关于20%和30%

NO.PZ2024120401000067

问题如下：

We regressed daily returns of a stock (dependent variable) against a market index (independent variable). The regression produced a beta for the stock, with respect to the market index, of 1.050. The stock's volatility was 30.0% and the market's volatility was 20.0%. If the regression's total sum of squares (TSS) is 0.300, what is the regression's explained sum of squares (ESS)?

选项：

0.0960

0.1470

0.4900

1.2500

解释：

As β = Cov(stock, index) / σ²(index) = ρ * σ(stock) / σ(index), it follows that:

ρ = β * σ(index) / σ(stock).

in this case, ρ = 1.050*20%/30% = 0.70, and R² = correlation² = 0.70² = 0.49.

Since R2 = ESS/TSS, ESS = R2 * TSS. In this case, ESS = 0.49*0.30 = 0.1470.

volatility是代表方差还是标准差？用不用开根号。

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1 个答案

李坏_品职助教 · 2025年06月07日

嗨，努力学习的PZer你好：

volatility代表的是标准差。

这道题里面The stock's volatility was 30.0% ，所以股票的σ = 0.3.

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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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NO.PZ2024120401000067 问题如下 We regresseily returns of a sto(pennt variable) against a market inx (inpennt variable). The regression procea beta for the stock, with respeto the market inx, of 1.050. The stock's volatility w30.0% anthe market's volatility w20.0%. If the regression's totsum of squares (TSS) is 0.300, whis the regression's explainesum of squares (ESS)? A.0.0960 B.0.1470 C.0.4900 1.2500 β = Cov(stock, inx) / σ2(inx) = ρ * σ(stock) / σ(inx), it follows that: ρ = β * σ(inx) / σ(stock).in this case, ρ = 1.050*20%/30% = 0.70, anR2 = correlation2 = 0.702 = 0.49. SinR2 = ESS/TSS, ESS = R2 * TSS. In this case, ESS = 0.49*0.30 = 0.1470. 这题stock是pennt variable啊，所以应该是1.050*0.3/0.2才对吧。。

2025-06-21 22:15 1 · 回答