- CFA Exams
- CFA Exam: Level II 2021
- 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 we have the three portfolios with factor sensitivities given in the table below. Using the information in the table, create an arbitrage portfolio using a short position in A and B and a long position in C. What is the expected cash flow on the arbitrage portfolio for a $10,000 investment in C?

A | 0.12 | 2

B | 0.06 | 1

C | 0.08 | 1.25

B. $50

C. $80

Portfolio | Expected Return | Factor Sensitivity

A | 0.12 | 2

B | 0.06 | 1

C | 0.08 | 1.25

A. $30

B. $50

C. $80

Correct Answer: B

The arbitrage portfolio must have zero sensitivity to the factor. We first need to find the proportions of A and B in short positions that combine to produce a factor sensitivity equal to 1.25, the factor sensitivity of C, which we will hold long. Using w as the weight on A in the short position,

2w + 1(1 -?? w) = 1.25 -> w = 0.25

Hence, the weights on A and B are -??0.25 and -??0.75, respectively. These sum to -??1. The arbitrage portfolio has zero net investment. The weight on C in the arbitrage portfolio must be 1, so that combined with the short position, the net investment is 0. The expected return on the arbitrage portfolio is 1(0.08) -?? 0.25(0.12) -?? 0.75(0.06) = 0.08 ?- 0.075 = 0.005 or 0.5 percent. For $10,000 invested in C, this represents a $10,000 x 0.005 = $50 arbitrage profit.

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