Question

A payment of $5,000 is due in 9 years. To cover this cost, two assets are acquired. The first asset is expected to return $Y in X years, where X<9. The second asset is expected to return $3,000 in 12 years. The annual effective rate of interest is 8%. Calculate the minimum amount returned by the first asset ($Y) under the conditions of Redington immunization.

1. 1,310

2. 1,415

3. 2,123

4. 2,619

5. 3,809

Answer 1

Immunization is used for mitigating the risk in order to protect the portfolio from interest rate changes.

In the above case we ll try matching the assets and liability payments ie by discounting back the amounts.

so after discounting back the payment to time 0 ie 5000/(1+0.08)^9=2501.224. Similarly discounting back 3000 for 12 years we get 1191. Subtracting this we get 1309. Thus if we invest 1415 for one year we will get 1310 ie the minimum amount required. Answer is 1415