- Sources of Return from Investing in a Bond
- How to Calculate Current Yield
- How to Calculate Yield to Maturity
- Bond Equivalent Yield Convention
- Yield to Maturity (YTM) Approximation Formula
- YTM and Reinvestment Risk
- Factors Affecting Reinvestment Risk
- Calculate Bond-Equivalent Yield of Annual-Pay Bonds
- How to Calculate Yield to Call of a Bond
- Cash Flow Yield
- Bootstrapping Spot Rate Curve (Zero Curve)
- How to Price a Bond Using Spot Rates (Zero Curve)
- Nominal Spread
- Z-Spread: Definition and Calculation
- Option-adjusted Spreads (OAS)
- What are Forward Rates?
- How to Calculate Forward Rates from Spot Rates?
- How to Value a Bond Using Forward Rates

# How to Value a Bond Using Forward Rates

We have seen that a bond can be valued using spot rates by discounting each cash flow by the spot rate for the maturity. We also saw that forward rates can be derived from spot rates. If so, we can also value a bond using forward rates instead of spot rates.

Let’s take a specific cash flow in a bond to understand this. Say, a bond is going to pay $100 as coupon after 2 years. s_{2 }is the 2-year spot rate is 6%. The present value of this cash flow will be:

PV of $100 = $100/(1+s_{2})^{2}

We also know that

(1+s_{2})^{2 }= (1+s_{1}) (1+_{1}f_{1})

Replacing this is the PV calculation:

PV of $100 = $100/(1+s_{1}) (1+_{1}f_{1})

If s1 is 6% and _{1}f_{1} is 7%.

Here 1/(1+s_{1}) (1+_{1}f_{1}) is called the forward discount factor.

The resulting valuation using either spot rates or forward rates will be the same.

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