## What is Yield to Call?

Yield to call is the return on investment for a fixed income holder if the underlying security i.e. Callable Bond is held until the pre-determined call date and not the maturity date. The concept of yield to call is something that every fixed-income investor will be aware of. What P/E ratio is to equity, expiry for options, yield to call is to Bonds.

Understandably, this call date is much before the maturity date of the underlying instrument. Not every fixed-income instrument has the concept of call date. Only the bonds that are callable have this feature. Since these bonds provide an added feature to investors of redeeming the bond at a call date (at a pre-decided call price), they relatively demand more premium.

### Components of Yield to Call

To summarize the yield to call calculations are significant because it helps investor gauge the return on investments, he will be getting assuming the following factors

- The bond is held until the pre-decided call date and not the maturity date
- Bond’s purchase price is assumed to be the current market price instead of the Bond face value
- Even though there can be multiple call dates, for calculation purposes it is assumed that bond is calculated on the earliest possible date.

### Yield to Call Formula

The formula for yield to call is calculated through an iterative process and is not a direct formula even though it may look like one.

Mathematically, yield to call is calculated as :

**Yield to Call Formula = (C/2) * {(1- ( 1 + YTC/2) ^{-2t}) / (YTC/2)} + (CP/1 + YTC/2)^{2t})**

- B = Current Price of the Bonds
- C = Coupon payment paid out annually
- CP = Call price
- T= number of years pending until the call date.

As explained earlier, Yield to call is not calculated by just substituting values directly. In fact, an iterative process needs to be carried out. Fortunately, in the present era, we have computer programs to compute YTC by carrying out the iterations.

### Yield to Call Calculation

Let’s take an example of a callable bond that has a current face value of £ 1,000. Assume that this Bond pays a coupon of 10% on a semi-annual basis and has a maturity of 15 years. This bond can be callable at a price of £ 1100 in five years. The current price of the bond is £ 1200. Let’s calculate the yield to call of this callable bond.

Let us list down all the inputs that we have.

Since we are calculating yield to call, we are not concerned about the maturity period of 5 years. What matters is the time period of 5 years after which the bond can be called.

Substituting these values in the equation :

£1200 = (£100/2) * {(1 – ( 1 + YTC/2)^{(-2*5)})/(YTC/2)} + ( £ 1000/1 + YTC/2)^{(2*5)}

These values can be fed into a scientific calculator or computer software. Else it can be calculated through an iterative process if done manually. The result should be approx. 7.90 %. This effectively means even though the coupon promised is 10%, if the bond is called before maturity the effective return that an investor can expect is 7.9%.

### Important Points of Note

Although yield to maturity (YTM) is a much popular metric used to calculate the rate of returns on the bond, for callable bonds this calculation becomes a bit complex and might be misleading. The reason being callable bonds provide an added feature of a bond being called by the issuer as per his convenience. Naturally, the issue will look to refinance only when interest rates are low so that he can refinance the principal and reduce its cost of debt. Hence for a prudent investor, it makes sense to calculate both the parameters and be prepared for the worst case.

- Yield to call (YTC) is calculated as explained above based on the available callable dates.
- Yield to maturity (YTM) is calculated assuming the bond is never called in its lifetime and is held till maturity.

**Some Thumb Rules**

**YTC > YTM:**it’s in better interests of the investor to opt for the redemption.**YTM > YTC:**it’s advantageous to hold the bod till the maturity date.

- Yield to call calculation focuses on three aspects of return for an investor. These sources of potential return are coupon payments, capital gains and amount reinvested. The whole calculation is on the assumptions around these three important attributes of fixed income securities
- However, most analysts consider the assumption that the investor can reinvest the coupon payments at the same or better rate to be inappropriate. Also assuming that the investor will hold the bond until the call date is also faulty and can lead to misleading results if used for investment calculations.
- The yield of call for any callable bond at any given price until the maturity of the bonds will always be less than yield to maturity. This is because of the very provision that the bond can be called leads to an upper cap on bonds price appreciation.
- Hence if the interest rates fall the price of a callable bond will rise but only to some extent compared to a vanilla bond that has no upside potential. The reason is simple that the issuer will take care of the underlying security and will call it only when it can reissue at a lesser rate of interest. This is quite logical as bonds should be called only interest rates fall and then only the refinancing will make sense.

### Conclusion

Yield to call is one of the prudent ways for an investor to be prepared for the interest rate volatility. Although it is calculated based on the first call date, many investors calculate the yield on all dates when the issued security can be called off. Based on that, they decide the worst outcome possible and this derived yield is called as yield to the worst calculation.

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