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wuzx · 2021年08月22日

请问这个题目用的公式在讲义那页？

NO.PZ2016062402000022

问题如下：

A portfolio manager is interested in the systematic risk of a stock portfolio, so he estimates the linear regression: $R_{Pt}-R_F=\alpha_P+\beta_P{\lbrack R_{Mt}-R_F\rbrack}+\varepsilon_{Pt}$ ,where $R_{Pt}$ is the return of the portfolio at time t, $R_{Mt}$ is the return of the market portfolio at time t, and $R_F$ is the risk-free rate, which is constant over time. Suppose that α = 0.008, β = 0.977, $\sigma{(R_P)}$ = 0.167, and $\sigma{(R_M)}$ = 0.156.

What is the approximate coefficient of determination in this regression?

选项：

A.

0.913

B.

0.834

C.

0.977

D.

0.955

解释：

the R-squared is given by $\frac{\beta^2\sigma_M^2}{\sigma_P^2}=0.977^2\times\frac{0.156^2}{0.167^2}=0.83$

请问这个题目用的公式在讲义那页？

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李坏_品职助教 · 2021年08月22日

嗨，从没放弃的小努力你好：

讲义没有给出直接从beta去计算R^2的公式，但是可以这样来理解这道题目：

题目是一元线性回归，R^2就等于相关系数ρ^2。

而β = ρ * （σp / σm），我们把beta平方之后再乘以σm^2，除以σp的平方，就只剩下ρ^2了，也就是R^2

关于β的计算公式可以参考讲义P196页的例题。

----------------------------------------------
努力的时光都是限量版，加油！

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NO.PZ2016062402000022问题如下 A portfolio manager is interestein the systematic risk of a stoportfolio, so he estimates the lineregression: RPt−RF=αP+βP[RMt−RF]+εPtR_{Pt}-R_F=\alpha_P+\beta_P{\lbraR_{Mt}-R_F\rbrack}+\varepsilon_{Pt}RPt−RF=αP+βP[RMt−RF]+εPt,where RPtR_{Pt}RPt is the return of the portfolio time t, RMtR_{Mt}RMt is the return of the market portfolio time t, anRFR_FRF is the risk-free rate, whiis constant over time. Suppose thα = 0.008, β = 0.977, σ(RP)\sigma{(R_P)}σ(RP) = 0.167, anσ(RM)\sigma{(R_M)}σ(RM) = 0.156.Whis the approximate coefficient of termination in this regression? 0.913 0.834 0.977 0.955 the R-squareis given β2σM2σP2=0.9772×0.15620.1672=0.83\frac{\beta^2\sigma_M^2}{\sigma_P^2}=0.977^2\times\frac{0.156^2}{0.167^2}=0.83σP2β2σM2=0.9772×0.16720.1562=0.83 决策系数怎么就是拟合优度了？

2023-03-21 11:10 1 · 回答

NO.PZ2016062402000022问题如下 A portfolio manager is interestein the systematic risk of a stoportfolio, so he estimates the lineregression: RPt−RF=αP+βP[RMt−RF]+εPtR_{Pt}-R_F=\alpha_P+\beta_P{\lbraR_{Mt}-R_F\rbrack}+\varepsilon_{Pt}RPt−RF=αP+βP[RMt−RF]+εPt,where RPtR_{Pt}RPt is the return of the portfolio time t, RMtR_{Mt}RMt is the return of the market portfolio time t, anRFR_FRF is the risk-free rate, whiis constant over time. Suppose thα = 0.008, β = 0.977, σ(RP)\sigma{(R_P)}σ(RP) = 0.167, anσ(RM)\sigma{(R_M)}σ(RM) = 0.156.Whis the approximate coefficient of termination in this regression? 0.913 0.834 0.977 0.955 the R-squareis given β2σM2σP2=0.9772×0.15620.1672=0.83\frac{\beta^2\sigma_M^2}{\sigma_P^2}=0.977^2\times\frac{0.156^2}{0.167^2}=0.83σP2β2σM2=0.9772×0.16720.1562=0.83 请问这个公式源自哪里

2022-11-17 15:57 1 · 回答

NO.PZ2016062402000022 0.834 0.977 0.955 the R-squareis given β2σM2σP2=0.9772×0.15620.1672=0.83\frac{\beta^2\sigma_M^2}{\sigma_P^2}=0.977^2\times\frac{0.156^2}{0.167^2}=0.83σP2β2σM2=0.9772×0.16720.1562=0.83 老师，R-square的英文表述是coefficient of termination,那r(xy)呢？

2022-03-29 07:58 1 · 回答

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2022-01-16 13:42 1 · 回答