Reading 66: Introduction to the Measurement of Interest Rate market, change, selling, interest, 2010

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LOS b: Demonstrate the price volatility characteristics for option-free, callable, prepayable, and putable bonds when interest rates change.

With market interest rates at 6%, an analyst observes a 5-year, 5% coupon, $1,000 par value callable bond selling for $950. At the same time the analyst observes a non-callable bond, identical in all other respects to the callable bond, selling for $980. The analyst should estimate that the value of the call option on the callable bond is closest to:

A) $50.

B) $20.

C) $30.

The difference in price between the two bonds is the value of the option: $980 ? $950 = $30.

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In comparing the price volatility of putable bonds to that of option-free bonds, a putable bond will have:

A) less price volatility at higher yields.

B) less price volatility at low yields.

C) more price volatility at higher yields.

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The only true statement is that putable bonds will have less price volatility at higher yields. At higher yields the put becomes more valuable and reduces the decline in price of the putable bond relative to the option-free bond. On the other hand, when yields are low, the put option has little or no value and the putable bond will behave much like an option-free bond. Therefore at low yields a putable bond will not have more price volatility nor will it have less price volatility than a similar option-free bond.

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If interest rates fall, the:

A) callable bond's price rises more slowly than that of a noncallable but otherwise identical bond.

B) value of call option embedded in the callable bond falls.

C) callable bond's price rises faster than that of a noncallable but otherwise identical bond.

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When a callable bond's yield falls to a certain point, when the yields fall the price will increase at a decreasing rate.  Compare this to a noncallable bond where, as the yield falls the price rises at an increasing rate. 

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At a market rate of 7%, a $1,000 callable par value bond is priced at $910, while a similar bond that is non-callable is priced at $960. What is the value of the embedded call option?

A) $50.

B) $40.

C) $30.

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The value of the embedded call option is simply stated as: 

value of the straight bond component – callable bond value = value of embedded call option.

$960 – $910 = $50

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Consider the following two statements about putable bonds:

Statement #1: As yields fall, the price of putable bonds will rise less quickly than similar option-free bonds (beyond a critical point) due to the decrease in value of the embedded put option.

Statement #2: As yields rise, the price of putable bonds will fall more quickly than similar option-free bonds (beyond a critical point) due to the increase in value of the embedded put option.

You should:

A) disagree with both statements.

B) agree with both statements.

C) agree with only one statement.

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Both statements are false. As yields fall, the value of the embedded put option in a putable bond decreases and (beyond a critical point) the putable bond behaves much the same as an option-free bond. As yields rise, the value of the embedded put option increases and (beyond a critical point) the putable bond decreases in value less quickly than a similar option-free bond.

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An investor gathered the following information about two 7% annual-pay, option-free bonds:

• Bond R has 4 years to maturity and is priced to yield 6%
• Bond S has 7 years to maturity and is priced to yield 6%
• Both bonds have a par value of $1,000.

Given a 50 basis point parallel upward shift in interest rates, what is the value of the two-bond portfolio?

A) $2,044.

B) $2,030.

C) $2,086.

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Given the shift in interest rates, Bond R has a new value of $1,017 (N = 4; PMT = 70; FV = 1,000; I/Y = 6.50%; CPT → PV = 1,017). Bond S’s new value is $1,027 (N = 7; PMT = 70; FV = 1,000; I/Y = 6.50%; CPT → PV = 1,027). After the increase in interest rates, the new value of the two-bond portfolio is $2,044 (1,017 + 1,027).

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Which of the following bonds experience the greatest precentage price change when the market interest rates rise?

A) A high coupon, long maturity bond.

B) A low coupon, long maturity bond.

C) A low coupon, short maturity bond.

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There are three features that determine the magnitude of the bond price volatility:

1. The lower the coupon, the greater the bond price volatility.
2. The longer the term to maturity, the greater the price volatility.
3. The lower the initial yield, the greater the price volatility.

According to these three features the greatest price change will come from the bond with a low coupon and long maturity.

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Which of the following bonds is likely to exhibit the greatest volatility due to interest rate changes? A bond with a:

A) high coupon and a long maturity.

B) low coupon and a short maturity.

C) low coupon and a long maturity.

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There are three features that determine the magnitude of the bond price volatility:

(1) The lower the coupon, the greater the bond price volatility.
(2) The longer the term to maturity, the greater the price volatility.
(3) The lower the initial yield, the greater the price volatility.

So the bond with a low coupon and long maturity will have the greatest price volatility.

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A $1,000 face, 10-year, 8.00% semi-annual coupon, option-free bond is issued at par (market rates are thus 8.00%). Given that the bond price decreased 10.03% when market rates increased 150 basis points (bp), which of the following statements is TRUE? If market yields:

A) decrease by 150bp, the bond's price will decrease by more than 10.03%.

B) decrease by 150bp, the bond's price will increase by 10.03%.

C) decrease by 150bp, the bond's price will increase by more than 10.03%.

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All other choices are false because of positive convexity - bond prices rise faster than they fall. Positive convexity applies to both dollar and percentage price changes. For any given absolute change in yield, the increase in price will be more than the decrease in price for a fixed-coupon, noncallable bond. As yields increase, bond prices fall, and the price curve gets flatter, and changes in yield have a smaller effect on bond prices. As yields decrease, bond prices rise, and the price curve gets steeper, and changes in yield have a larger effect on bond prices. Here, for an absolute 150bp change, the price increase would be more than the price decrease. For a 100bp increase, the price decrease would be less than that for a 150bp increase.