My Finance

We did so many versions that we decided to focus on the simple one. We published it here. It has 8 innovation series.

5 asset classes (all returns are total, nominal):

1. US stocks
2. developed stocks
3. emerging stocks
4. 10-year Treasury bonds
5. corporate bonds

4 market factors:

1. Measure (last day of year)
2. Volatility (annual)
3. BAA rate (average daily December)
4. 10-year Treasury rate (average daily December)

Features: This is NOT a stationary model. All innovations are IID Gaussian, tested by Shapiro-Wilk and Jarque-Bera normality tests, and by the Ljung-Box test for 5 and 10 lags for original and absolute values of innovations.

Updates:

1. Volatility and S&P returns data thanks to Angel Piotrowski and Ian Anderson, 1928-2025
2. Rate data for BAA and 10-year Treasury extended back to 1925 from 1927
3. Corporate bond returns data extended 1926-1973 using Ibbotson SBBI data thanks to Smaila Amoanu
4. Yeo-Johnson transform of log volatility with index -0.5 modeled as autoregression with lag 1
5. Log risk spread of logs as autoregression with lag 1
6. Valuation measure modeled as autoregression with lag 1 with stochastic volatility
7. Log BAA rate as random walk with stochastic volatility
8. Treasury 10-year returns (coupon bonds) deterministic formula thanks to Aswath Damodaran
9. Corporate bond returns minus rates (log duration) as a function of rate change
10. Domestic, developed, emerging stocks vs rate change and valuation measure (not risk spread) with stochastic volatility

Future Research:

1. A version with an objective Bayes inference for regression coefficients
2. An online version instead of the old version with only 3 asset classes and non-Gaussian innovations
3. Front end redesign, Smaila promised to do this
4. New versions of the main model: For international stocks, its own dividend-based valuation measure rather than rely on US-based; for Treasury bonds, use actual returns data from SBBI or FRED to compare with predicted returns from Damodaran’s formula