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梦梦 · 2025年06月13日

为什么小盘股和成长股,大盘股和价值股不是互斥

NO.PZ2023101902000056

问题如下:

To conduct a Style Analysis on a mutual fund that cannot short securities, you regresses the fund's returns against five regressors: T-bills, a small capitalization index, a large capitalization index, a growth index and a value index. The regression returned is: R(t) = 0 ×TBILL - 0.2 ×SMALL + 1.4 ×LARGE + 0.3 ×GROWTH + 0.7 ×VALUE + 1.51. Your colleague Jane criticizes your style analysis with the following statements: I. You should not have a zero coefficient (0 ×TBILL) II. You should not have a non-zero intercept (1.51) III. You should not have a negative coefficient (-0.2 ×SMALL) IV. You should not have a coefficient that exceeds one (1.4 ×LARGE) V. The sum of the coefficients should not be different than 1.0 (0 - 0.2 + 1.4 + 0.3 + 0.7 = 2.2 which is not 1.0) Which of the criticisms is (are) correct?

选项:

A.None are correct, the regression is fine

B.II. I. and II. are correct only

C.III. IV. and V. are correct only

D.IV. All are correct

解释:

III. IV. and V. are correct only.The constraints are that the regression coefficients are between 0 and 1.0, and that they sum to 1.0 to represent comparison portfolio that is fully allocated to styles (and no negatives to reflect the prohibition on short positions).In regard to I., zero is an acceptable coefficient; i.e., the fund is not sensitive to T bills.In regard to II., the intercept is the return that cannot be attributed to a passive style (asset allocation) and "can be attributed to security selection within asset classes, as well as timing that shows up as periodic changes in allocation" (i.e., alpha; skill or luck).

老师好,但是我感觉这几类资产的部分并不是互斥的啊,比如小盘股和成长股,大盘股和价值股,这两大类就有交叉。

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