Question

1)If spot rates are 3.1% for one year, 3.5% for two years, and 3.8% for three years and 4.0% for four years, the price of a $100 face value, 4-year, annual-pay bond with a coupon rate of 5% is equal to:

2)

The following spot and forward rates are provided:

Current 1-year spot rate is 5.5%.

One-year forward rate one year from today is 6.63%.

One-year forward rate two years from today is 8.18%.

The value of a 3-year, 6% annual-pay, $100 par value bond is equal to:

3)The 3-year spot rate is 8.75%, and the 2-year spot rate is 8.65%. What is the 1- year forward rate two years from today

4)

Bond	Coupon Rate	Maturity (years)
A	6%	9
B	6%	6
C	8%	6

All three bonds are currently trading at par value.

Which bond will most likely experience the greatest percentage change in price and which one most likely experience the lowest percentage change if the market discount rates for all three bonds increase by 1%? Provide explanations.

Answer 1

1)

1 year spot rate = 3.1%

2 year spot rate = 3.5%

3 year spot rate = 3.8%

4 year spot rate = 4%

Coupon rate = 5%

Face Value = 100

Each coupon payment are discounted by their subsequent Spot Rates. At the end of 4th year Coupon and Fave Value is discounted back to present by Spot rate of 4th year.

2)

Spot rate of 1st year is given as 5.5% and to bring out Spot rate for 2nd andd 3rd year, we need to utilize One-year forward rate one year for 2nd year spot rate from now and One-year forward rate two years from now for 3rd year spot rate.

2nd year spot rate :

One-year forward rate one year is written as "1y1y"

%

FR1,1 = One-year forward rate one year from now

SR1 = 1st year Spot rate

SR2 = 2nd year Spot rate

One-year forward rate two years from now is written as "2y1y"

%

3)

1- year forward rate two years from today is written as "2y1"

%

So, 1- year forward rate two years from today is 8.95%.

4)

Change in Price by Change in Interest rate is refer as Modified Duration.

We need to calculate Modified Duration of each bond with increase in Interest Rate by 1%.

Modified Duration of Bond A =  

PV- = Present Value of Bond A when Interest rate goes down by 1% = 107.11

PV+ = Present Value of Bond A when Interest rate goes up by 1% = 93.48

Change in Interest rate [ 1%= 100 basis point = 100/ 10000 = 0.01]

PV0 = Current Value of Bond = 100

Modified Duration of Bond B =  

PV- = Present Value of Bond A when Interest rate goes down by 1% = 105.07

PV+ = Present Value of Bond A when Interest rate goes up by 1% = 95.23

Change in Interest rate [ 1%= 100 basis point = 100/ 10000 = 0.01]

PV0 = Current Value of Bond = 100

Modified Duration of Bond C =   

PV- = Present Value of Bond A when Interest rate goes down by 1% = 95.23

PV+ = Present Value of Bond A when Interest rate goes up by 1% = 86.54

Change in Interest rate [ 1%= 100 basis point = 100/ 10000 = 0.01]

PV0 = Current Value of Bond = 100

Which bond will most likely experience the greatest percentage change in price?

Sol : Bond with Highest Modified Duration will experience the greatest percentage change in price. So, Bond A has a Modified Duration of 6.81 as compared to Bond B (4.92) and Bond C (4.35).

Which one most likely experience the lowest percentage change?

Sol : Bond with Lowest Modified Duration will experience the lowest percentage change. So, Bond C has a Modified Duration of 4.35 as compared to Bond A (6.81) and Bond B (4.92).