Can No-Arbitrage SDF Models with Regime Shifts Explain the Correlations between Commodity, Stock, and Bond Returns?

We investigate whether it is possible to find a Stochastic Discount Factor (SDF) that jointly prices the cross-section of eight U.S. portfolios of stocks, Treasuries, corporate bonds, and commodities and replicates their observed moments, and especially correlations. We use the first three principal components extracted from a set of 112 U.S. macro variables as pricing factors. We also introduce commodity-based factors in the SDF, motivated by commodity pricing theories and we use them either separately or in conjunction with the macro-based ones. We report that it is not impossible to find a set of macroeconomic factors able to jointly price the cross section of stocks, bonds, and commodities; however, this task is accomplished by a small set of commodity-based factors. Observed correlations for commodities are perfectly matched by a parsimonious, single state, diagonal factor VAR model where only three commodity-based factors enter the SDF. While introducing regimes does not improve the performance in all cases, they could be beneficial to replicating correlations among commodity and bond portfolios