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这是名字 · 2025年06月21日

对本题答案有疑问

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:

A.

0.0960

B.

0.1470

C.

0.4900

D.

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.

这题stock是dependent variable啊,所以应该是1.050*0.3/0.2才对吧。。

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