What is a Bond?
A bond is a fixed-income financial instrument that represents a loan given by an investor to a borrower, typically a corporation or government. When you purchase a bond, you are essentially lending money to the issuer in exchange for periodic interest payments (coupon payments) and the return of the principal amount at maturity. Bonds are considered relatively stable investments compared to stocks and are often used for portfolio diversification and income generation.
What is Bond Yield?
Determining the value of bond yield depends on various factors, such as compounding interest payments and time value. This leads to complex calculations like bond equivalent yield and yield to maturity. Let us look at these two concepts in detail to understand what the meaning of yield and the significance it carries.
What is Yield to Maturity?
Yield to maturity measures the total return investors achieve if investors carry the bond until maturity.
It includes all possible cash flows of the future while evaluating the YTM.
Suppose a company issues bonds with the following terms:
Face value = Rs. 1,000
Coupon rate = 10%
Periodicity of payments = Once a year
Maturity = 5 years
Date of bond issue = 01 September 2020
Assuming you purchase the bond when it is issued, you are buying it at face value. The bond will pay a coupon of 10% on 01 September 2021.
If the bond sells at a discount to the face value, it implies that the coupon rate is less than the current interest rates. As a result, the bonds became less attractive, which pushed their prices downwards. In this case, the YTM would be higher than the coupon rate. Similarly, if the bond sells at a premium to the face value, it implies that the current rate of interest is less than the coupon rate. This indicates that the coupon rate is higher than the YTM.
Formula and Calculation of Bond Price Yield
The most straightforward method to calculate a bond yield is by dividing the annual coupon payment by the bond's face value. This result is referred to as the coupon rate.
Coupon Rate = Annual Coupon Payment / Bond’s Current Market Price
For instance, if a bond has a face value of $1,000 and pays an annual interest of $100, the coupon rate would be 10%, derived from dividing $100 by $1,000. Bonds function as loans made to issuers, and they are generally perceived as secure investments. Unlike stocks, the value of bonds tends to remain more stable. This stability allows bondholders to receive consistent income throughout the bond's life.
Understanding the bond yield meaning is essential for investors. Generally, a higher bond yield suggests a greater risk associated with the investment, while a lower yield indicates a safer option. Yield to Maturity (YTM) translates to the total anticipated return on a particular bond if it is kept until it matures. This calculation takes into account the bond’s present market price, the interest payments, and the time left until maturity. Understanding YTM is key to assessing a bond's overall profitability, making it a crucial metric for evaluating the bond's price and yield.
Additional Bond Yield Calculations
Apart from the basic bond yield, you can also calculate yields like the Yield to Maturity (YTM), Effective Annual Yield (EAY), and Bond Equivalent Yield (BEY). These calculations help you understand how different factors impact bond yields and provide a more accurate picture of your returns over time.
Yield to Maturity (YTM)
Yield to Maturity (YTM) estimates the annual return you earn if you hold a bond until it matures, considering all coupon payments and the face value. It reflects the bond’s overall yield, accounting for its current price, coupon payments, and maturity value.
YTM = [C + (FV - PV)/T] / [(FV + PV)/2].
Where:
- C = Annual coupon payment
- FV = Face Value (Par Value)
- PV = Present Value (Current bond price)
- T = Years to maturity
- YTM = Yield to maturity
Suppose you buy a bond with a face value of ₹10,000, a coupon rate of 7%, and four years to maturity. The bond is currently priced at ₹9,200. You receive an annual coupon payment based on the 7% rate. To calculate the YTM, you add the annual coupon payment to the average annual gain from the bond’s discount. This gain is the difference between the face value and the current price, divided by the remaining years to maturity. You then divide this total by the average of the bond’s face value and its current price. In this example, the calculated YTM is approximately 9.38%, indicating the annual return if you hold the bond until it matures.
Effective Annual Yield (EAY)
Effective Annual Yield (EAY) accounts for the compounding effect on bond income, making it more accurate than the nominal interest rate. It shows the true annual return, considering multiple compounding periods.
Formula:
EAY= [1 + (i/n)]n – 1
Where:
- EAY = Effective Annual Yield
- i = Nominal interest rate (as a decimal)
- n = Number of compounding periods per year
Suppose you invest in a bond that pays interest semi-annually at a nominal interest rate of 8%. To calculate the Effective Annual Yield (EAY), you consider the impact of compounding over two periods in a year. The nominal rate of 8% is divided by two, resulting in a semi-annual rate of 4%. You then calculate how much the bond earns annually, accounting for both compounding periods. In this case, the EAY comes out to 8.16%, slightly higher than the nominal rate due to the effect of semi-annual compounding.
Bond Yield Calculation Issues
Calculating bond yields accurately can become tricky when dealing with fractional periods. If a bond has four years and eight months to maturity, the remaining time is expressed as a decimal to adjust the calculations. This ensures the yield reflects the exact remaining period.
Accrued interest also complicates calculations. If you buy a bond with two months left until the next coupon payment, you’re entitled to the entire coupon amount. However, since the seller held the bond for four months, the bond’s price will include accrued interest to compensate the seller for their holding period.
Bond prices can be quoted as clean or dirty prices. The clean price excludes accrued interest, while the dirty price includes it. Financial terminals like Bloomberg and Reuters typically display the clean price, so always confirm whether accrued interest is factored in when assessing bond yields.
The bond equivalent yield measures the annual percentage yield on fixed-income securities. While selecting various fixed-income investments, investors can use BEY to compare whether a particular investment is better or worse than other investments.
BEY = [(Face value -Purchase price) / Purchase Price]* (365/d)* 100
Where d denoted the days until maturity.
The Link Between Bond Yield vs Bond Price
Bond yields typically have an inverse relationship with bond prices, i.e. higher bond prices are linked with lower yield and vice versa. Let us understand how.
Suppose your bond has a face value of Rs. 1000 and a coupon rate of 10%. You earn 10% of 1000 as coupon payments, i.e. Rs. 100. |
Scenario I: Bond trades at a discount | Suppose the bond price is Rs. 700 in the secondary market. This implies that the bond trades at a discount of Rs. 300 to its face value.
Yield = coupon rate/bond price, i.e. 100/700 = 14.28% |
Scenario II: Bond trades at a premium | Let us assume the bond price in the secondary market increases from Rs. 700 to Rs. 1300. The bond now trades at a premium to its face value.
Yield = 100/1300 = 7.69% |
Conclusion
Bonds can serve as the ideal financial instruments to diversify your portfolio. However, before you begin investing, understand the basics, such as what is the meaning of bond, factors influencing bond prices, the rise and fall of bond yields, the relationship between bond prices and yields etc., to achieve maximum return on your investments.