Investment and Risk Management 022-2023 Tutorial Arbitrage Pricing Theory and Multifactor Models Question 1

Portfolio	Expected Return
Factor Sensitivity
A	0.20	0.80
B	0.15	1.00
C	0.24	1.20

Assuming the one-factor model is correct and based on the data provided for Portfolios A, B, and C, determine if an arbitrage opportunity exists and explain how it might be exploited.

4. 
   Which type of factor model is most directly applicable to an analysis of the style orientation (for example, growth vs. value) of an active equity investment manager? Justify your answer.
   
5. 
   Suppose an active equity manager has earned an active return of 110 basis points, of which 80 basis points is the result of security selection ability. Explain the likely source of the remaining 30 basis points of active return.
   
6. 
   Address the following questions about the information ratio.
   

1. 
   What is the information ratio of an index fund that effectively meets its investment objective?
   

2. 
   What are the two types of risk an active investment manager can assume in seeking to increase his information ratio?
   

7. 
   A wealthy investor has no other source of income beyond her investments and that income is expected to reliably meet all her needs. Her investment advisor recommends that she tilt her portfolio to cyclical stocks and high-yield bonds. Explain the advisor’s advice in terms of comparative advantage in bearing risk.
   

Question 2
Carlos Altuve is a manager-of-managers at an investment company that uses quantitative models extensively. Altuve seeks to construct a multi-manager portfolio using some of the funds managed by portfolio managers within the firm. Maya Zapata is assisting him.
Altuve uses arbitrage pricing theory (APT) as a basis for evaluating strategies and managing risks. From his earlier analysis, Zapata knows that Funds A and B in Exhibit 1 are well diversified. He has not previously worked with Fund C and is puzzled by the data because it is inconsistent with APT. He asks Zapata gather additional information on Fund C’s holdings and to determine if an arbitrage opportunity exists among these three investment alternatives. Her analysis, using the data in Exhibit 1, confirms that an arbitrage opportunity does exist.
Exhibit 1. Expected Returns and Factor Sensitivities (One-Factor Model)