## Callable Bonds 101

This is a crash course on everything you need to know about callable bonds for the CFA Level 1 exam.

**Bond Basics**

As you know, bond prices have an inverse relationship with interest rates.

- If interest rates rise, bond prices fall ( r ↑, P ↓)
- If interest rates fall, then bond prices go up ( r ↓, P ↑)

This inverse relationship occurs because the present value of all the remaining payments decreases as the interest rate increases.

Thus as a bond investor you face two main types of interest rate risk—price risk and reinvestment risk.

** Price risk, **or

*interest rate risk*, is the decrease (or increase) in bond prices caused by a rise (fall) in interest rates. It tell us how much the value of the portfolio fluctuates. The longer the duration of a bond the greater its price volatility. In other words a change in interest rates has a greater effect on the price of a longer duration bond than a shorter one.

** Reinvestment risk** refers to the increase (decrease) in cash flow or investment income caused by a rise (fall) in interest rates. If interest rates go up, any new money you invest in a bond will have a higher coupon or cash payment.

An investor in a callable bond faces both less potential price appreciation if interest rates decline and much more reinvestment risk.

## Defining Callable Bonds

*Always remember embedded options benefit the party that has the right to exercise them.*

Callable bonds give the *issuer *the right (but not the obligation) to buy the bond at a specified call price. The embedded call option is beneficial to an issuer as it allows them to take advantage of either a fall in market interest rates or an improvement in their creditworthiness.

**Callable bonds and Yield**

Because of the value of being long the call option an issuer that is selling a bond with an embedded call option will have to offer a higher coupon rate to entice investors to purchase it. Otherwise they'll just purchase the other company's option-free bond and not be exposed to so much reinvestment risk.

It also means we calculate the yield for callable bonds slightly differently using one of two measures:

**Yield-to-first-call:**Calculated the same as YTM except instead of using par value and the stated maturity, we use the call price and first call date**Yield-to-worst:**You can calculate price for a callable bond at every possible call date. The yield-to-worst is the lowest yielding / worst potential return result.

This exact calculation is unlikely to be extensively tested on the CFA L1 exam.

**How does the presence of a call option change a bond's payouts? **

The price of a callable bond is always lower than the price of an identical non-callable bond. The difference between the two prices is the value of the embedded call option. In other words:

The presence of a call option also impacts the way a callable bond reacts to changes in interest rates:

- If
**r ↓,****P**↑: The incentive for the issuer to call the bond at par increases. Therefore, the price of a callable bond will not rise as quickly as the price of a on-callable bond. - If
**r****↑, P****↓,**the price of a callable bond will not fall as much (or as steeply) as that of a non-callable bond because the call option will become less valuable (and the bondholder is short the call option)

It looks like this (and this is a must understand graph for any level of the CFA exams, including Level 1):

Graphically, you can see that how much of an impact the call has on bond prices varies based on the relationship of interest rates relative to the coupon rates.

**If interest rates are HIGH relative to the coupon rate:**

- The issuer is unlikely to call the bond and the option value is relatively worthless
- The bond will perform very similar to a non-callable bond
- When this is true using modified duration is appropriate

**If interest rates are LOW relative to the coupon rate:**

- The issuer is more likely to exercise the call option and refinance at lower rates (the call option increases in value, and the effective duration of the bond falls)
- The price of the callable bond will not increase as much as a non-callable bond. It suffers from what is known as price compression.
- When yields are very low and the call is in the money, callable bonds will exhibit
*negative convexity.*Negative convexity means that as market yields decrease, duration decreases as well.[1]

** Key takeaway:** Callable bonds will underperform when interest rates fall relative to the coupon rate, and will perform similar to an option-free bond in a period of rising interest rates.

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[1] Visually, this means the shape of the yield curve will be concave (downward sloping) for the yields/price where the bond is in the money.