Question

In: Finance

Consider the following information and assume that both bonds pay interest semi-annually, so that below are...

Consider the following information and assume that both bonds pay interest semi-annually, so
that below are semiannual bond equivalent yields.

	A
Coupon	8
YTM	8
Maturity	2
Par	100
Price	100

1. Calculate the Macaulay duration of bond A.

2. Calculate the modified duration of bond A.

3. Compute the approximate modified duration for bonds A B using the shortcut formula by changing yields by 20 basis points and compare your answers with those calculated in the last question. Hint: calculate the price of the bond when interest rate increase by 20 bsp and decrease by 20 bsp. Then plug in the formula we have in class.

4. Compute the approximate convexity measure for both bonds A (use 10 bsp as the change in interest rate) Hint: calculate the price of the bond when interest rate increase by 10 bsp and decrease by 10 bsp. Then plug in the formula we have in class.

Round to 4 decimal places.

Expert Solution

Solution:

1. Given that Coupon payment, = 100*0.08/2 = $40, Number of years, = 2*2 = 4, Price, = 100 and Par value, = 100

Period (n)	C	PV @ 4%	C*PV	CPVn
1	4	1/1.04 = 0.9615	3.8462	3.8462
2	4	1/1.04^2 = 0.9246	3.6982	7.3965
3	4	1/1.04^3 = 0.8890	3.5560	10.6680
4	104	1/1.04^4 = 0.8548	88.900	355.599
Total			100	377.5091

Macaulay duration =

Macaulay duration = 3.77509 years

Macaulay duration (half years) = 3.77509/2 = 1.8875 year

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b. The modified duration is calculated using the formula:-

Modified duration = 1.81495 year

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c. First, we increase the bond yield from 8% to 8.20%. The price of bond, with yield, = 8.20% is

= $99.6379

Now, we decrease the bond yield from 8% to 7.80%, The price of bond, with yield, = 7.80% is

= $100.3638

The formula for approximate duration is given as follows

Approximate duration =

Approximate duration = 1.81495 years

------------------------------------------------------------------------------------------------------------------------------

d. The formula for convexity is given below

= 125,000 (0.145196) - 16,438.542 + 0

= 17.10935

Convexity (in years) = 17.1093/4 = 4.2773 years

jeff jeffy answered 7 months ago

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