开发者:上海品职教育科技有限公司 隐私政策详情

应用版本:4.2.11(IOS)｜3.2.5(安卓)APP下载

返回

梦梦 · 2024年09月03日

mean variance和efficient frontier

  1. FRM I
  2. Valuation And Risk Models

NO.PZ2023091701000082

问题如下：

The investment committee of a large pension fund is evaluating a range of investment options using the mean-variance framework. The committee assumes that the fund can borrow and lend at the risk-free rate and wants to invest only in portfolios that are represented by points on the efficient frontier.


If there are only two investable risky assets, A and B, and the market is in equilibrium, which of the following statements would be correct about the committee’s target portfolio according to the mean-variance framework?


选项：

A.If the committee’s aversion to risk changes, the proportion of asset A to asset B held in the fund’s target portfolio will change.

B.The proportion of asset A to asset B held in the target portfolio will be constant and in proportion to the assets’ respective share of all investable assets.

C.The proportion of asset A to asset B held in the target portfolio will be constant and in proportion to the assets’ relative risk contributions to the total market risk.

D.The proportion of asset A to asset B held in the target portfolio will be constant and a function of the assets’ respective expected returns.

解释：

B is correct. Within the mean-variance framework, the point M is the market portfolio – consisting of all investments in the market with the proportional amount of any investment in the portfolio being the same as the proportion of all available investments that it represents. If an asset is under(over)-represented by this criterion, the market price will fall(rise) until the criterion is satisfied.

A is incorrect. If the market is in equilibrium, all investors should choose to invest in the same portfolio of risky assets, represented by point M. They should then reflect their risk appetite by borrowing or lending at the risk-free rate.

C and D are incorrect. The proportion of A and B reflects the proportion of the assets’ share of all available investments.

老师，在讲解这道题的时候有几个地方不太明白：

1、M点里面是指曲线下方的斜线部分？就是黄色荧光笔部分？

只有红色曲线是有效前沿吧？黄色部分不是资产最优组合吧，因为同样的风险，收益没有达到最大比如C点。

2、红线和黄色区域都是AB权重不变？AB权重以市值占比为准？

3、M下方的点和上方的点是风险厌恶还是喜欢风险，是看效用曲线吧？

4、M下方投资了rf，咋看出是lend？

5、这道题和mean variance有啥关系啊

添加评论
3 个答案
已采纳答案

pzqa39 · 2024年09月09日

嗨，努力学习的PZer你好：


这个我们是要基于m点的定义去看，M点是把100%的资产投资于市场组合,所以图像对应的y轴是Rm，风险是σm。在M点的右侧要求的回报和风险都高于市场组合，是因为举杠杆了，也就是额外借钱去投资市场组合了。M点左侧的风险和回报都低于市场，是因为有一部分投资于无风险资产，也就是把钱借给银行。

----------------------------------------------
就算太阳没有迎着我们而来，我们正在朝着它而去，加油！

梦梦 · 2024年09月09日

哦哦，就是这么看啊，好的，谢谢老师🙏

pzqa39 · 2024年11月12日

嗨，努力学习的PZer你好：


1、在均值-方差框架下，投资者会选择一个风险与回报的最优组合，也就是在有效前沿（Efficient Frontier）上的投资组合。题目提到，投资委员会希望选择“在有效前沿上的组合”，这表明他们在追求最优的风险与回报配比，符合均值-方差优化的目标。

2、在均值-方差框架中，假设投资者可以在无风险利率下借入和借出资金。在市场均衡时，所有投资者会选择同一个市场组合（即图中的点 M），然后根据风险偏好选择在该市场组合与无风险资产之间进行借贷或投资，从而形成资本市场线（CML）。题目中提到市场均衡，并且所有投资者都选择点 M 作为投资组合，这就是均值-方差理论的一个基本结论。

3、在均衡状态下，市场组合的构成是固定的，即每个风险资产在市场组合中的权重与其在所有可投资资产中的比例相同。因此，无论投资者的风险厌恶程度如何变化，他们都投资于相同的市场组合，仅通过无风险借贷调整整体风险水平。这是均值-方差框架下的资本市场理论（CAPM）推导的一个重要结论。

