## What is Yield to Worst (YTW)?

The yield to worst (YTW) can be defined as the minimum yield that can be received on a bond assuming the issuer doesn’t default on any of its payments. YTW particularly makes sense for bonds where the issuer exercises its options like calls, prepayments or sinking funds.

It is estimated by taking all possible scenarios under consideration where the bonds may be retired before maturity. A YTW estimate gives the investors a fair idea of how their future income may be impacted in the worst scenario and what they can do to hedge any such potential risks.

### Yield to Worst (YTW) Calculation

Theoretically, Formula to calculate yield to worst has two broad components:

- YTW itself is one of the three yield metrics used in the bond market, yield-to-maturity and yield to call being the other two. Yield-to-maturity is the rate of return received assuming the bond is held until expiration and the issuer doesn’t default while yield to call is the rate of return realized if the bond is called by the issuer at the call date.
- In the case of callable bonds, YTW is the lower of the yield-to-call and yield-to-maturity.

### Example of Yield to Worst (YTW) Calculation

Assuming you hold a callable bond issued by ABC Inc. The bond has an annual coupon rate of 6%, $1,000 par value, and maturity of 4 years. The bond is currently priced at $1,020 and has a 2-year embedded call option.

**#1 – Calculating Yield to Maturity (YTM)**

Price of bond = Coupon_{1}/ (1+y) ^{1} + Coupon_{2}/ (1+y)^{2} + Coupon_{3}/ (1+y)^{3} + Coupon_{4}/ (1+y)^{4 }

1020 = 60/(1+y) ^{1 }+ 60/(1+y)^{2 }+ 60/(1+y)^{3} +60/(1+y)^{4}

Value of y can be calculated using a financial calculator.

Inputting N=4, PMT=60, PV= -1020. CPT àI/Y

- Where N= no. of periods
- PMT= Payment per period
- PV= Present value (always negative since it is the outflow of money i.e. current price that the investor will pay now to buy the bond)
- CPT= Calculate (Command was given to a financial calculator to derive a solution)
- I/Y= YTM

Hence, the value returned by a financial calculator, in this case, will be 5.43%.

**#2 – Calculating Yield to Call (YTC)**

Calculating YTC the same way we calculated YTM but by **inputting N=2** (since the bond is callable in two years,

YTC = 4.93%.

Therefore, the worst-case scenario is that the company will call the bond in two years, and you will realize a yield of 4.93% instead of 5.43%.

**Since YTW is lower of the two; it will be 4.93% in this case.**

**Note:**

- If the call price is different than par value, the current price will be substituted by call price.
- If a bond has more than one call date, YTW is the lowest of YTC and YTM calculated for each call date.
- For a non-callable bond, YTW is essentially the same as YTM.

### Advantages

Callable bonds favor the issuer rather than the investor. In the event of declining interest rates, companies often choose to exercise their call option so that they can refinance their debt at lower rates, leaving the investor to deal with reinvestment risk.

- YTW calculation is very crucial for investors since it gives them a balanced idea of what to expect in the future.
- YTW calculation is especially important in high yield markets where a bond is trading above its face value.
- This metric may make some investors wary of callable bonds but there is no negative aspect to this measure. Investors are often adequately compensated for the call ability features embedded in the bond and YTW makes then more prepared to face the uncertain future.

### Limitations

- YTW calculations are irrelevant for zero-coupon bonds since there are no periodic coupon payments and are mostly sold at deep discounts to par value.
- No matter how clearly the YTW is stated, there is no assurance that the actual cash flows will be similar to the calculation of the one during YTW estimation.

### Conclusion

YTW evolved as a necessary upgrade over YTM and YTC but its usage remains restricted due to a number of reasons including the uncertain cash flows over longer durations. It is however still considered as a useful measure of credit risk and YTWs of all bonds in one portfolio can be utilized to present a unified picture for hedging purposes.

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