Immunization of a single obligation

CFA Level III Fixed Income
#1

Schweser Bk 3 LOSE 20f, Pg 21

I have given the text and my questions/understanding gaps on the text

· If portfolio duration is less than liability duration, the portfolio is exposed to reinvestment risk. If interest rates are decreasing, the losses from reinvested coupon and principal payments would more than offset any gains from appreciation in the value of outstanding bonds. Under this scenario, the cash :flows generated from assets would be insufficient to meet the targeted obligation.

Q1. How can we know that the losses from reinvested coupon and principal payment would be more than the gains from the appreciation in the values of bonds in the portfolio?

Q2. The above does not discuss how the changes in the interest would cause the impact on the liability flows and its contribution to the reinvestment risk. What is the impact of decreasing interest rates on the liability?

• If portfolio duration is greater than liability duration, the portfolio is exposed to price risk. If interest rates are increasing, this would indicate that the bJsses from the market value of outstanding bonds would more than offset any gains from the additional revenue being generated on reinvested principal and coupon payments. Under this scenario, the cash :flows generated from assets would be insufficient to meet the targeted obligation

Q3. How can we know that the losses from market value of outstanding bonds would more than offset any gains from the additional revenue being generated on reinvested principal and coupon payments?

Q4. The above does not discuss how the changes in the interest would cause the impact on the liability flows and its contribution to the reinvestment risk. What is the impact of decreasing interest rates on the liability?

Kindly help.

Thank you

#2

P=100; L=100; PD=10; LD=20; Surplus=0 Int rates decrease1%: P=110; L=120 Surplus=-10

Q1. How can we know that the losses from reinvested coupon and principal payment would be more than the gains from the appreciation in the values of bonds in the portfolio?

The duration has the information contained in it.

Q2. The above does not discuss how the changes in the interest would cause the impact on the liability flows and its contribution to the reinvestment risk. What is the impact of decreasing interest rates on the liability?

The duration has the information contained in it.

P=100; L=100; PD=20; LD=10; Surplus=0 Int rates increase 1%: P=80; L=90 Surplus=-10

Ditto

#3

Hi Ov25,

Thank you for the response.

I am struggling to comprehend. Propabably a bit more detail explanation will help close the understanding gap.

Can you please refer to me any material?

Thank you

#4

Duration 10 mean 1% drop (raise) in interest rates is going to raise (decrease) 10% value in the portfolio

PD = Portfolio duration LD = Liabilitiy Duration; P=Portfolio Value L=Liability Value

Situation 1:

P=100; L=100; PD=10; LD=20; Surplus=0 For ex Int rates decrease1%: > portfolio inc 10% so Portfoli = 110 P=110; L=120 Surplus=-10

Situation 2:

P=100; L=100; PD=20; LD=10; Surplus=0 Int rates increase 1%: P=80; L=90 Surplus=-10

See if this is better

#5

ov25,

Thank you now I can see how the value of the assets and liabiities are changing.

Now my struggle is how do I identify which is a price risk and and reinvestment risk.

As these both are the components of the interest rate risk.

Now when the interest rates change, one of these two will have a higher bearing on the surplus.

Highly appreciate your time and effort.

Thank you