# Factors Affecting Yield Spreads

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,

$$BEI = \theta+\pi$$

## Question

Which of the following elements is least likely to influence the break-even inflation rate (BEI)?

1. Expected inflation
2. The risk premium for inflation uncertainty
3. 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 44: Economics and Investment Markets

LOS 44 (e) Describe the factors that affect yield spreads between non-inflation adjusted and inflation-indexed bonds.

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