Immunization

Immunization

Obligaton = FILL IN.
Mkt interest rate = FILL IN (Decimal).
Obligation due in FILL IN. years

PV(Obligation) = FILL IN.

1. To immunize, need to find the duration of the asset and liability, equate them,
and solve for optimal weights of investment in the zeros and in the perpetuity.

Duration of obligation = FILL IN. years
Duration of zeros = FILL IN. years
Duration of perpetuity = (1+r)/r = FILL IN. years

Let w be the percentage of funds invested in the zeros.
Then (1-w) = percentage of funds invested in the perpetuity.

Setting D(assets) = D(liabilities) yields WRITE FORUMULA WITH NUMBERS.

The above equation yields w = FILL IN.
Also, 1-w = FILL IN.

Therefore, invest FILL IN. in zeros
and FILL IN. in the perpetuity.

2. One year has passed, and market rate is still = FILL IN AS DECIMAL.

Is obligation still fully funded? To answer this question,
need to see if amounts invested in assets still equal the new PV(obligation).

PV(obligation) is now FILL IN.

PV(zeros) = FILL IN.
PV(perpetuity) = FILL IN.
Perpetuity has paid coupon = FILL IN.
So, total PV(asset) is now = FILL IN.

Is obligation still fully funded? FILL IN ANSWER.

Is position still immunized? Need to see if weights need to be changed
by recalculating D(assets) and D(liability), equating them, and solving for w.

D(liability) now = FILL IN. years.
D(zeros) now = FILL IN. years.
D(perpetuity) = FILL IN. years.

So, setting D(asset) = D(liability) yields WRITE FORUMULA WITH NUMBERS.
This equation yields w = FILL IN. , so (1-w) = FILL IN.

Based on w and 1-w, is the position still immunized? ANSWER HERE.

Therefore, to re-immunize our portfolio, invest
FILL IN. in zeros and FILL IN. in perpetuity.