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大龄考生宋一国 · 2024年01月26日

有效前沿不是convex吗

  1. CFA III
  2. Equity

NO.PZ2019012201000079

问题如下：

Which of following is correct regarding on Implementation Constraints?

选项：

A.

Twice the absolute risk will lead to twice the return.

B.

Markowitz efficient frontier shows that the relationship between return and risk is convex.

C.

There is a level of leverage beyond which volatility reduces expected returns.

解释：

C is corrent. Portfolios may face implementation constraints that decrease the IR if active risk increases beyond a specific level; Portfolios with high absolute risk targets face limited diversification opportunities, which may lead to a decrease in the SR. There is a level of leverage beyond which volatility reduces expected returns.

主要是说当杠杆过高，虽然可能会带来收益，但是风险也会增加，带来更大的波动，反而会降低收益。打个比方，昨天跌了10%，今天涨了10%，看起来好像是一样的。但是实际不是一回事，反而是亏损的（亏损1%），加杠杆后会进一步降低收益。

There may be constraints that prevent Manager A from scaling his active weights.So twice the absolute risk will not lead to twice the return, Markowitz efficient frontier shows that the relationship between return and risk is concave.

如题，B为什么错，有效前沿不是凸的嘛

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1 个答案

笛子_品职助教 · 2024年01月26日

嗨，努力学习的PZer你好：


如题，B为什么错，有效前沿不是凸的嘛

Hello，亲爱的同学~

凸是指：随着风险增加，收益增加得比风险更多。

反之，如果随着风险的增加，收益增加得比风险更少，就是凹的。


有效前沿不是凸的，是凹的。这意味着随着风险的增加，预期回报增加的速度逐渐减缓。

图形如下：横轴是风险，纵轴是收益：


这个图形是凹的。




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