ChatGPT model: (Expert: please correct if this is wrong)

ASSUME yield trending up

You said:

assume 20 treasury bond with fixed 5% yield, what would price be in 10 years if the inflation would increase 0.25% per year? 

ChatGPT said:

To estimate the price of a 20-year Treasury bond with a fixed 5% yield in 10 years, we need to consider how inflation affects interest rates and hence bond prices. Here’s a breakdown of the situation and the assumptions we'll use:

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Bond Details

• Coupon Rate: 5% (fixed, paid annually)

• Face Value: $1000 (typical assumption)

• Term: 20 years

• Years remaining in 10 years: 10 years

• Original Yield = Coupon Rate = 5%, so bond is issued at par ($1000)

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Inflation Assumption

• Inflation increases 0.25% every year for 10 years

• Starting from, say, 2%, the final year's inflation is 2% + (0.25% × 9) = 4.25%

• This likely raises nominal interest rates, affecting bond prices inversely

To price the bond in year 10, we assume the prevailing interest rate (new yield) reflects the increased inflation.

Let’s assume:

• Market yield in year 10 ≈ 5% + 0.25% × 10 = 7.5%

  • (Not a perfect proxy, but good for estimation if we assume real rates are constant and inflation fully passes into yields.)

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Pricing the bond in year 10

In year 10, the bond has 10 years left. It still pays a 5% annual coupon on $1000 = $50/year.

We discount the remaining cash flows at the new yield of 7.5%:

Let me calculate that for you.

 

In 10 years, if inflation steadily increases by 0.25% per year (raising the market yield to about 7.5%), the price of the 20-year Treasury bond with a fixed 5% yield would drop to approximately $828.40.

This reflects the market discounting older, lower-yielding bonds when new bonds offer higher yields due to inflation.