Question

Answer the questions for the bond below, which pays interests semi-annually. The modified duration is 3.9944 years and convexity measure is 19.7636 years. (Assume par value is $1000). Coupon rate: 9%, current yield to maturity: 8%, maturity: 5 years. (1) Calculate the price value of a basis point if the new yield to maturity becomes 8.01% (2) Calculate the actual price of the bond for a 50-basis-point increase in interest rates (yield changes from 8% to 8.5%) (3) Using duration, estimate the approximate price of the bond for a 50-basis point increase in interest rates (yield changes from 8% to 8.5%) (4) Using both duration and convexity measure, estimate the approximate price of the bond for a 50-basis-point increase in interest rates (yield changes from 8% to 8.5%) (5) Compare your results in (3) and (4) and explain which is closer to the actual price in (2)

Answer 1

The percentage change in Price of a bond is given by:

% Price change = [-duration * (change in yield) ] + [1/2 * Convexity * (change in yield)² ]

(The above formula will be used

Part 1

As the new yield is increasing from 8.0% to 8.01%, this 1 basis point (bps) change in yield.

Using the given values in the above equation:

% Price change = [-3.9944 * 0.0001 ] + [1/2 * 19.7636 * (0.0001)² ]

• % price change = - 0.0004 or -0.04%.

Therefore, the price of the bond will decrease by 0.04%.

Part 2

% Price change = [-3.9944 * 0.0005] + [1/2 * 19.7636 * (0.0005)² ]

• % price change = - 0.002 or -0.2%.

Therefore, the price of the bond will decrease by 0.2%.

(Note: The bond price is not given in the question, so multiply -0.2% by the bond price, you will get the answer).

Part 3

Using only the duration measure,

% Price change = [-duration * (change in yield) ]

% Price change = [-3.9944 * 0.0005]

• % price change = - 0.001997 or -0.1997%

Therefore, the price of the bond will decrease by 0.1997%.

(Note: The other parts can’t be answered as price of the bond is not provided)