Calculating Yield to Maturity (YTM) on Debt Instruments

Debt yield refers to the rate of return an investor can expect to earn if he/she holds a debt instrument until maturity. Such instruments include government-backed T-billsTreasury Bills (T-Bills)Treasury Bills (or T-Bills for short) are a short-term financial instrument issued by the US Treasury with maturity periods from a few days up to 52 weeks., corporate bondsBondsBonds are fixed-income securities that are issued by corporations and governments to raise capital. The bond issuer borrows capital from the bondholder and makes fixed payments to them at a fixed (or variable) interest rate for a specified period., private debt agreements, and other fixed income securitiesFixed Income SecuritiesFixed income securities are a type of debt instrument that provides returns in the form of regular, or fixed, interest payments and repayments of the. In this article, we will explore the four different types of yields: Bank Discount, Holding Period, Money Market, and Effective Annual.

Bank Discount Yield (BDY)

The BDY formula is best suited to calculating yield on short-term debt instruments such as government T-bills. The formula for calculating BDY is:

Where:

D – Discount/premium from face value (face value – market price)

F – Face value

360 – Number of days in a year (as per banking conventions)

t – Number of days until maturity

BDY Example

An investor wants to buy a U.S. T-bill. The current market price is $490 and the security has a face value of $500. The T-bill matures in 200 days from today. Should the investor buy the T-bill today, what is the expected BDY?

The BDY on this investment is 3.6%.

Holding Period Yield (HPY)

HPY measures any capital gains and/or losses from debt investments that have occurred over a specified holding period. The formula for calculating HPY is:

Where:

P1 – Price of security at the end of the holding period (maturity)

P0 – Price of security at the beginning of the holding period (purchase price)

D1 – Cash distributions during holding period (coupons)

HPY Example

An investor buys a T-bill at a face value for $500. He then sells the T-bill at maturity for $510. What is his HPY?

The HPY on this investment is 2%. Note that T-bills are zero-coupon securities and do not pay a monthly coupon to investors. Thus, the D1 term in this example is equal to 0.

Money Market Yield (MMY)

MMY calculates the return on highly liquid, short-term debt instruments such as certificates of deposits, commercial paper, or T-bills. MMY is different from BDY, as it computes yield based on the purchase price of the security rather than on the security’s face value. The equation for MMY is:

Where:

360 – Number of days in a year (as per banking conventions)

t – Number of days until maturity

MMY Example

This example uses the same numbers as the HPY example above. Now, we learn that the T-bill was a 3-month T-bill that matures in 90 days. What is the investment’s MMY?

Using the HPY that we calculated earlier, the MMY on this investment is 8%.

Effective Annual Yield (EAY)

EAY is essentially the annualized version of HPY. It provides a number that is easily comparable to the annual returns of other securities. The equation for EAY is:

Where:

365 – Number of days in the year (different from bank convention)

t – Number of days until maturity

EAY Example

This example uses the same numbers as the HPY and MMY examples above, where HPY is 0.02 and t is 90 days.

The annualized return for this investment is 8.4%.

More Resources

We hope you enjoyed CFI’s explanation of yield on debt. CFI offers the Financial Modeling & Valuation Analyst (FMVA)™Become a Certified Financial Modeling & Valuation Analyst (FMVA)®CFI's Financial Modeling and Valuation Analyst (FMVA)® certification will help you gain the confidence you need in your finance career. Enroll today! certification program for those looking to take their careers to the next level. To learn more about related topics, check out the following CFI resources:

• Convertible BondConvertible BondA convertible bond is a type of debt security that provides an investor with a right or an obligation to exchange the bond for a predetermined number of shares in the issuing company at certain times of a bond’s lifetime. A convertible bond is a hybrid security
• Risk-Free RateRisk-Free RateThe risk-free rate of return is the interest rate an investor can expect to earn on an investment that carries zero risk. In practice, the risk-free rate is commonly considered to equal to the interest paid on a 3-month government Treasury bill, generally the safest investment an investor can make.
• Liquidity PremiumLiquidity PremiumA liquidity premium compensates investors for investing in securities with low liquidity. Liquidity refers to how easily an investment can be sold for cash. T-bills and stocks are considered to be highly liquid since they can usually be sold at any time at the prevailing market price. On the other hand, investments such as real estate or debt instruments
• Fixed Income Fundamentals Course – CFI