NO.PZ202209060200004703
问题如下：
Rumson Shrewsbury and Sandy Silver are field consultants with Fair Haven Advisers, LLC, an investment consultant firm specializing in fixed-income investing. They plan to expand their practice to focus on such clients as retirement schemes, insurance companies, and others that require solutions to meet liability streams. They meet to discuss Fair Haven’s approach to this new business segment, and Shrewsbury makes the following points to Silver.
Point 1: Life-insurance companies and defined benefit (DB) pension schemes both use liability-driven investing (LDI), which is a special form of asset–liability management (ALM). In both cases, the liabilities are defined and assets are managed in a way that considers the profile and characteristics of the liability.
Point 2: Asset-driven liabilities (ADLs), like LDI, are special cases of ALM. Financing companies accumulate assets as a result of their underlying business. They use ADLs to structure their assets in a way that matches the maturities of the liabilities.
Point 3: An LDI strategy requires estimating the amount and timing of cash outlays in order to estimate the interest rate sensitivity of the liabilities.
Silver tells Shrewsbury, “Managing fixed-income portfolios to meet obligations requires an understanding of the nature of the liabilities. Clients with liability types such as those listed in Exhibit 1 use yield statistics, such as Macaulay, modified duration, money durations, and the present value of a basis point (PVBP), when implementing immunization strategies.”
Exhibit 1 Classification of Liabilities
Shrewsbury responds, “Only Type I clients can measure the interest rate sensitivity of liabilities using yield statistics. Those with Type II, III, and IV liabilities must use a curve duration statistic, such as effective duration, to estimate interest rate sensitivity.”
Silver and Shrewsbury begin discussing a client that sponsors a US DB plan. The client wants to immunize the liabilities such that changes in interest rates under various scenarios will not cause a deterioration in funded status. Key data for the plan assets and liabilities are provided in Exhibit 2. Silver’s forecast is that interest rates will rise in a non-parallel fashion. In fact, he expects a bear steepening of the curve as inflation accelerates because of rising wages.
Exhibit 2 Defined Benefit Plan Characteristics
*Projected benefit obligation.
Silver and Shrewsbury continue their discussion regarding hedging the economic and market risks for a DB plan. Shrewsbury explains that any hedging program can fall short of its objective owing to a number of risks. Silver believes they can use various instruments to hedge interest rate risk but that certain risks can be more difficult to address. He tells Silver, “One risk you face in hedging the liabilities is that the yield of high-quality bonds is used in the discounting process, whereas most investment solutions use a more diversified and lower-quality portfolio of corporate bonds. Conversely, you can face the opposite problem, if you use Treasury futures or interest rate swaps to hedge the liabilities.”
Silver considers alternatives to a cash bond portfolio for hedging the liabilities because he is concerned that as time passes and market conditions change, the initially established hedging program may drift from target levels. Some of his clients with DB plans are underfunded and have interest rate hedge ratios well below 100%. These clients expect rates to rise, and should their view prove correct, the duration gap will improve funded status. He believes these clients should at least consider a costless derivative position to protect from rates falling further if their view is incorrect while also increasing the hedge ratio if rates rise.
Shrewsbury knows that some of his clients do not favor active portfolio management strategies, particularly given their higher fee structures relative to passive strategies. He evaluates alternate ways to establish passive bond market exposure. His preference is to select an instrument that hedges not only the interest rate component of the liability’s discount rate but also the credit component. The obligation should reference a corporate bond index but be structured as a synthetic secured financing transaction.
QuestionBased on the data in Exhibit 2, will the client discussed most likely be able to immunize its DB plan given the interest rate scenario described by Silver?
选项：
A. Yes
B. No, because of the differences in money duration
C. No, because of the differences in convexity and dispersion
解释：
SolutionC is correct. The money duration of the assets and liabilities are equal: 517,342,000 × 12.66 = 6,548,381,000, and 500,000,000 × 13.10 = 6,548,381,000. For parallel changes, the equal money durations and PV01 imply that assets and liabilities would move in tandem. Silver expects a bear steepener; that is, long rates will rise faster than short rates. In a bear steepener, long rates rise faster than short rates in a non-parallel fashion. Given that the assets have lower convexity and dispersion than the liabilities, they will underperform; that is, the liabilities would change by a greater amount than the assets.
A is incorrect because Silver expects a bear steepener; that is, long rates will rise faster than short rates. In a bear steepener, long rates rise faster than short rates in a non-parallel fashion. Given that the assets have lower convexity and dispersion than the liabilities, they will underperform.
B is incorrect because the differences in convexity and dispersion are unfavorable; that is, they are lower for the assets than for the liabilities. If the opposite were the case, then the liabilities would be immunized.
這題解答中的money duration 不是MV乘以modified duration 嗎？為什麼可以乘Macaulay duration?