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WOO2019 · 2023年01月26日

本题high risk asset should use wider corridor range以避免发生交易,从而增加成本。框架图讲义里high volatilty should use narrower range,以避免该类资产在组合中波动出去太多

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NO.PZ201803130100000102

问题如下:

Megan Beade and Hanna Müller are senior analysts for a large, multi-divisional money management firm. Beade supports the institutional portfolio managers, and Müller does the same for the private wealth portfolio managers.

Beade reviews the asset allocation in Exhibit 1, derived from a mean–variance optimization (MVO) model for an institutional client, noting that details of the MVO are lacking.

Exhibit1 Asset Allocation and Market Weights(in percent)

The firm’s policy is to rebalance a portfolio when the asset class weight falls outside of a corridor around the target allocation. The width of each corridor is customized for each client and proportional to the target allocation. Beade recommends wider corridor widths for high-risk asset classes, narrower corridor widths for less liquid asset classes, and narrower corridor widths for taxable clients with high capital gains tax rates.

One client sponsors a defined benefit pension plan where the present value of the liabilities is $241 million and the market value of plan assets is $205 million. Beade expects interest rates to rise and both the present value of plan liabilities and the market value of plan assets to decrease by $25 million, changing the pension plan’s funding ratio.

Beade uses a surplus optimization approach to liability-relative asset allocation based on the objective function Um =E (Rm) - 0.005λσm2

where E(Rs,m) is the expected surplus return for portfolio m, λ is the risk aversion coefficient, and σ2(Rs,m) is the variance of the surplus return. Beade establishes the expected surplus return and surplus variance for three different asset allocations, shown in Exhibit 2. Given λ = 1.50, she chooses the optimal asset mix.

Exhibit 2 Expected Surplus Return and Volatility for Three Portfolios

Client Haunani Kealoha has a large fixed obligation due in 10 years. Beade assesses that Kealoha has substantially more funds than are required to meet the fixed obligation. The client wants to earn a competitive risk-adjusted rate of return while maintaining a high level of certainty that there will be sufficient assets to meet the fixed obligation.

In the private wealth area, the firm has designed five sub-portfolios with differing asset allocations that are used to fund different client goals over a five-year horizon. Exhibit 3 shows the expected returns and volatilities of the sub-portfolios and the probabilities that the sub-portfolios will exceed an expected minimum return. Client Luis Rodríguez wants to satisfy two goals. Goal 1 requires a conservative portfolio providing the highest possible minimum return that will be met at least 95% of the time. Goal 2 requires a riskier portfolio that provides the highest minimum return that will be exceeded at least 85% of the time.

Exhibit3 Characteristics of Sub-portfolios

Müller uses a risk parity asset allocation approach with a client’s four–asset class portfolio. The expected return of the domestic bond asset class is the lowest of the asset classes, and the returns of the domestic bond asset class have the lowest covariance with other asset class returns. Müller estimates the weight that should be placed on domestic bonds.

Müller and a client discuss other approaches to asset allocation that are not based on optimization models or goals-based models. Müller makes the following comments to the client:

Comment 1 An advantage of the "120 minus your age" heuristic over the 60/40 stock/bond heuristic is that it incorporates an age-based stock/bond allocation.

Comment 2 The Yale model emphasizes traditional investments and a commitment to active management.

Comment 3 A client’s asset allocation using the 1/N rule depends on the investment characteristics of each asset class.


For clients concerned about rebalancing-related transactions costs, which of Beade’s suggested changes in the corridor width of the rebalancing policy is correct? The change with respect to

选项:

A.

high-risk asset classes.

B.

less liquid asset classes.

C.

taxable clients with high capital gains tax rates.

解释:

A is correct.

Theoretically, higher-risk assets would warrant a narrow corridor because high-risk assets are more likely to stray from the desired strategic asset allocation. However, narrow corridors will likely result in more frequent rebalancing and increased transaction costs, so in practice corridor width is often specifed to be proportionally greater the higher the asset class’s volatility. Thus, higher-risk assets should have a wider corridor to avoid frequent, costly rebalancing costs. Her other suggestions are not correct. Less-liquid asset classes should have a wider, not narrower, corridor width. Less-liquid assets should have a wider corridor to avoid frequent rebalancing costs. For taxable investors, transactions trigger capital gains in jurisdictions that tax them. For such investors, higher tax rates on capital gains should be associated with wider (not narrower) corridor widths.

high risk asset不就是high volatilty asset吗?好像从哪个角度解释都行啊,到底是,wider还是narrower

1 个答案

lynn_品职助教 · 2023年01月27日

嗨,从没放弃的小努力你好:


high risk asset不就是high volatilty asset吗?

是的,两者是可以划等号的。


这道题目考法特殊,通常情况下,高风险的资产应当设定更窄的调整区间,


但是题目强调了客户同时还考虑交易成本 “clients concerned about rebalancing-related transactions costs”。调整区间窄,则调整频率高,带来的交易成本就高。


因此,在节约成本的要求下,高风险的资产反而应该设定比较宽的区间。


这个点很特殊,是教材明确出现了机构IPS和AA内容矛盾。


题high risk asset should use wider corridor range以避免发生交易,从而增加成本。框架图讲义里high volatilty should use narrower range,以避免该类资产在组合中波动出去太多


机构IPS中在335页提到Systematic rebalancing policies.相关的知识点,而AA里面的结论确实是波动率越大,range越窄,这两个结论相悖,如果是一级二级,我肯定会给同学建议,看到题目先分析是哪个科目,再根据该科目的结论来解题,三级的选择题也可以用这个办法,但是其实三级的case题时间比较紧张,很难区分,我建议同学多读题干,抓住细节,然后以AA为主。


一、AA的逻辑


(1)波动率越大,range越窄。因为波动性比较高,说明资产的风险比较大,所以需要做频繁调整,那么就要设定一个比较窄的调整区间。


(2)税收越高, range越宽,避免频繁调整实现资本利得产生税费。


(3)结论:有税→税后波动率小→ range宽,结果跟成本角度是一样的


关于Rebalance rang我这里有一个总结的方法,所有的因素都可以归总到两个方面,第一需要不需要,第二能不能(一般是看成本)。


波动率越大,range越窄。因为波动性比较高,说明资产的风险比较大,所以需要做频繁调整,那么就要设定一个比较窄的调整区间。


二、机构IPS的案例题中是这么一个逻辑:


流动性越差的资产,这个Rebalancing band就定的宽一点,因为流动性差的资产,很难执行交易,交易成本很高,


如果把Rebalancing band定的很窄的话,可能随随便便的市场波动就会让该资产的权重超出Rebalancing band,于是Portfolio就需要进行频繁的调整。


那这样的话,Portfolio需要调整的频率就很大,加大了交易成本。


为了避免这种情况,流动性差的资产、波动大的资产,Rebalancing band需要定得宽一点。

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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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