----------------------------------------------
虽然现在很辛苦，但努力过的感觉真的很好，加油！

梦梦 · 2024年11月12日

好的，x x

pzqa39 · 2024年09月04日

嗨，从没放弃的小努力你好：


1、“只有红色曲线是有效前沿吧？黄色部分不是资产最优组合吧” 是的

2、关于M点的问题，老师上课说的M点里面就是指M这个点，不是黄色的区域。组成M这个点的AB权重不变，以市值为准。

3、关于lend和borrow以及风险厌恶的问题，我们假设M点是把100%的资产投资于市场组合，M右侧是指除了把自己手里的钱拿去投资之外，还要额外在市场上借钱去投资，风险厌恶程度低；而M点左侧没有把全部的资金投资到市场，而是一部分投资市场一部分投资于无风险资产，比如把钱放在银行，这样可以看作lender，而且这部分人的风险厌恶程度是比较高的。

----------------------------------------------
虽然现在很辛苦，但努力过的感觉真的很好，加油！

梦梦 · 2024年09月08日

“M右侧是指除了把自己手里的钱拿去投资之外，还要额外在市场上借钱去投资，风险厌恶程度低；而M点左侧没有把全部的资金投资到市场，而是一部分投资市场一部分投资于无风险资产”这段解释在图形中怎么看呢？

梦梦 · 2024年11月11日

“5、这道题和mean variance有啥关系啊”这个问题好像没解释

  • 3

    回答

  • 0

    关注

  • 149

    浏览
相关问题

NO.PZ2023091701000082 问题如下 The investment committee ofa large pension funis evaluating a range of investment options using the mean-varianceframework. The committee assumes ththe funborrow anlenthe risk-free rate anwants to invest only inportfolios thare representepoints on the efficient frontier.Ifthere are only two investable risky assets, A ananthe market is inequilibrium, whiof the following statements woulcorreabout thecommittee’s target portfolio accorng to the mean-varianframework? A.If the committee’s aversion to risk changes, theproportion of asset A to asset B helin the funs target portfolio willchange. B.The proportion of asset A to asset B helin thetarget portfolio will constant anin proportion to the assets’ respectiveshare of all investable assets. C.The proportion of asset A to asset B helin thetarget portfolio will constant anin proportion to the assets’ relativerisk contributions to the totmarket risk. The proportion of asset A toasset B helin the target portfolio will constant ana function of theassets’ respective expectereturns. B is correct. Withinthe mean-varianframework, the point M is the market portfolio – consistingof all investments in the market with the proportionamount of any investmentin the portfolio being the same the proportion of all available investmentsthit represents. If asset is unr(over)-representethis criterion,the market priwill fall(rise) until the criterion is satisfieA is incorrect. Ifthe market is in equilibrium, all investors shoulchoose to invest in the sameportfolio of risky assets, representepoint M. They shoulthen reflecttheir risk appetite borrowing or lenng the risk-free rate.C anareincorrect. The proportion of A anB reflects the proportion of the assets’share of all available investments. 请问这个在经典题的哪个视频下面可以找到呀。

2024-11-04 13:31 1 · 回答

NO.PZ2023091701000082 问题如下 The investment committee ofa large pension funis evaluating a range of investment options using the mean-varianceframework. The committee assumes ththe funborrow anlenthe risk-free rate anwants to invest only inportfolios thare representepoints on the efficient frontier.Ifthere are only two investable risky assets, A ananthe market is inequilibrium, whiof the following statements woulcorreabout thecommittee’s target portfolio accorng to the mean-varianframework? A.If the committee’s aversion to risk changes, theproportion of asset A to asset B helin the funs target portfolio willchange. B.The proportion of asset A to asset B helin thetarget portfolio will constant anin proportion to the assets’ respectiveshare of all investable assets. C.The proportion of asset A to asset B helin thetarget portfolio will constant anin proportion to the assets’ relativerisk contributions to the totmarket risk. The proportion of asset A toasset B helin the target portfolio will constant ana function of theassets’ respective expectereturns. B is correct. Withinthe mean-varianframework, the point M is the market portfolio – consistingof all investments in the market with the proportionamount of any investmentin the portfolio being the same the proportion of all available investmentsthit represents. If asset is unr(over)-representethis criterion,the market priwill fall(rise) until the criterion is satisfieA is incorrect. Ifthe market is in equilibrium, all investors shoulchoose to invest in the sameportfolio of risky assets, representepoint M. They shoulthen reflecttheir risk appetite borrowing or lenng the risk-free rate.C anareincorrect. The proportion of A anB reflects the proportion of the assets’share of all available investments.

2024-04-19 21:22 1 · 回答