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西红柿面 · 2025年07月04日

关于用Swap rate还是用Futures更好的问题

* 问题详情,请 查看题干

NO.PZ202209060200004704

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.

Question


The risk that Silver describes to Shrewsbury in hedging the liabilities is most likely:

选项:

A.model risk. B.spread risk. C.liquidity risk.

解释:

Solution

B is correct. Silver is referring to spread risk in his discussion with Shrewsbury regarding risks in hedging DB plan liabilities. The liabilities are estimated—that is, calculation of the PBO—using high-quality corporate bonds. The typically wider spreads of lower-quality bonds may underperform the spreads of higher-quality bonds in a market sell-off. Conversely, hedging the liabilities with swaps may not provide enough of a spread risk hedge relative to using corporate bonds such that if spreads tighten, high-quality corporate bonds (used to discount liabilities) may outperform swaps. Model risk refers to making incorrect assumptions regarding future liabilities or approximations being inaccurate. Liquidity risk is associated with exhausting available collateral funds to meet margin calls on derivative positions or to pay benefits.

A is incorrect because model risk refers to making incorrect assumptions regarding future liabilities or approximations being inaccurate.

C is incorrect because liquidity risk is associated with exhausting available collateral funds to meet margin calls on derivative positions or to pay benefits.

l 引入衍生品进行Hedge会引发Spread risk。衍生品和现货变动不统一,Futures用的折现率是国债收益率,Swap使用的Swap rate更接近公司债的收益率,

所以说引入衍生品Hedge的时候用Swap rate还是用Futures更好呢?

1 个答案

发亮_品职助教 · 2025年07月06日

是的,存在这个现象。这个得要看资产和负债的类型。

如果说资产和负债的质量是国债级别的,或者比较接近,用futures会更好。可以保证影响futures、资产,负债的利率尽可能相似,降低了spread risk。


但是资产和负债以公司债为主,这时候如果用futures反而会有较大误差。因为会额外引入国债利率,国债利率的变动和公司债利率的变动相对有更大的误差。

反而是swap rate更好,因为swap rate是质量还不错,但达不到国债层级的金融机构决定的,swap rate相当于反映的是质量还不错的公司债风险,对标的利率可以看成是公司债利率。引入swap的话,影响资产、负债,衍生品的利率更接近,发生的spread risk会更小。


这算一个很细节的点了。就是讨论futures和swap谁更合适,这个角度是其中一个思考点。具体到hedge时,可能还要参考其他优缺点,如信用风险的大小,是否要每日结算产生现金流需求,抵押物的要求,头寸是否需要定制化等等。

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