<p>Yes, the number you give is an approximation. If you wanted to calculate the true economic breakeven, you would need to include the effect of the lag used in the indexation process (which includes known inflation information), coupon cash flows, seasonality of inflation, etc. If there is a maturity mismatch, then you would need to decide how to handle that as well.</p>

<p>However, the deviation between the economic breakeven and the approximation is normally small. In fact, the market convention is (or at least it was) to ignore compounding and just use the spread between quoted rates.</p>

<p>You would need a full fixed income pricing suite to calculate the true economic breakeven, so a course would stick to the approximation.</p>

CC BY-SA 4.0
2019-04-09T16:35:30.317Z
What is a full fixed income pricing suit?
Jhonny
CC BY-SA 4.0
2019-04-10T10:46:56.180Z
@Jhonny Suite. It’s a library of pricing algorithms.
Brian Romanchuk
CC BY-SA 4.0
2019-04-07T14:27:21.460Z
2019-04-07T14:27:21.460Z
Brian Romanchuk
<p>In my introductory monetary economics course we have learned that inflation expectations can be calculated by comparing yields on index-linked and conventional bonds of equal maturity and assuming a risk neutral investor. One simple example given is:</p>

<hr>

<p>A risk-neutral investor is indifferent between 1-year conventional and index-linked gilts (issued at par value, i.e. p = F) if expected returns until maturity equal:
<span class="math-container">$$ (1+i) F = (1+r) (1+\pi) F $$</span> so knowing <span class="math-container">$i$</span> and <span class="math-container">$r$</span> (from financial data), we can calculate <span class="math-container">$\pi$</span>, the inflation expectation. </p>

<hr>

<p>Now this I am completely fine with, but then the lecture goes on to the following example:</p>

<blockquote>
  <p>Extracting inflation expectations from gilts (assuming risk
  neutrality) Use Tr 4.5pc ‘42: i = 1.71%, and IL 0.625pc ‘42: r =
  −1.66% [Tradeweb] <span class="math-container">$$(1 + 0.0171)^N = (1 − 0.0166)^N (1+\pi^e_N)^N$$</span> 
  giving <span class="math-container">$\pi_N^e \approx 3.43%$</span> break-even inflation for a horizon of N =
  23 Years</p>
</blockquote>

<p>My question is: <strong>how can this calculation be valid when the coupon rates are different for the two gilts?</strong> What are the assumptions (eg issued at face value)? </p>

<p>My thinking is that to extract inflation expectations, we must equate the expected returns of the bonds until maturity, just as in the earlier simple example. The rate of return is however clearly tied to the coupon payments, which each need to be multiplied at the relevant accrued yield, leading to a much more complicated equation for the inflation expectation. </p>

<inflation><interest-rate><bonds>
Extraction of Inflation Expectation from bond yields
Jhonny
# Extraction of Inflation Expectation from bond yields

(Asked by: username_0 on 2019-04-07)

In my introductory monetary economics course we have learned that inflation expectations can be calculated by comparing yields on index-linked and conventional bonds of equal maturity and assuming a risk neutral investor. One simple example given is:

---

A risk-neutral investor is indifferent between 1-year conventional and index-linked gilts (issued at par value, i.e. p = F) if expected returns until maturity equal:
$$ (1+i) F = (1+r) (1+\pi) F $$ so knowing $i$ and $r$ (from financial data), we can calculate $\pi$, the inflation expectation.

---

Now this I am completely fine with, but then the lecture goes on to the following example:

> Extracting inflation expectations from gilts (assuming risk
> neutrality) Use Tr 4.5pc ‘42: i = 1.71%, and IL 0.625pc ‘42: r =
> −1.66% [Tradeweb] $$(1 + 0.0171)^N = (1 − 0.0166)^N (1+\pi^e\_N)^N$$
> giving $\pi\_N^e \approx 3.43%$ break-even inflation for a horizon of N =
> 23 Years

My question is: **how can this calculation be valid when the coupon rates are different for the two gilts?** What are the assumptions (eg issued at face value)?

My thinking is that to extract inflation expectations, we must equate the expected returns of the bonds until maturity, just as in the earlier simple example. The rate of return is however clearly tied to the coupon payments, which each need to be multiplied at the relevant accrued yield, leading to a much more complicated equation for the inflation expectation.

**Tags:** inflation, interest-rate, bonds

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## 1 answers

### Answer by username_1 on 2019-04-07. Score: 4 | Accepted answer

Yes, the number you give is an approximation. If you wanted to calculate the true economic breakeven, you would need to include the effect of the lag used in the indexation process (which includes known inflation information), coupon cash flows, seasonality of inflation, etc. If there is a maturity mismatch, then you would need to decide how to handle that as well.

However, the deviation between the economic breakeven and the approximation is normally small. In fact, the market convention is (or at least it was) to ignore compounding and just use the spread between quoted rates.

You would need a full fixed income pricing suite to calculate the true economic breakeven, so a course would stick to the approximation.

> **Comments:**
> **username_0**: What is a full fixed income pricing suit?  
> **username_1**: @Jhonny Suite. It’s a library of pricing algorithms.  

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