- CFA Exams
- CFA Level I Exam
- Study Session 16. Portfolio Management (1)
- Reading 44. Using Multifactor Models
- Subject 2. Factors and types of multifactor models

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**CFA Practice Question**

Suppose that an institution holds Portfolio X. The institution wants to use Portfolio Y to hedge its exposure to inflation. Specifically, it wants to combine X and Y to reduce its inflation exposure to 0. Portfolios X and Y are well diversified, so the manager can ignore the risk of individual assets and assume that the only source of uncertainty in the portfolio are the surprises in the two factors. The returns to the two portfolios are

R

_{X}= 0.08 + 0.5 F_{INFL}+ 1.0 F_{GDP}R

_{Y}= 0.06 + 1.5 F_{INFL}+ 2.5 F_{GDP}Calculate the weights that a manager should have on X and Y to achieve this goal.

A. 1.5 on X, and -0.5 on Y.

B. -1.5 on X, and 1 on Y

C. This is impossible, since the inflation sensitivity factors are both positive.

**Explanation:**We need to combine Portfolios X and Y in such a way that sensitivity to the inflation factor is zero. The inflation sensitivities of Portfolios X and Y are 0.5 and 1.5, respectively. With w the weight on Portfolio Y, we have

0 = 0.5 (1 -? w) + 1.5 w -> w = -??0.5

The weight on Portfolio Y in the new portfolio is -??0.5, and the weight on Portfolio X is 1.5 (-??0.5 + 1.5 = 1). For every $1.50 invested on Portfolio X, the institution shorts $0.50 of Portfolio Y. The new portfolio'??s return is

R = 0.09 + 0.25 F

_{GDP}

The intercept is computed as (1.50 x? 0.08) + (-0.5 x? 0.06) = 0.09, and sensitivity to the GDP factor is computed as (1.50 x 1.0) + (-??0.5 x? 2.5) = 0.25.

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