The Return Shortfall in Equity Markets by Robert Michaud
The fundamental relation between economy-wide growth and return on risky assets is given by rrisky = reconomy * leveragerisky. Since the leverage of risky assets is must be greater than one, this formula contradicts the popular notion that the stock market cannot grow faster than the economy forever. We note that this relation does not seem to hold well historically in all economies, and that returns are typically lower than predicted. Where, then, does this money go? We estimate the percentage of profits that are not returned to shareholders in the major economies and attempt to provide an explanation.
Portfolio Choice and the Market Risk Premium with Multi-Period Rebalancing by Robert Michaud
In an economy with one risk-free and a number of risky assets, investors optimize their portfolio each period according to their preferences. If none of the parameters of their optimization problem change, then neither does the portfolio weights of the assets in the optimal portfolio. For example, with stationary return distributions and CRRA preferences, then assets will always be demanded in exactly the same proportions. We assume investors will rebalance their portfolio back to the optimal weights after every market move. We show that when investors optimize every period and there is a fixed supply of the assets, the risk premium will change to support a no trade equilibrium. Alternatively, we show that new debt and equities will necessarily be issued or retired to maintain a constant equity premium. Which of these two scenarios is closer to the truth, we leave to the reader.
How to Statistically Estimate APT Factors: Two Tests of the Most Common Statistical Factor Estimation Methods by Robert Michaud
This paper proposes and implements two tests to help identify the superior statistical factor estimation method with two sets of data, one using historical data, and the other a simulation using a linear factor model with excess returns. The hope is that under most general scenarios one estimation method will prove superior. We test standard principal components analysis on its own and with a Bayesian shrinkage method (Ledoit 1997), and the Connor Korajczyk (1986) variant of PCA. For each of these, we further examine constraining and bootstrapping each method. We find CK to perform well in-sample, but not out-of-sample, and both bootstrapping and the market portfolio constraint to improve upon it.
