### Effect of Credit Spread on Yield-to-maturity

The yield-to-maturity on a corporate bond is comprised of a government benchmark yield and a spread over that benchmark.

The building-blocks approach implies that the yield-to-maturity changes can be broken down further. The benchmark yield could change because of either a change in expected inflation rate or in expected real interest rate. Furthermore, a spread change could also arise due to a change in the credit risk of the issuer or because of the liquidity of the bond.

## Example

Assume that a bond with a modified duration of 4.00 and a convexity of 25.00 will appreciate by around 0.81%, regardless of the source of the yield-to-maturity change, if the yield-to-maturity decreases by 20 bps.

$$\%ΔPF^{FULL}≈(-4.000×0.0020)+(\frac{1}{2}×25×(-0.0020)^2 )=0.0081$$

## Credit Risk

Let’s now assume that the yield to maturity on a corporate bond is 6.75%. When the benchmark (government) yield is 4%, the spread is 2.75%, which is the difference between the benchmark yield and the yield on our bond.

In the fixed-income market, credit risk is referred to as the probability of default and the recovery of assets in case of default. In our example, assume credit risk is estimated to be 2.25% from the spread of 2.75% and liquidity risk represents the remaining 0.50%.

## Liquidity Risk

Liquidity risk is much smaller when there is a greater frequency of trading and higher volumes of trading.

There is a difference between the bid (or purchase) price and the offer (or sale) price. The difference depends on the type of bond, the size of the transaction, and some other factors. For instance, government bonds often trade just a few basis points between purchase and sale prices. Thinly traded corporate bonds could have a much wider difference between bid and offer prices, hence creating more liquidity risk in the event that the investor wishes to sell his bond.

## Question

A corporate bond’s yield-to-maturity is 8% while a similar risk-free government bond’s yield is 3%. If the liquidity risk is assumed to be 1.75%, which of the following is closest to the credit risk on this bond?

A. 2.75%

B. 3.25%

C. 5%

Solution

Spread = 8% – 3% = 5%

Spread = Credit risk + Liquidity risk

5% = Credit risk + 1.75%

Credit risk = 5% – 1.75% = 3.25%

Explain how changes in credit spread and liquidity affect yield-to-maturity of a bond and how duration and convexity can be used to estimate the price effect of the changes

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