above the G-spread signals that Treasury yields sat a little above swap rates on that day.