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Stella · 2024年07月21日

请问mvo与surpluse-optimization的差别是什么

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NO.PZ202206210100000301

问题如下:

Sabonete Case Scenario

Sabonete, S.A., is a multi-national consumer products company headquartered in Lisbon, Portugal, with annual revenue of approximately €2 billion. Over the past several years, the company’s growth strategy has centered on expanding market share in emerging markets. Over half of revenues are from emerging markets, and the remainder are from developed European economies. Oni Falana serves as the chief investment officer of Sabonete’s defined benefit pension plan (SPP).

Falana has engaged an outside consultant, Isabel Horvath, for assistance with asset allocation. Falana describes to Horvath the company’s key objectives with respect to the SPP:

  • reach fully funded (100%) status in five years, at which point the liabilities will be fully hedged,

  • minimize fluctuations in expected year-to-year required contributions, and

  • minimize the administrative and investment costs associated with managing the fund.

Falana provides Horvath with the following key facts and assumptions regarding Sabonete and the SPP:

  • The fund is closed to new employees, but existing employees continue to accrue benefits under the original terms.

  • The fund is 90% funded (€5 billion in assets and an accrued benefit obligation of €5.55 billion).

  • A €75 million contribution will be made to the fund at the end of this quarter. Future contributions are likely to be substantially smaller.

  • The average participant is 45 years old, and employee turnover has been low.

  • The salary growth rate is 3.2%

  • The liability discount rate, currently 3.5%, is benchmarked to 10-year AA corporate bonds.

  • The risk-free rate is currently 3.0%, and short-term interest rates are expected to remain stable.

  • The current asset allocation and other statistics (expected return, volatility, and correlation with global equities) of each asset class are indicated in Exhibit 1.

Exhibit 1 SPP Current Asset Allocation and Other Statistics by Asset Class


Horvath starts by preparing an economic balance sheet for the SPP and makes the following notes:

  • · Emerging market equities have a 10% weight in the global market portfolio. However, given the firm’s familiarity with and the opportunities they perceive in emerging markets, the SPP has historically been over-weighted (25%) in this asset class.

  • · 60% of company revenue is from sales in emerging markets, of which half is attributable to sales in Africa. The revenue growth rate for Sabonete’s African business is high but very volatile. The firm’s revenues and profitability are quite sensitive to emerging markets.

  • · The firm has significant investments in African real estate. It recently acquired several large parcels of land in Africa for €200 million and is planning to make a major investment in new manufacturing facilities to boost margins.

Based on these factors and the information from Exhibit 1, Horvath presents the current asset allocation of the plan along with two other options for consideration (see Exhibit 2).

Exhibit 2

Current and Proposed Asset Allocation Options


Recee Radell, an analyst in SPP’s pension office, makes the following statements regarding Option 1:


Horvath states, “Option 1 provides a 95% probability of meeting the goal of reaching fully funded status in five years, but interim contributions are likely to be quite variable. Option 2 is likely to result in a more stable contribution rate but with a lower probability of meeting the funding goal.”

Falana plans to recommend Option 2, believing that the greater certainty of meeting the required year-to-year contributions is the more important objective. She asks Radell to recommend a rebalancing policy for Option 2. He proposes the ranges shown in Exhibit 3 and provides an estimate of the related transaction costs.

Exhibit 3

Rebalancing Ranges for Option 2



Radell justifies his recommendation on the basis of the following statements:

  • A wide rebalancing range for global fixed income is appropriate because of its low volatility, low transaction costs, and low correlation with other asset classes in the portfolio.

  • The allocation for private equity is challenging because a low-cost passive investment vehicle does not exist and modeling with a private equity index captures only the return aspects of private equity without an appropriate representation of risk.

Falana discusses the recommended asset allocation with the Pension Committee. A new committee member, James D’Alessandro, states that his preference would be Option 1 because the best pension funds have adopted the endowment model of asset allocation, which has a higher allocation to alternative investments.

Question


From the description of Sabonete’s objectives for the SPP, the most appropriate asset allocation approach is:

选项:

A.mean–variance optimization. B.a basic two-portfolio approach. C.an integrated asset–liability approach.

解释:

SoluC is correct. Based on the objectives described, the integrated asset–liability approach is the most appropriate asset allocation approach for the SPP, which is currently under-funded and seeks to achieve fully funded status in five years. Mean–variance optimization is an asset-only approach to asset allocation and fails to consider Sabonete’s goal of fully funding the liabilities. The basic two-portfolio approach assumes the pension plan has a surplus that can be allocated to a return-seeking portfolio.

C is correct. Based on the objectives described, the integrated asset–liability approach is the most appropriate asset allocation approach for the SPP, which is currently under-funded and seeks to achieve fully funded status in five years. Mean–variance optimization is an asset-only approach to asset allocation and fails to consider Sabonete’s goal of fully funding the liabilities. The basic two-portfolio approach assumes the pension plan has a surplus that can be allocated to a return-seeking portfolio.

A is incorrect. Mean–variance optimization is an asset-only approach to asset allocation and fails to consider Sabonete’s goal of fully funding the liabilities.

B is incorrect. The basic two-portfolio approach assumes the pension plan has a surplus that can be allocated to a return-seeking portfolio.

如题。已知mvo为asset only的方法,surplus为liability driven的方法,但请助教进行进一步区分、最终不都是mvo最优化的方法么?

1 个答案

lynn_品职助教 · 2024年07月22日

嗨,努力学习的PZer你好:


如题。已知mvo为asset only的方法,surplus为liability driven的方法,但请助教进行进一步区分、最终不都是mvo最优化的方法么?


同学这个前提是从哪里 来的呢,这道题应该是The basic two-portfolio approach assumes the pension plan has a surplus that can be allocated to a return-seeking portfolio.

也就是Hedging/Return-Seeking Portfolio Approach是liability driven的方法。


1、Hedging/Return-Seeking Portfolio Approach要求overfunded,要求有surplus


因为它要求先Cover掉liability,所以是liability driven的方法


2、surplus optimization approach不要求overfunded,不要求有surplus


没有“surplus",或者说surplus可以是负数的,不要被“surplus”的名字给误导了,不管surplus是正是负, surplus optimization 的目标都是最大化surplus utility。


举个栗子Asset 是8,Liability是10,我们就是对 -2进行optimization,那么就是让负数更小。


surplus方法与AO方法的mvo做起来是一样的,公式也一样,但是E(R)要换成surplus,也因此“surplus”不需要大于0。

MVO输入变量E(r), σ, ρ,给定公式 U= E(R) – 0.005 λσ2,交给电脑去做 U的最大化求解。


surplus optimization输入变量为E(Rs), σs, ρ,给定公式 Us= E(Rs) – 0.005 λσs2,原理完全相同。

其中E(Rs) = Change in asset value―Change in liability value)/(Initial asset value).

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虽然现在很辛苦,但努力过的感觉真的很好,加油!

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