Question

Bond Return and Convexity. Consider a self-financed convexity trade.

Three zero couple bonds:

i. 2Y zero at 1.60%; ii. 10Y zero at 1.85%; iii. 30Y zero at 2.30%

a)What is the total PnL for a 10 bps upward parallel movement of yield curve?

Answer 1

We find the present value of bond and value of bond when interest rate increases by 10 bps

Bond valuation is the determination of the fair price of a bond. As with any security or capital investment, the expected value of a bond is the present value of the stream of cash flows it is expected to generate. Hence, the value of a bond is obtained by discounting the bond's expected cash flows to the present using an appropriate discount rate

1) 2 Year ZCB @ 1.6%

N = 2

I.Y = 1.6

FV = 100

PMT = 0

PV = 96.88

When I.Y Increases to 1.7%

N = 2

I.Y = 1.7

FV = 100

PMT = 0

PV = 96.68

% Change = (96.68 / 96.88 )- 1 = -0.20%

b) 10 Year ZCB @ 1.85%

N = 10

I.Y = 1.85

FV = 100

PMT = 0

PV = 83.25

When I.Y Increases to 1.95%

N = 10

I.Y = 1.95

FV = 100

PMT = 0

PV = 82.44

% Change = (82.44 / 83.25)- 1 = -0.97%

c) 30 Year ZCB @ 2.30%

N = 30

I.Y = 2.30

FV = 100

PMT = 0

PV = 50.55

When I.Y Increases to 2.40%

N = 30

I.Y = 2.40

FV = 100

PMT = 0

PV = 49.09

% Change = (49.09/ 50.55)- 1 = -2.89%

What do we observe?

As interest rate increases, prices of bond decreases.

Also Bonds with higher maturity are more sensitive to change in interest rate as Bond 3 moves the most by 2.89% compared to Bond 1 which moved by 0.20%