NO.PZ202209060200004002
问题如下：
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
The benchmark of the Abiquia asset portfolio is complex and is composed of fixed weights of a variety of global fixed-income indexes. Recently, a decision was made to add South American debt to the benchmark at a 6% weight. Puhuyesva’s assistant, Alo Honanie, is tasked with finding an appropriate index for South American debt securities. He narrows his choices to three: Deuda Sudamericana (DS), Renta Fija Sudamericana (RFS), and Bonos de Sur y Centro America (BSCA). All three contain similar mixtures of corporate and government debt with credit rating weightings that are essentially the same. Summary information for these indexes is found in Exhibit 2.
Exhibit 2: South American Debt Indexes
Honanie and Puhuyesva meet to discuss the choice of debt indexes. Puhuyesva expresses her concerns about the difficulties they will face in trying to purchase securities to match the index chosen: “Whatever index we choose, my goal is to match it as closely as possible while minimizing costs. We will need to focus on minimizing tracking risk. One advantage we have over equity portfolio managers is that fixed-income valuation models are much more reliable than those for equities; therefore, it is much easier to determine the value of a fixed-income portfolio than an equity portfolio.”
Honanie responds, “Because of the intended size of our South American debt portfolio, it would be too expensive to attempt full replication of any of these indexes. The two choices available to us are purchasing securities that, together, match the primary risk characteristics of the chosen index or purchasing pooled investments, such as mutual funds or exchange-traded funds. A synthetic strategy cannot be pursued because there are no exchange-traded derivative contracts for these indexes.”
The Abiquia asset portfolio benchmark has a US Treasury debt component. Puhuyesva asks Honanie to explore choices for that piece of the portfolio and provide an executive summary to her. Honanie’s summary compares laddered, bullet, and barbell portfolio structures, assuming the same portfolio value and duration, and highlights three key differences.
Difference 1: The laddered portfolio would have lower convexity than the other portfolio styles.
Difference 2: The laddered portfolio would provide for better liquidity management relative to the other portfolio styles.
Difference 3: The laddered portfolio would provide better diversification over the interest rate cycle compared with the other portfolio styles.
The most appropriate action given Puhuyesva’s views on interest rates and the information in Exhibit 1 would be to buy:
选项：
A.492 contracts. B.614 contracts. C.552 contracts.解释：
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
where BPV is basis point value (of the liability portfolio, asset portfolio, and futures contract, respectively).
In this case, , 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.
想问一下是不是因为，interest rate 现在会上涨，我计算出的future是552 就可以cover BPV的gap了，但是现在为了保持surplus，我可以long 更多的futures ？
但是case中没有体现这个意图啊
