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The current value of a real default-free bond (inflation-adjusted) is given by:

$$ P_0=\sum_{t=1}^{n}\frac{CF_t}{\left[1+R\right]^t} $$

For a default-free nominal coupon-paying bond (non-inflation adjusted), we have:

$$ P_0=\sum_{t=1}^{n}\frac{CF_t}{\left[1+R+\theta+\pi\right]^t} $$

The difference between the yield on non-inflation adjusted (nominal) and inflation-indexed bonds with the same maturity is called the **break-even inflation (BEI) rate**. The inflation expectations, \({\theta}\), and the risk premium demanded by investors as compensation for the uncertainty of future inflation, \({\pi}\), determine the break-even inflation rate.

Therefore,

$$ BEI = \theta+\pi $$

QuestionWhich of the following elements is

least likelyto influence the break-even inflation rate (BEI)?

- Expected inflation
- The risk premium for inflation uncertainty
- The risk-free rate
## Solution

The correct answer is C.The break-even inflation (BEI) rate is the difference between the yield on non-inflation adjusted (nominal) and inflation-indexed bonds with the same maturity. The break-even inflation rate stems from inflation expectations \((\theta)\) and the risk premium demanded by investors as compensation for the uncertainty of future inflation \((\pi)\). Mathematically,

$$ BEI = \theta+\pi $$

Reading 43: Economics and Investment Markets

*LOS 43 (e) Describe the factors that affect yield spreads between non-inflation adjusted and inflation-indexed bonds.*