Calculating Yield on Debt

How can we calculate Yield on Debt?

The yield on Debt is the return investors can expect after holding security until its maturity. It can be calculated differently depending on what kind of security is in question.

This metric helps investors decide whether a particular security is profitable or not or if it is advantageous in comparison to other securities. This metric is used for both capital and money market securities.

It is more complicated to calculate money market securities because the maturity is less than a year. Capital market securities are used in mortgage markets for investors who want to calculate their return if the borrower defaults on a loan.

It differs from the interest rate because an interest rate is an investor's periodic return due to holding debt securities (ex: coupon payments). However, the debt yield encapsulates the interest rate and is the total return on investment. 

What is the Yield on Debt?

It is the rate of return an investor can expect if they hold a debt instrument until its maturity. It is also commonly known as Yield to Maturity (YTM).

Multiple types of it are calculated differently due to their applicability to all credit securities. It can be used in both money and capital markets.

Determining investment returns is more straightforward with long-term securities. However, short-term debt securities tend to be more complicated because they use different conventions to convert the period into a year.

Investors use this metric to determine how profitable their investments will be after holding them until maturity. It is also helpful to investors because they can use this metric to compare multiple assets.

The different types of YTM can be divided into two categories:

1. Money market YTM
2. Capital market YTM

Money market YTMs are more complex to calculate due to their nature of maturing in less than one year.

Types of Yields on Debt

These are the main types of return metrics for short-term and long-term securities:

• Bank Discount 
• Holding Period  
• Effective Annual  
• Money Market  
• Mortgage Loan Debt 

How to Calculate Bank Discount Yield (BDY)

It is calculated by dividing the difference between the par value and purchase price of the security by its par value to find its discount and multiplying it by 360 over its days left to maturity.

This formula assumes there are twelve 30-day months in a year. The number 360 is used as a convention instead of 365. This can pose challenges because the calculations that use different ways will not match.

The BDY is the rate of return on a bond sold at a discount on its face value. That type of bond is called a discount bond. BDY is commonly used for money market securities such as Treasury Bills (T-Bills), municipal bonds, zero-coupon bonds, commercial paper, etc.

The formula for finding the BYD is as follows:

BDY Example

Say you want to purchase a bond for 11,500$, whose face value is 12,000$. It means that the bond was bought at a 500$ discount. It was issued on December 1, 2021, and will mature in 95 days. Using the formula as follows:

= 0.16 or 16%

Therefore, the return for this bond is 16%. However, if an investor chooses multiple discount bonds, they would choose the one with a higher return.  

Flaws of BDY

The BDY's annualized formula is flawed and doesn't give the most accurate return on investment (ROI). For one thing, it doesn't consider potential compound returns because it assumes a 360-day year.

Likewise, the time simplification of assuming a 360-day year instead of an actual 365-day year can create errors. For example, Treasury Bills (T-Bills) are calculated on a 365-day basis. Therefore, the time convention of the formula can lead to contrasting values. The upcoming calculations are generally taught to be more accurate in determining investor returns. 

How to calculate Holding Period Yield (HPY)

An HPY calculates the return received from holding an asset or group of assets over some time, known as a holding period, and is typically expressed as a percentage.

It is calculated based on total asset returns from the asset or portfolio (income + changes in value). Stocks and other securities are considered financial assets.

A holding period can be used in both money and capital markets. It is not annualized, so the number of days isn't included. The formula for HPY is as follows:

Where;

• P1= Amount received at maturity 
• P0= Purchase price of the investment 
• D1= Distribution paid at maturity

HPY Example

Say you have a security that you hold until maturity. You received 5,000$ on maturity and purchased 4,800$ prior. The distribution you received was an additional 250$. Using the formula as follows:

= 0.03 or 3%

Therefore the return on holding this security is 3%. The security that pays dividends is usually stocks. However, in the case of T-Bills, there would be no distribution or dividend because they don't pay any. So, in that case, D1 would be 0.

How to Calculate Effective Annual Yield (EAY) 

The EAY is the rate of return on a bond with its interest payments reinvested at the same rate as its bondholder.

It is usually expressed in percentage form and can give a more accurate return than HPY because it is annualized. This is especially true when alternative investments are available, which can compound the returns.

This formula incorporates the previous calculation of the HPY and is as follows:

Where;

• t= number of days until maturity

EAY Example

For instance, to build up on the previous example, if the HPY on your investment is 3% and there are 175 days left until maturity:

= 0.0635 or 6.3% 

Note that the compounding frequency can significantly alter the results of the equation.

How to calculate the Money Market Yield (MMY)

MMY is calculated by multiplying the HPY with 360 and dividing it by days left to maturity. It is only used to assess returns in the money market. Therefore, an interest rate is earned by investing in securities with high liquidity and maturities of less than a year.

MMY (also known as a Credit Deposit equivalent ) allows the quoted return (on T-Bills) to be compared to an interest-bearing money market instrument.

This is because Treasury Bills have zero default risk and their returns are low compared to most corporate bonds and some certificates of deposit. Therefore, they are a safe investment and a good base comparison for other money market instruments.

As money market instruments quote on a 360-day basis, the MMY formula also uses 360-days in its calculations. The formula goes as follows:

MMY Example

An example would be if an investor had security with an HPY of 8.6%, with 235 days left to maturity.

= 0.131or 13%

Therefore, the return on this money market security would be much higher than on T-Bills, because the return on T-Bills does not exceed 5%.
Assuming the year is 360 days also helps investors compare returns of securities that pay coupons annually, semi-annually, and quarterly.

Debt Yield in Mortgage Markets 

It is an essential assessment of risk for lenders in mortgage markets. It evaluates how quickly it would take lenders to regain their losses should they possess a property after a loan default.

It also ensures that the loan amount isn't inflated due to low market cap rates, low-interest rates, and high amortization periods.

Mortgage markets are a subcategory of capital markets that deal with long-term credit securities (more than a year). Therefore, the formulas for calculating returns in these markets use capital market principles.

► How to Calculate the Debt Yield in Mortgage Markets:

The formula is as follows:

Where;

• NOI = Net Operating Income

So, as an example, let's say that the commercial property's NOI is 200,000$, and the loan amount was 1,500,000$. Then, according to the formula, the answer would be:

= 0.133 or 13%

The Bottom Line

There are four ways of calculating money market credit returns: BDY, HPY, EAY, MMY, and Mortgage Loan Debt Yield. They are all mainly used as tools for comparing and evaluating investments.

Likewise, in capital markets, the debt yield is used to calculate the return a lender would receive if the borrower were to default on the loan. It is a handy metric for decision-making, but it is pretty basic and should be used in addition to other metrics.

To address some commonly asked questions, the difference between a yield and an interest rate is that the yield considers the interest rate.

It is important to lenders because it lets them compare and assess the profitability of different securities.

Lastly, it has an inverse relationship with the price because coupon payments stay the same when the price decreases. Therefore, the value of the coupon payments increases, and the bond is sold at a premium.

Researched and authored by Anja Corbolokovic | Linkedin

Free Resources

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