Consider the following yields att=0

t=0, expressed in percentage points:

T

y(0,T)

1

6.00

2

5.80

3

5.62

4

5.46

5

5.33

T

y(0,T)

1

6.00

2

5.80

3

5.62

4

5.46

5

5.33

Given is a bond portfolio with the following cash flows in 1,...,5 years:

T

Cash flow

1

6

2

8

3

106

4

7

5

9

T

Cashflow

1

6

2

8

3

106

4

7

5

9

Suppose there are two coupon bonds in the market that serve as hedging instruments: Bond 1 is a 2-year coupon bond with annual coupons of 4%, and Bond 2 is a 4-year coupon bond with annual coupons of 10%. Both bonds have principal 100. Answer the following four questions:

a) Implement a duration hedge of the bond portfolio using Bond 2. How many units of Bond 2 do you need? Round your answer to 2 decimal places.

b) Suppose the yield curve moves up by 2 percentage points for all maturities. Calculate the relative price change of the duration hedged bond portfolio. Express your answer in basis points and round to 2 decimal places.

c) Implement a convexity hedge of the bond portfolio using Bond 1 and Bond 2. How many units of Bond 2 do you need? Round your answer to 2 decimal places.

d) Suppose the yield curve moves up by 2 percentage points for all maturities. Calculate the relative price change of the convexity hedged bond portfolio. Express your answer in basis points and round to 2 decimal places.