NO.PZ2023040502000015
问题如下:
Anna Gabor is an analyst with an investment management firm. She is investigating the impact of leverage on annual ROE in the firm's Eurozone equities fund ("the fund").She collects data on the 72 stocks in the fund, including company size as an independent variable.
Exhibit 1 shows the results from estimating the model
As part of her analysis Gabor compares the predictions of her model
with the actual ROE for two stocks in the portfolio which have the same debt
ratio: A and B, which have market capitalizations EUR 100 million and EUR 200
million respectively.
选项:
A.0.83
B.1.2
C.6.36
解释:
A is correct because this reflects the right application of the
results of the regression.
The coefficient of the independent variable Sizei is b1
= -0.012. This implies a negative relationship between the log of market
capitalization and ROE.
The prediction of ROE, according to the regression, is given by the
equation: Ri = b0 + b1(Sizei) +
b2(D/Ei)
Or, reading the coefficients from Exhibit 1: Ri = 0.2248 -
0.012(Sizei) - 0.0172(D/Ei)
We are told that the debt/equity ratio D/E is the same for both
companies, therefore 0.2248 - 0.0172(D/Ei) is the same amount for
both companies A and B; let us say that 0.2248 - 0.0172(D/Ei) = K (a
constant) for both A and B
Then Ri = K - 0.012(Sizei)
The market cap of Company A is EUR 100 million, therefore SizeA
= ln (100)
The market cap of Company B is EUR 200 million, therefore SizeB
= ln (200) = ln (2) + ln (100)
ROE for Company A is K - 0.012*ln(100) and the ROE for Company B is: K
- 0.012*ln(100) - 0.012*ln(2)
So
ROE for Company A exceeds that for Company B by: 0.012 * ln (2) = 0.008318 or
approximately 0.83 percentage points.
为什么size要用ln100,ln200,而不是直接代入?题目里哪里可以看到用ln?