Understanding and Calculating Treasury Forward Rates

Law of One Price

The Law of One Price is “an economic concept that states that the price of an identical asset or commodity will have the same price globally, regardless of location, when certain factors are considered.” Simply put, similar asset types (in this case US Treasuries) should have consistent pricing.

For example, imagine you have a 1-year treasury bond with an interest rate of 5.0%. According to the Law of One Price, if you instead choose to invest in a 6-month treasury bond and then reinvest in another 6-month treasury bond after the first one matures, you should expect to earn the same 5.0% annual return.

Here’s the breakdown:

• The 1-year treasury bond offers a 5.0% interest rate.
• If you buy a 6-month treasury bond today and then reinvest in another 6-month treasury bond after the first one matures (total term of 1-year), the combined interest rate of these two investments should also equal 5.0%.

This consistency ensures that no matter how you invest in these bonds, the return will be the same, maintaining fairness and efficiency in the market.

Spot Rates

A spot rate is the current yield (interest rate) for a bond. For example, on 6/15/2024 the spot rate for a 1-month US Treasury was 5.34%.

Forward Rates

A forward rate is the future expected spot rate on a bond, it is also referred to as the breakeven rate. Without getting too far in the weeds, a forward rate is “backed into” by using the spot rates for bonds with different maturities. Here is the formula used to determine a forward rate:

Example Calculation

Let’s calculate the 6-month Treasury rate, 6-months forward. This means we want to know what the interest rate should be for the 6-month US Treasury, 6 months in the future. To do this, we will need the spot rates for the 6-month Treasury, and the 1-year Treasury.

6-month rate = 5.34%

1-year rate = 5.06%

Now let’s throw this into our equation, and solve for r₂:

If you do the math, the forward rate comes out to be 4.74%.

Conclusion

Understanding forward rates is crucial for making informed investment decisions in the Treasury market. The Law of One Price ensures consistent returns across similar investments, and calculating forward rates helps predict future interest rates based on current spot rates.

For more detailed analysis and ongoing updates, make sure to check back regularly on my blog. If you have any questions or need further clarification on any points, feel free to leave a comment or reach out directly.

Works Cited

Investopedia. "Law of One Price." Investopedia.

Investopedia. "What Is the Difference Between a Forward Rate and a Spot Rate?" Investopedia.