Mimicking Portfolio construction

Construction of mimicking portfolio

In this post, I apply the mimicking portfolio analysis based on the method from Vassalou (2003), who use double-sorted equity portfolios as the proxy of future GDP growth.

I construct the mimicking portfolio in the following steps:

• First, run the simple regression of macroeconomic variable on several groups of base assets one by one

\[ MP_{m} = \alpha + B\ C + e_m, \quad \text{for} \quad m=1,2, \cdots, M, \]

where $ MP_{m} $ is the \(T\times 1\) matrix of macro factor \(m\), \(B\) is the \(T \times N\) base assets matrix and \(C\) is the \(N \times 1\) corresponding coefficient vector of mimicking portfolios on base assets. N is the number of base assets, which depends on the selected model (FF3, FF5, Q5 or firm characteristics).

• Second, the macro factor-mimicking portfolio equals to the base assets times the corresponding coefficients. \[ r_{MP} = B \ C\]

Note:

1. We should use the sorted portfolios' returns rather than the long-short factor to build the mimicking portfolios. For example, we will have 25 portfolios if choose two factors.
2. Think about whether to demean the factors or not.

   • I collect the macro factors from FRED-MD and adjust them by following McCracken and Ng (2016). They provide a method to demean and standardise the factors.

   • For the right-hand side, I follow Giglio and Xiu (2021) to use the market portfolio and FF3 to build the mimicking portfolios.

Test

1. T-test for time-series of mimicking portfolios with Newey and West (1987) adjustment.

2. Run with famous factors, such as SMB, HML and MKT, and examine whether the pricing model can explain the mimicking portfolio returns with insignificant alpha.

Reference

Giglio, Stefano, and Dacheng Xiu. 2021. “Asset Pricing with Omitted Factors.” Journal of Political Economy 129 (7). The University of Chicago Press: 1947–90. doi:10.1086/714090.

McCracken, Michael W, and Serena Ng. 2016. “FRED-MD: A Monthly Database for Macroeconomic Research.” Journal of Business & Economic Statistics 34 (4): 574–89. doi:10.1080/07350015.2015.1086655.

Newey, Whitney K., and Kenneth D. West. 1987. “A Simple, Positive Semi-Definite, Heteroskedasticity and Autocorrelation Consistent Covariance Matrix.” Econometrica 55 (3). [Wiley, Econometric Society]: 703–8. doi:10.2307/1913610.

Vassalou, Maria. 2003. “News Related to Future GDP Growth as a Risk Factor in Equity Returns.” Journal of Financial Economics 68 (1): 47–73. doi:10.1016/S0304-405X(02)00248-9.