# Exploring Bond Yield Measures | CFA Level I Fixed Income

In this article, we will look at various bond yield measures and learn how to calculate and interpret them for fixed-rate bonds. We will also understand the differences in yields based on coupon payment frequency and other factors that affect yield calculations.

## Yield Measures for Fixed-Rate Bonds

**Yield-to-maturity (YTM)** is a common yield measure for bonds, but there are other yield measures that provide more insight into the returns from investing in a bond. Let’s explore some of these alternative yield measures.

### Yield and Periodicity

For bonds with different coupon payment frequencies, the holding period yield and the yield-to-maturity can be the same. However, the effective yield increases with the periodicity.

**Annual-pay bond:**Effective yield is 10% (same as YTM)**Semi-annual coupon bond:**Effective yield is 10.25%**Quarterly coupon bond:**Effective yield is 10.38%

### Yield-to-Maturity vs. Effective Yield

When choosing between two bonds with similar ratings, a bond fund manager may consider the yield-to-maturity and the effective yield to make a decision.

**EXAMPLE**

**A bond fund manager is tasked to choose between 2 bonds of similar ratings to invest in for the next eight and a half years. Which bond should he choose, based on the yield-to-maturity and the effective yield?**

**Answer:** Bond A has a yield-to-maturity of 7.62%, while Bond B has a yield-to-maturity of 7.6%. Based on yield-to-maturity, the fund manager should choose Bond A. However, Bond B has an effective yield of 7.82%, which is higher than Bond A’s effective yield of 7.77%. Based on effective yield, the fund manager should choose Bond B.

### True Yield and Street Convention Yield

Due to weekends and holidays, coupon payment dates may be delayed, resulting in a slightly lower actual yield (true yield) compared to the quoted yield (street convention yield). True yield is never higher than street convention yield because weekends and holidays delay the time to payment.

### Government Equivalent Yield and Current Yield

A government equivalent yield restates a yield-to-maturity for a corporate bond based on the actual-actual convention, which can be used to obtain the spread over the government yield.

**Current yield = Sum of Coupon Payments in a year / Flat Price**

### Yield Measures for Callable Bonds

For callable bonds, investors’ yield depends on whether and when the bond is called. The lowest of yield-to-maturity and the various yields-to-call is termed the **yield-to-worst**.

The **option-adjusted yield** is a more precise approach for callable bonds, which considers the value of the embedded call option.

## Floating Rate Notes: Coupon Rates, Quoted Margin, and Discount Margin

When it comes to **floating rate notes**, the coupon rate is set based on a reference rate, plus or minus a fixed margin. This margin is determined by the issuer’s credit risk, relative to the reference rate instrument’s credit risk, and is called the **quoted margin**.

**EXAMPLE:** **Consider a 2-year, $1000 par, semi-annual pay floating rate note with a reference rate of the 180-day market reference rate. At issuance, the 180-day market reference is 2%, and the quoted margin is 1.7%. The coupon rate for the first payment will be 3.7%.**

For FRNs, we can use a simplified pricing model by fixing all future coupons at the most recent rate, plus the quoted margin. The discount rate applied is the latest 180-day market reference rate, plus the **discount margin**.

The discount margin represents the issuer’s credit risk compared to the reference rate instrument. While it starts as the same value as the quoted margin, it can change over time as the issuer’s credit risk changes.

**EXAMPLE:** **Assume the discount margin narrows to 1.4% after the first coupon payout. We’ll use a discount rate of 4.4% to calculate the value of the FRN, with 3 periods to maturity, an interest per period of 2.2%, a payment per period of $23.50, and an FV of $1000. Solving for PV, the value of the FRN is $1004.31.**

## Money Market Instruments: Yield Measures and Comparisons

**Money market instruments** are short-term debt securities with original maturities of 1 year or less, such as government issues, commercial paper, and certificates of deposit. Their yield measures and quotes differ significantly from the bond market, and can be based on a 360-day or 365-day year.

**U.S. T-bills:**quoted as annualized discounts from face value based on a 360-day year.**Commercial paper:**usually quoted on a 360-day basis, with US commercial paper on a discount basis, and Euro-commercial paper on a discount basis or add-on yield.**Certificate of deposits:**usually quoted on an add-on yield basis, either on a 360 or 365-day basis.

Money market instruments are quoted based on simple annual interest, distinguishing them from bonds, which use compounding interest.

### Calculating Actual Payments and Comparing Yields

To calculate actual payments and compare yields on different securities, we can use the following examples:

**For a $1000 par, 90-day U.S. T-bill with a quoted discount rate of 1.4%, the discount at issuance is $3.50, and the issuance price is $996.50. To find the equivalent add-on yield, divide the interest by the price at issuance, giving us 0.351%. To annualize it based on a 365-day convention, multiply it by 365/90, resulting in an equivalent add-on yield of 1.424%.**

**For a hypothetical 90-day commercial paper with a quoted interest rate of 1.4% on an add-on basis, the interest is $3.50, given on maturity. To annualize this add-on yield based on a 365-day convention, multiply it by 365/90, giving an equivalent add-on yield of 1.419%.**

**For a hypothetical 90-day certificate of deposit with a quoted interest of 1.4% on a 365-day basis, the interest is slightly lower at $3.452. Since the quoted interest is already on an add-on basis and 365-day convention, no adjustments are needed.**

As shown in these examples, the actual yield can differ even if all three instruments have the same quoted interest of 1.4%. Be sure to convert quoted interest from one basis to another to make accurate comparisons in the exam.

### Bond Equivalent Yield

To compare interest rates to the yield-to-maturity of a semi-annual coupon bond, we use the **bond equivalent yield**. Using the commercial paper example, we can illustrate the method:

- Convert the money market security’s holding period return to an effective semi-annual yield and double it.
- Calculate the effective annual yield by compounding the holding period factor (1.419%) by 365/90 days, minus 1, giving 1.427%.
- Find the semi-annual yield by compounding the effective annual yield by half, giving 0.711%.
- Finally, the bond equivalent yield is double the semi-annual yield, resulting in 1.422%.

And that concludes our discussion on bond yield measures. In the next lesson, we’ll dive into the maturity structure of interest rates.

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