My Finance

Well-diversified stock portfolios are well-explained by three factors:

• market exposure to the equity premium (total returns minus risk-free returns)
• size (market capitalization) computed as returns of small minus returns of large stocks
• value (measured by book-to-market ratio) computed as returns of stocks with high minus low ratio

The is usually very high. Of course, such factors might be not constant over time. For example, the is famously unstable. To model properly such portfolios, we must model also the evolution of these factors, by showing how the size and value are changing. I am working on this based on

The market exposure is already modeled since equity premium divided by annual volatility is independent identically distributed Gaussian. Thus I decided to model returns of size and value factors. I took annual returns 1927-2025 from Dartmouth College data library. See the GitHub repository.

We succeeded for value but failed for size. We cannot use this in our future research!