[original post removed]
This sounds like a Level III question. Are you sure that you posted it in the correct forum? This is the Level I forum.
Quite rusty but will have a go…
(note - as Magician said this looks to be out of scope for L1, I have replied in L3 and putting the same comment hear for anyone curious or want further idea / discussion on it)
Create a potfolio of the two assets such that:
- PV of Asset Portfolio (PVA) = PV Liabilities (PVL)
PVL can be immediately calculated from the data given. For PVA we can calculate the current price of each of the 5 & 10 - year ZCBs, and then assume X units of the 5-Year ZCB & Y units of the 10-Year ZCB are bought we can form a simple linear equation that equates to the PVL (which we know).
- Duration of the Asset Porfolio = Duration of Liabilities
Similarly, as with the PVs, we can do the same for the Durations and get a second linear equation. Then we can solve for X & Y based on the two linear equations. I did this quickly in a spreadsheet and got the following (by no mean claiming this is correct becasue did it really quickly): PVL = $45,081 Price of 5-Year ZCB= $81.9 Price of 10-Year ZCB = $67.0 X = 316 Y = 286
I would suppose this is a similar idea as above but:
- We have another unknown, i.e. “n”.
- So since no values are being asked for I would think its more of a qualitative question to explain the process and importantly exlain Redington Immunization conditions … and setting up systems of linear equations (3 in this case)…The third equation comes in because of the next bullet point.
- …the condition that: Convexity of Asset Portfolio (CA) > Convexity of Liabilities (CL).
There may be more …?
I think this is solving the system of three equations to calculate 3 unknowns X, Y, n ? …and more? Hope I am making sense and you find it useful.