# Definition of worst-case propagation

## What is the worst propagation?

Spread-to-worst (STW) measures the dispersion of returns between the best performing and the worst performing security in a given market, typically bond markets, or between the returns of different markets.

Key points to remember

- Spread-to-worst (STW) measures the dispersion of returns between the best performing and the worst performing security in a given market, typically bond markets, or between the returns of different markets.
- The STW in bond markets is the difference between the yield-to-worst (YTW) of a bond and the yield to maturity (YTW) of a US Treasury security of similar duration.
- Applying the spread to worst to different markets can guide an investor in making decisions that can optimize the value of his portfolio.

## Understanding Worst Spread (STW)

The STW in bond markets is the difference between the worst-case yield (YTW) on a bond and the worst-case yield on a US Treasury security of similar duration. STW is either Yield to Call (YTC) or Yield to Maturity (YTM), whichever is less, and is expressed in “basis points (bps)”.

STW uses the YTW, which is the lowest potential return that can be received on a bond without the issuer actually defaulting. If a bond is callable, an investor runs the risk of lower returns on the bond. Indeed, in a declining interest rate environment, the bond investor should reinvest in low yield fixed income securities. Corporate and municipal bonds generally have appeal clauses.

The YTW of a bond is calculated on all possible call dates before maturity. It is assumed that a prepayment takes place if the bond has a call option and the issuer can reissue at a lower coupon rate. YTW is the lower of YTC or YRM. YTC is the annual rate of return assuming the bond is redeemed by the issuer on the next call date. The YTW of a premium bond is equivalent to YTC because the bond issuer is likely to call it. A bond traded at a premium means that the coupon rate is higher than the market yield.

Applying STW to different markets can guide an investor in making decisions that can optimize the value of their portfolio. For example, if the STW between stocks and US Treasuries were high, say over 40%, then the investor might consider skewing their portfolio weight in favor of stocks. As is the case with most market reactive measures, STW will be highly dependent on variables such as short or long term interest rates, investor confidence, and other similar measures.

## Special considerations

Figuring out which is the lowest can be done quickly by understanding a few tips. First, if a bond is callable, there will be a YTC. Otherwise, YTM is de facto the lowest yield and will be used for STW. However, if the bond is callable and trades at a premium to the face value, the YTC will be lower than YTM.

Callable bonds are most likely called when interest rates are low. The yield on callable bonds is generally higher because of the risk that investors will have to reinvest the proceeds at a lower interest rate, also known as reinvestment risk.

## Example of worst-case propagation (STW)

Suppose a callable high yield bond is issued with a 10-year maturity and a five-year no-call protection clause (i.e. the issuer is not allowed to redeem the bond in every five years). After three years, the interest rates are lower, which means that it is possible for the issuer to call the bond in order to refinance at a lower coupon rate.

The bond held by the investor now trades at a premium. The YTC is compared to the yield on a two-year Treasury bill: five years of no-call protection minus the three years that have passed. The difference is the STW, expressed in basis points.