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考拉 · 2024年02月02日

为什么pure index 的tracking error 最低,不应该考虑交易成本么?

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NO.PZ201812020100000402

问题如下:

SD&R Capital (SD&R), a global asset management company, specializes in ­fixed-income investments. Molly, chief investment officer, is meeting with a prospective client, Leah of DePuy Financial Company (DFC).

Leah informs Molly that DFC’s previous ­fixed-income manager focused on the interest rate sensitivities of assets and liabilities when making asset allocation decisions. Molly explains that, in contrast, SD&R’s investment process ­first analyzes the size and timing of client liabilities, and then it builds an asset portfolio based on the interest rate sensitivity of those liabilities.

Molly notes that SD&R generally uses actively managed portfolios designed to earn a return in excess of the benchmark portfolio. For clients interested in passive exposure to ­fixed-income instruments, SD&R offers two additional approaches.

  • Approach 1: Seeks to fully replicate a small range of benchmarks consisting of government bonds.
  • Approach 2: Follows an enhanced indexing process for a subset of the bonds included in the Bloomberg Barclays US Aggregate Bond Index. Approach 2 may also be customized to reflect client preferences.
To illustrate SD&R’s immunization approach for controlling portfolio interest rate risk, Molly discusses a hypothetical portfolio composed of two non-callable, investment-grade bonds. The portfolio has a weighted average yield- to-maturity of 9.55%, a weighted average coupon rate of 10.25%, and a cash flow yield of 9.85%.

Leah informs Molly that DFC has a single $500 million liability due in nine years, and she wants SD&R to construct a bond portfolio that earns a rate of return sufficient to pay off the obligation. Leah expresses concern about the risks associated with an immunization strategy for this obligation. In response, Molly makes the following statements about liability-driven investing:

  • Statement 1: Although the amount and date of SD&R’s liability is known with certainty, measurement errors associated with key parameters relative to interest rate changes may adversely affect the bond portfolios.
  • Statement 2: A cash flow matching strategy will mitigate the risk from non-parallel shifts in the yield curve.
Molly provides the four US dollar–denominated bond portfolios in Exhibit 1 for consideration. Molly explains that the portfolios consist of non-callable, investment-grade corporate and government bonds of various maturities because zero-coupon bonds are unavailable.



The discussion turns to benchmark selection. DFC’s previous fixed-income manager used a custom benchmark with the following characteristics:

  • Characteristic 1: The benchmark portfolio invests only in investment-grade bonds of US corporations with a minimum issuance size of $250 million.
  • Characteristic 2: Valuation occurs on a weekly basis, because many of the bonds in the index are valued weekly.
  • Characteristic 3: Historical prices and portfolio turnover are available for review.
Molly explains that, in order to evaluate the asset allocation process, fixed-income portfolios should have an appropriate benchmark. Leah asks for benchmark advice regarding DFC’s portfolio of short-term and intermediate-term bonds, all denominated in US dollars. Molly presents three possible benchmarks in Exhibit 2.



Relative to Approach 1 of gaining passive exposure, an advantage of Approach 2 is that it:

选项:

A.

minimizes tracking error.

B.

requires less risk analysis

C.

is more appropriate for socially responsible investors

解释:

C is correct. Enhanced indexing is especially useful for investors who consider environmental, social, or other factors when selecting a fixed-income portfolio. Environmental, social, and corporate governance (ESG) investing, also called socially responsible investing, refers to the explicit inclusion or exclusion of some sectors, which is more appropriate for an enhanced index strategy relative to a full index replication strategy. In particular, Approach 2 may be customized to reflect client preferences.

前面有老师回答:tracking error=active return/active risk。用来衡量主动管理的active return(Rp-Rb)的波动程度,tracking error越大,表明portfolio的收益与benchmark收益deviation的越大,所以,主动管理的程度越高。明白了这一点,从tracking error的角度,pure index<enhance indexing<active management。pure index基本没有tracking errer。


之前做过一道类似的题,答案并不是完全复制的tracking risk 最小,因为还要考虑交易费用和其他成本。

1 个答案

pzqa31 · 2024年02月03日

嗨,爱思考的PZer你好:


同学,你说的题目不是固收的题目吧?在固定收益里面,Fully-replication(Pure indexing)的方法模拟指数的特点就是:完美模拟。

指数中有啥,我们的Portfolio就要买啥,且Portfolio的配比、权重要和指数一样。指数经过什么样的调仓,我们的Portfolio就要跟着做,所以他追求的是完美模拟指数,所以tracking error最小。在固收里面tracking error和交易成本是两个方面,并没有这样的关系,可以参考讲义。

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就算太阳没有迎着我们而来,我们正在朝着它而去,加油!

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