My Finance

We found a connection between Moody’s BAA bond rates and investment-grade corporate bond returns (measured by a Bank of America wealth index) Also, BAA bond rates are well modeled by a simple autoregression. This enables us to model both large stock returns and corporate bond returns. Previously, we modeled large stock returns (measured by S&P) using annual volatility and the new valuation measure. We also used bond spreads but not rates, including them in our model. Our next actions are:

• Replicate this blog with real corporate bond returns, after adjusting for inflation. We will replace (nominal) bond rates with real rates: Subtract past year’s inflation from the end of past year rate. This will be enough for an autoregression of rates. But for bond returns, we might include both nominal rate and inflation rate. Update: We failed to do this, since for the simple regression of real returns minus real rates vs duration. This is too low, and adding volatility does not improve this. See the GitHub/asarantsev repository Corporate-Bonds-Annual-Data. To be fair, residuals are IID normal for all these regressions, but this doesn’t matter.
• We need to model inflation separately, presumably as an autoregression process with volatility: If is the inflation rate in year then try or Update: We used data 1928-2024 and failed. All autocorrelation plots are unacceptable, and residuals never follow normal distribution. All normality tests fail, and the autocorrelation function L1 norm for first 5 lags are not compatible with IID assumption. See the GitHub/asarantsev repository Inflation-Modeling-1928-2024 for data and code. Strange, because we have both nominal and real returns divided by volatility modeled as IID Gaussian. So the difference between them: inflation/volatility should be IID Gaussian.
• Include these rates in the new valuation measure modeling of stock market returns. For real returns, pick real rates. for nominal returns, include nominal rates. Or maybe include both rates, real and nominal? Equivalently, include nominal rate and last year’s inflation.
• Is the distribution of residuals important? (a) simulate using kernel density estimation with Silverman’s bandwidth. Unfortunately, we cannot rely on existing functions in Python: They can only make identity covariance matrix of simulated data. (b) simulate using multivariate normal distribution with covariance matrix estimated from the data. Then compare average total returns. This will answer the second question from this post.
• Add small stocks to our research, replicating this manuscript. We can then fix capitalization ratio to the benchmark, for example 10 times smaller capitalization than S&P 500.

Then we need to update the simulator accordingly. First, we create a complete version in Python, when we can change initial values and the simulation of residuals. Second, we create a simplified version of this simulator as a web app. We will have two sliders: (a) Stocks size; (b) Bonds vs stocks.

We could make a similar slider for bond ratings, but it’s hard to quantify bond ratings similarly to stock size.