# How the Shape of the Yield Curve Affects the Value of Embedder Bonds

The value of a callable or putable bond is also affected by changes in the level and shape of the yield curve.

### Callable bond

#### The Level Effect

As interest rates decrease, the value of a straight bond increases. However, part of this increase is offset by the increase in the value of the call option.

This means that the value of the callable bond rises less quickly than the value of a comparable straight bond, putting a ceiling on the investor’s upside potential.

#### The Shape of the Yield Curve

The value of a call option increases while that of a callable bond decreases as the yield curve shifts from an upward-sloping shape to a flat or inverted shape.

In an upward sloping yield curve, the one-period forward rates rise, and opportunities to call the bond decrease. When the yield curve flattens or inverts, the forward rates become lower, increasing the chances to call.

### Putable bond

#### The Level Effect

As interest rates rise, the value of a straight bond falls, but the decline is partially offset by an increase in the value of the put option. Thus, the value of the putable bond falls less rapidly than the value of a comparable straight bond.

Put options are used to hedge against rising interest rates for investors.

#### The Shape of the Yield Curve

Holding all else constant, the value of a put option declines as the yield curve shifts from an upward sloping shape to a flat to inverted shape, and the value of the putable bond falls.

The one-period forward rates are high when the yield curve is upward sloping, creating more opportunities for investors to put the bond. The opportunities to put decline as the yield curve flattens or inverts.

## Question

All else being equal, as the yield curve flattens or inverts, the value of the put option in putable bonds most likely:

1. Decreases.
2. Increases.
3. Remains the same.

#### Solution

The correct answer is A.

The value of the put option decreases as the yield curve moves from being upward sloping, to flat, to inverted because the opportunities to put the bond decline.

Reading 30: Valuation and Analysis of Bonds with Embedded Options

LOS 30 (e) Explain how changes in the level and shape of the yield curve affect the value of a callable or putable bond.

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