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Combined Simulator of Annual S&P Returns vs Volatility + (maybe) Earnings Yield

We combine two models: S&P total returns vs volatility only or vs volatility and earnings yield. See the data and code in https://github.com/asarantsev/earnings-yield-annual-simulator

This research continues blog posts on modeling returns vs earnings yield and volatility and returns vs only volatility. But previous Python code combines fitting of this model and simulation. Here, we removed plots (quantile-quantile and autocorrelation function for residuals) and analysis of skewness, kurtosis, etc. We only keep fitting regression code necessary for actual simulations. Also, we combine these two options (with or without earnings yield) so a person can make a choice. We also present a choice between simulating innovations using Gaussian multivariate distribution or kernel density estimation.

We also change the models slightly: Previously, we normalized returns Q(t) and earnings growth G(t) by dividing them by annual volatility V(t). Here, we instead model these as regression

Q(t)/V(t) = a/V(t) + b + Z(t).

Future research will include Shiller CAPE (with various averaging windows), the new valuation measure (also adapted for various averaging windows), and bond spreads.

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Andrey Sarantsev

Responses

  1. Simulator of S&P Returns using volatility only or with Shiller CAPE – My Finance

    […] the previous blog, I wrote combined simulator for Standard & Poor 500 annual total returns with two […]

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  2. Annual simulator with volatility and the new valuation measure of S&P 500 – My Finance

    […] This is similar to the combined simulator for volatility and cyclically adjusted earnings yield: see this post and this post. We do not allow the user to choose initial conditions for the simulator, instead […]

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