Spot Rate (Zero-Coupon) Calculator
Calculate the theoretical yield for zero-coupon instruments
How to Calculate Spot Rate in Excel
The spot rate, often referred to as the zero-coupon rate, represents the yield to maturity of a zero-coupon bond. Unlike coupon bonds, zero-coupon bonds are sold at a discount and provide a single payment at maturity. Understanding how to calculate this is essential for fixed-income analysis and constructing the yield curve.
The Mathematical Formula
To manually calculate the spot rate ($r$), use the following formula:
Where:
- Face Value: The amount paid at maturity.
- Market Price: The current purchase price of the bond.
- t: Total years until maturity.
- n: Number of compounding periods per year.
Step-by-Step Guide for Excel
Excel does not have a single "SPOTRATE" function, but you can easily calculate it using the RRI function or basic arithmetic. Here are the two primary methods:
Method 1: Using the RRI Function
The RRI function returns an equivalent interest rate for the growth of an investment. In Excel, enter:
=RRI(periods, market_price, face_value)
If you have a 2-year bond bought at 95 with a face value of 100, the formula is =RRI(2, 95, 100).
Method 2: Manual Power Formula
For more control over compounding, use the power formula in an Excel cell:
=((Face_Value / Market_Price)^(1 / Years)) - 1
Practical Example
Imagine a Treasury Zero-Coupon bond maturing in 5 years. The current market price is 820.00 and the face value is 1,000.00. Using the annual compounding method:
- Divide 1,000 by 820 = 1.2195
- Raise 1.2195 to the power of (1/5) = 1.0405
- Subtract 1 = 0.0405 or 4.05%