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柚柚_柚 · 2020年05月29日

问一道题：NO.PZ2016062402000022 [ FRM I ]

  1. FRM I
  2. Quantitative

问题如下：

A portfolio manager is interested in the systematic risk of a stock portfolio, so he estimates the linear regression: RPt−RF=αP+βP[RMt−RF]+εPtR_{Pt}-R_F=\alpha_P+\beta_P{\lbrack R_{Mt}-R_F\rbrack}+\varepsilon_{Pt},where RPtR_{Pt} is the return of the portfolio at time t, RMtR_{Mt} is the return of the market portfolio at time t, and RFR_F is the risk-free rate, which is constant over time. Suppose that α = 0.008, β = 0.977, σ(RP)\sigma{(R_P)} = 0.167, and σ(RM)\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 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}=0.83

这个相关系数的公式错了吧，market 的方差应该在下面, 反了
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小刘_品职助教 · 2020年05月29日

同学你好，这个公式没有错哈~你再看一下呢~~

coefficient of determination即决定系数，就是R方。一元回归中，R方等于rho的平方。

β=ρ*σp/σm，变形后ρ=β*σm/σp，等号两边同取平方即可。

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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}=0.83σP2​β2σM2​​=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}=0.83σP2​β2σM2​​=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}=0.83σP2​β2σM2​​=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

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}=0.83σP2​β2σM2​​=0.9772×0.16720.1562​=0.83 p是coefficient 那coefficient termination就代表p的平方吗

2022-01-16 13:42 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}=0.83σP2​β2σM2​​=0.9772×0.16720.1562​=0.83 请问这个题目用的公式在讲义那页？

2021-08-22 14:21 1 · 回答