Chosovi Puhuyesva is the chief investment officer of Abiquia Mutual Assurance Company, a provider of life insurance, which is headquartered in Albuquerque, New Mexico. Puhuyesva manages an asset portfolio of fixed-income securities designed to fund Abiquia’s insurance liabilities and grow its surplus so as to protect members from premium increases or possibly allow for premium reductions.
Puhuyesva’s approach matches the interest rate sensitivity of the asset portfolio to that of the liabilities. If she has reasonably strong beliefs about how interest rates will change in the near future and the surplus exceeds her threshold of 10% of assets, she will adjust the interest rate sensitivity of the asset portfolio to attempt to increase the surplus. She typically uses derivatives positions to adjust the asset portfolio’s interest rate sensitivity, rather than buying and selling securities.
Puhuyesva believes interest rates will fall over the next three months and wants to position the asset portfolio accordingly. She intends to use futures contracts on the 10-year Treasury bond. The three-month contract has a par value of USD100,000 and a basis point value of USD102.30 per contract. Exhibit 1 provides current information about the asset and liability portfolios.
Exhibit 1
Abiquia’s Assets and Liabilities
Assets | Liabilities | |
Value | USD217.3 million | USD206.8 million |
Modified duration | 11.2 years | 14.5 years |
Basis point value (BPV) | USD243,376 | USD299,860 |
The most appropriate action given Puhuyesva’s views on interest rates and the information in Exhibit 1 would be to buy:
- 492 contracts.
- 614 contracts.
- 552 contracts.
Solution
B is correct. The number of futures contracts needed to fully remove the duration gap between the asset and liability portfolios is given by Nf=BPVL−BPVABPVf��=����−��������, where BPV is basis point value (of the liability portfolio, asset portfolio, and futures contract, respectively). In this case, Nf=299,860−243,376102.30=+552.1��=299,860−243,376102.30=+552.1, where the plus sign indicates a long position in or buying 552 futures contracts. Because the value of assets is more than 2% greater than the value of liabilities (217.3/206.8 – 1 = 5.1%) and Puhuyesva believes interest rates will fall, the duration of assets should be greater than the duration of liabilities so that the surplus will rise if interest rates do fall. Therefore, more than 552 contracts should be bought.
A is incorrect because buying 492 contracts would leave the duration of assets lower than the duration of liabilities and the surplus would decrease if interest rates fall.
C is incorrect because buying 552 contracts would fully immunize the surplus and it would neither increase nor decrease if interest rates fall.
When there is condition that attempt to increase surplus will be done only when surplus has exceeded 10% then why an attempt to increase surplus made when it is only 5% ? where did barrier of 2% come from?
Most probably, it’s a mistake in the case study. They wrote 10% barrier instead of 2%