Bond Calculator
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What is a Bond?
A bond is a type of loan where an investor lends money to an entity (like a government or corporation) for a specific period. In return, the issuer promises to pay the investor periodic interest payments, known as coupons, and to repay the principal amount, or "face value," of the loan at a future date, called the maturity date. Bonds are considered fixed-income securities because the interest payments are typically fixed.
How Bond Pricing Works
The price of a bond is determined by the present value of its future cash flows. These cash flows consist of all the future coupon payments and the final repayment of the face value at maturity. The key factor used to discount these future cash flows to their present value is the current market interest rate, also known as the Yield to Maturity (YTM).
- When Coupon Rate = YTM: The bond sells at its face value (par).
- When Coupon Rate > YTM: The bond's fixed payments are more attractive than what the market offers, so it sells for more than its face value (at a premium).
- When Coupon Rate < YTM: The bond's fixed payments are less attractive, so it sells for less than its face value (at a discount).
As a bond gets closer to its maturity date, its price will naturally move towards its face value, a phenomenon known as "pull to par."
Bond Yield Explained
Yield is a measure of the return an investor gets from a bond. There are several types:
- Coupon Rate: The fixed annual interest rate set when the bond is issued, calculated on the face value.
- Current Yield: The annual coupon payment divided by the bond's current market price. It provides a simple snapshot of the return on the current price.
- Yield to Maturity (YTM): The most comprehensive measure, representing the total annualized return an investor will receive if they hold the bond until it matures. It accounts for all coupon payments, the face value, and the difference between the purchase price and the face value.
Duration & Risk
Duration is one of the most important concepts for understanding a bond's risk. It measures how sensitive a bond's price is to changes in interest rates. It is expressed in years, but it's not simply the time to maturity. Instead, it's a weighted average of the times until each cash flow (coupon and principal) is received.
Modified Duration is a more direct measure of price sensitivity. It estimates the percentage change in the bond's price for a 1% change in market interest rates. For example, if a bond has a modified duration of 5 years, its price will drop by approximately 5% if interest rates rise by 1%, and vice versa. A higher duration implies greater interest rate risk.
Frequently Asked Questions (FAQ)
What is a bond?
A bond is a fixed-income instrument that represents a loan made by an investor to a borrower (typically corporate or governmental). The borrower agrees to pay interest (the coupon) for a defined period and repay the principal amount (face value) at a future date, known as the maturity date.
How do you calculate a bond's price?
A bond's price is the present value of all its future cash flows, which include the periodic coupon payments and the face value returned at maturity. These cash flows are discounted using the market interest rate (or Yield to Maturity). If the market rate is higher than the coupon rate, the bond sells at a discount; if lower, it sells at a premium.
What is Yield to Maturity (YTM)?
Yield to Maturity (YTM) is the total anticipated return on a bond if it is held until it matures. It's expressed as an annual rate and takes into account the bond's current market price, par value, coupon interest rate, and time to maturity. It is the discount rate at which the sum of all future cash flows from the bond equals the current price of the bond.
What is the difference between coupon rate and yield?
The Coupon Rate is the fixed annual interest rate paid on the bond's face value, set when the bond is issued. The Yield (specifically Yield to Maturity) is the total return an investor can expect, reflecting the current market price of the bond. While the coupon rate is fixed, the yield fluctuates with market interest rates and the bond's price.
What does bond duration mean?
Bond duration is a measure of a bond's price sensitivity to changes in interest rates, expressed in years. Specifically, Modified Duration indicates the percentage change in a bond's price for a 1% change in interest rates. A higher duration means greater interest rate risk.
How do I use this calculator?
Enter the bond's Face Value (principal), the Annual Coupon Rate, the current market interest rate (YTM), the number of years until maturity, and the payment frequency. Optionally, provide Settlement and Maturity dates for accrued interest calculation. Click 'Calculate' to see the bond's price, duration, and other key metrics.
