Yield to Worst (YTW)

The yield to worst (YTW) is a measure of the return an investor will receive if they hold a bond to maturity. It is calculated by taking the weighted average of the bond's yield to call and yield to maturity. The yield to call is the return an investor will receive if the bond is called before maturity. The yield to maturity is the return an investor will receive if the bond is held to maturity.

The YTW is used to compare bonds with different call dates and maturities. It can also be used to determine the value of a bond that is trading below its par value.

The YTW is calculated using the following formula:

```
YTW = (C / N) * YTC + (1 - C / N) * YTM
```

Where:

* C is the call price of the bond
* N is the number of years until the call date
* YTC is the yield to call
* YTM is the yield to maturity

For example, consider a bond with a par value of $1,000, a coupon rate of 5%, a call price of $1,050, and a maturity date of 10 years. The bond is currently trading at $950.

The yield to call is calculated as follows:

```
YTC = (1050 - 950) / 10 = 10%
```

The yield to maturity is calculated as follows:

```
YTM = (50 / 10) * 10 + (1 - 50 / 10) * 5 = 4.5%
```

The YTW is calculated as follows:

```
YTW = (1050 / 10) * 10% + (1 - 1050 / 10) * 4.5% = 4.75%
```

Therefore, the YTW of this bond is 4.75%.

The YTW is a useful tool for investors who are considering purchasing a bond. It can help investors to determine the best price to pay for a bond and to compare bonds with different call dates and maturities.