11、Using the following interest rate tree of semiannual interest rates what is the value of an option free semiannual bond that has one year remaining to maturity and has a 6 percent coupon rate?

         6.53%

6.30%

         5.67%

A) 97.53.

B) 99.81.

C) 98.52.

D) 100.16.

The correct answer is B

The option-free bond price tree is as follows:

 100.00

A ==> 99.74

99.81  100.00

 100.16 

 100.00

As an example, the price at node A is obtained as follows:

PriceA = (prob * (Pup + coupon/2) + prob * (Pdown + coupon/2))/(1 + rate/2) = (0.5 * (100 + 3) + 0.5 * (100 + 3))/(1 + 0.0653/2) = 99.74. The bond values at the other nodes are obtained in the same way.

The calculation for node 0 or time 0 is

0.5[(99.74 + 3)/(1+ .063/2) + (100.16 + 3)/(1 + .063/2)] =

0.5 (99.60252 + 100.00969) = 99.80611

AIM 7: Explain the impact of embedded options on a fixed-income security’s price.

1、Mortgages are subject to prepayment when interest rates fall. This results in duration extending when interest rates rise, but shortening when interest rates fall. This characteristic is called:

A) positive convexity.

B) negative duration.

C) negative convexity. 

D) reverse duration.

The correct answer is C

An instrument that declines more in value when interest rates rise than it increases when interest rates fall is said to have negative convexity. Mortgage-backed securities have this characteristic because of the mortgagor’s option to prepay.

2、With respect to bond investing, reinvestment risk is a very important component of what other type of risk?

A) Default risk.

B) Liquidity risk.

C) Call risk.

D) Downgrade risk.

The correct answer is C

Call risk is composed of three components: the unpredictability of the cash flows, the compression of the bond’s price, and the high probability that when the bond is called the investor will be faced with less attractive investment opportunities. This latter risk is reinvestment risk. Reinvestment risk is not a directly related to any of the other choices.

3、If a put feature expires on a bond so that it becomes option-free, then the curve depicting the price and yield relationship of the bond will become:

A) more convex. 

B) a straight line. 

C) less convex. 

D) inversely convex. 

 The correct answer is C

When the option expires, the prices at the lower end of the curve will become lower. This will make the curve less convex.