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wukefu · 2024年07月09日

为什么选择c

* 问题详情,请 查看题干

NO.PZ202209060200004705

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


What contingent strategies would Shrewsbury’s DB clients most likely enter into under the scenario he outlines?

选项:

A.Short a receiver swap B.Long a payer swaption, short a receiver swaption C.Long a receiver swaption, short a payer swaption

解释:

Solution

C is correct. The plan is not fully funded and is also not fully hedged; that is, the money durations of the assets and liabilities are not matched. If the clients’ view is incorrect and rates fall further, the mismatch will result in the liabilities increasing in value while the assets will appreciate by a lesser amount. Swaptions are a contingent security on interest rate swaps. A receiver swaption would allow the plan to receive a fixed (higher) rate if rates rally, but at the cost of the swaption premium. To finance this receiver swaption, the DB plan can sell a payer swaption to collect a premium that finances the receiver swaption. If rates rise above some level, the plan would increase its duration by virtue of being put a swap. The plan may have anticipated closing the duration gap at higher interest rate levels, so being put a swap is in line with an LDI program.

A is incorrect because a receiver swap is not a contingent security.

B is incorrect because it is the reverse of the correct solution—long a receiver swaption, short a payer swaption.

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.


从题目的情况看是BPA (A)< BPV (L), 如果以上这句话是答题点,要如何选择swap 呢?

1 个答案
已采纳答案

发亮_品职助教 · 2024年07月09日

从题目的情况看是BPA (A)< BPV (L), 如果以上这句话是答题点,要如何选择swap 呢?


正常来讲,背景是Asset BPV < Liability BPV,且投资者预期未来的利率会上升(These clients expect rates to rise),基于这样的预期,他们应该尽可能地降低资产端的BPV。因为当利率上升时,负债端的BPV更大,负债的Value下降会更多,这会使得养老金的surplus扩大。

所以,已经是Asset BPV < Liability BPV的基础下,可以不用管了,保留这个缺口享受预期的利率上升。

或者还可以更激进一点,如果对利率的预期特别有把握,那可以进一步降低资产端的BPV,可以进入pay fixed-receive floating的swap,这个swap相当于是(short fixed-rate bond + long floating rate bond)的组合,这样的组合会获得负的duraiton,会进一步降低资产端的BPV。


但swap的问题是在于,一旦利率预测错了,那将会进一步加大亏损,使得养老金的surplus进一步变差。


从这道题的题干来看,直接排除swap。因为下面这段话给了3个信息:

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.


第一,在利率预测错的情况下,可以起到保护作用,这显然是option的效果,如果是swap的话,预测错的背景下一定会产生亏损。

第二,预测对的情况下(rates rise),会进一步提升hedge ratio


从上面2点可以判断,这是一个分段的收益策略,要在不同的利率背景下,有不同的策略,那肯定是option,因为option才会有分段的收益。

然后题干又说一个costless的策略,即成本低的策略,那基本可以判断是option collar了。因为只有collar才会降低option的成本。


下面就是选哪个swaption collar,那就从以上2个情景的策略分析看。


如果利率预测错了——将来利率是下降,这个option要起到保护作用。

那利率下降时,资产负债的value上升,但由于初始状态是资产BPV小于负债BPV,所以这会加大亏损,保护作用就是这个swaption可以产生盈利弥补这个亏损。所以要考虑在利率下降时,可以盈利的swaption。显然这个swaption是c选项的long receiver swaption,因为当利率下降,我们行权,进入receive fixed-pay floating swap,会存在收益。


下来就是预测对的情况下——将来利率上升时,要进一步提升hedge ratio。

进一步提升hedge ratio的意思是进一步加大资产端的BPV,使得资产端与负债端的BPV缺口缩小。所以,在利率上升时,这个swaption会行权且会加大duration/BPV。那C选项的short payer swaption可以实现。因为利率上升时,对手方行权,对手方进入一个pay fixed receive floating的swap,那我们就被迫进入一个receive fixed-pay floating的swap,这个swap相当于是一个long fixed-rate bond + short floating的组合,该组合的duration为正,可以增加资产端的BPV。完全符合题干的要求。

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