CFA Practice Question

There are 119 practice questions for this study session.

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?

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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