[Paper Reading] In-sample and Out-of-sample Sharpe Ratios of Multi-factor Asset Pricing Models
Title: In-sample and Out-of-sample Sharpe Ratios of Multi-factor Asset Pricing Models Author(s): Raymond Kan*, Xiaolu Wang, Xinghua Zheng Year: 2019, visited the version revised on 22 Feb 2021 URL: https://papers.ssrn.com/sol3/papers.cfm?abstract_id=3454628 Definitions Optimal portfolio weight: For a mean-variance investor who wants to hold a portfolio with a target standard deviation of $\sigma$, then their optimal portfolio has weights of $$ w^* = \frac{\sigma}{\theta} \Sigma^{-1} \mu, $$ where $\mu = \mathbb{E}[r_t]$, $\Sigma = Var[r_t]$, and $r_t$ is the return of risky assets in excess of risk-free rate. $\theta$ is the Sharpe ratio. Sharpe Ratio: $\theta = \sqrt{\mu' \Sigma^{-1}\mu}$. In practice, the investor does not know the mean and covariance matrix of the factors; he has to estimate $\theta$ using historical data. Thus, we have the in-sample and out-of-sample Sharpe ratio as follows. In-sample...