Yield to Call and Yield to Put Calculations

4.2.2 Yield to Call and Yield to Put Calculations

Understanding the concepts of Yield to Call (YTC) and Yield to Put (YTP) is crucial for investors dealing with callable and putable bonds. These yield measures offer insights into the potential returns of bonds with embedded options, providing a comprehensive view of the bond’s performance under various scenarios. This section will guide you through the definitions, calculations, and practical implications of YTC and YTP, equipping you with the knowledge to make informed investment decisions.

Yield to Call (YTC)

Definition

Yield to Call (YTC) is the total return an investor can expect to earn on a callable bond if it is held until the call date, rather than its maturity date. Callable bonds give the issuer the right to redeem the bond before it matures, typically at a premium to the face value. YTC is particularly important as it reflects the return under the worst-case scenario for the investor if interest rates decline and the issuer decides to call the bond.

Calculation

The calculation of YTC is similar to that of Yield to Maturity (YTM), but it uses the call date as the time horizon and the call price instead of the face value. The formula for calculating YTC is:

Where:

• \( P \) = Current market price of the bond
• \( C \) = Annual coupon payment
• \( c \) = Number of years until the call date
• \( Call\ Price \) = Price at which the issuer can redeem the bond

Importance of YTC

YTC is a critical measure for investors as it provides the yield assuming the bond is called at the earliest possible date. It helps investors assess the potential impact of a call provision on their returns, particularly in a declining interest rate environment where issuers are more likely to call bonds to refinance at lower rates.

Yield to Put (YTP)

Definition

Yield to Put (YTP) is the return an investor can expect to earn on a putable bond if the investor exercises the put option at the earliest date allowed. Putable bonds give the bondholder the right to sell the bond back to the issuer at a predetermined price on specified dates. YTP is useful for understanding the minimum yield an investor can expect if they choose to put the bond back to the issuer.

Calculation

The calculation of YTP is similar to YTM, but it uses the put date and put price. The formula for calculating YTP is:

Where:

• \( P \) = Current market price of the bond
• \( C \) = Annual coupon payment
• \( p \) = Number of years until the put date
• \( Put\ Price \) = Price at which the investor can sell the bond back to the issuer

Importance of YTP

YTP provides insight into the minimum yield an investor can expect if they choose to exercise the put option. It is particularly valuable in rising interest rate environments, where investors may prefer to put the bond back to the issuer and reinvest in higher-yielding securities.

Calculating YTC and YTP

Step-by-Step Guide

1. Identify the Call/Put Date and Call/Put Price:

   • Determine the earliest date the bond can be called or put and the corresponding call or put price.

2. Calculate the Present Value of Future Cash Flows:

   • For YTC, calculate the present value of coupon payments and the call price up to the call date.
   • For YTP, calculate the present value of coupon payments and the put price up to the put date.

3. Solve for the Discount Rate:

   • Use the present value equation to solve for the discount rate (YTC or YTP) that equates the present value to the bond’s current market price.

Example – Yield to Call

Consider a bond with the following details:

• Face value = $1,000
• Annual coupon = $60 (6% coupon rate)
• Current market price = $1,050
• Callable in 5 years at $1,020

To calculate the YTC, solve the following equation:

Using iterative methods or financial calculators, you find that YTC ≈ 5.11%.

Yield to Worst (YTW)

Yield to Worst (YTW) is the lowest yield among YTM, YTC, and YTP. It reflects the worst-case scenario yield for the investor, considering all call and put provisions. YTW is an essential measure for risk-averse investors who want to understand the minimum yield they can expect under adverse conditions.

Glossary

• Yield to Call (YTC): The rate of return expected if the bond is held until the call date.
• Yield to Put (YTP): The rate of return expected if the bondholder sells the bond back to the issuer at the put date.
• Yield to Worst (YTW): The lowest potential yield considering all call and put provisions.

References

• Investopedia – Yield to Call (YTC)
• Investopedia – Yield to Put (YTP)
• Corporate Finance Institute – Yield to Worst

Bonds and Fixed Income Securities Quiz: Yield to Call and Yield to Put Calculations

By mastering the calculations of Yield to Call and Yield to Put, you can better evaluate the potential returns and risks associated with bonds that have embedded options. This knowledge is essential for making informed investment decisions in the fixed income market.