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Factor Analytics Capital Management makes portfolio recommendations using various factor models. Mauricio Rodriguez, a Factor Analytics research analyst, is examining the prospects of two portfolios, the FACM Century Fund (CF) and the FACM Esquire Fund (EF).
The variance of returns are identical for the two funds. The estimates in Exhibit 1 were derived for CF and EF using monthly data for the past five years.
Supervisor Barbara Woodson asks Rodriguez to use the Capita! Asset Pricing Model (CAPM) and a multifactor model (APT) to make a decision to continue or discontinue the EF fund. The two factors in the multifactor model are not identified. To help with the decision, Woodson provides Rodriguez with the capital market forecasts in Exhibit 2.
After examining the prospects for the EF portfolio, Rodriguez derives the forecasts in Exhibit 3.
Rodriguez also develops a 2-factor macroeconomic factor model for the EF portfolio. The two factors used in the model are the surprise in GDP growth and the surprise in Investor Sentiment. The equation for the macro factor model is:
During an investment committee meeting, Woodson makes the following statements related to the 2-factor macroeconomic factor model.
Statement 1: An investment combination in CF and EF that provides a GDP growth factor beta equal to one and an Investor Sentiment factor beta equal to zero will have lower active factor risk than a tracking portfolio consisting of CF and EF.
Statement 2: When markets are in equilibrium, no combination of CF and EF will produce an arbitrage opportunity
In their final meeting, Rodriguez informs Woodson that the CF portfolio consistently outperformed its benchmark over the past five years. Rodriguez makes the following comments to Woodson: "The consistency with which CF outperformed its benchmark is amazing. The difference between the CF monthly return and its benchmark return was nearly always positive and varied little over time."
Are Woodson's Statements 1 and 2 regarding the macro factor model correct?
First, calculate the continuously compounded risk-free rate as ln( 1.040811) = 4% and then calculate the theoretically correct futures price as follows:
Then, compare the theoretical price to the observed market price: 1.035 - 1,025 = 10. The futures contract is overpriced. To take advantage of the arbitrage opportunity, the investor should sell the (overpriced) futures contract and buy the underlying asset (the equity index) using borrowed funds. Norris has suggested the opposite. (Study Session 16, LOS 59.f)