Let ConsRiskyAssetModel handle time-varying Rfree

[Mv77]

I was getting errors trying to get ConsPortfolio to use time varying interest rates Rfree.

The culprit was that the share-limit calculation assumed Rfree is constant. This PR fixes the issue.

• Tests for new functionality/models or Tests to reproduce the bug-fix in code.
• Updated documentation of features that add new functionality.
• Update CHANGELOG.md with major/minor changes.

[codecov]

Codecov Report

Patch coverage: 75.00% and project coverage change: +0.02% 🎉

Comparison is base (b18c71f) 72.68% compared to head (39abdcd) 72.71%.

Additional details and impacted files

@@            Coverage Diff             @@
##           master    #1343      +/-   ##
==========================================
+ Coverage   72.68%   72.71%   +0.02%     
==========================================
  Files          78       78              
  Lines       13052    13057       +5     
==========================================
+ Hits         9487     9494       +7     
+ Misses       3565     3563       -2     

Files Changed	Coverage Δ
HARK/ConsumptionSaving/ConsRiskyAssetModel.py	44.55% <71.42%> (+0.18%)	⬆️
...ConsumptionSaving/tests/test_ConsPortfolioModel.py	100.00% <100.00%> (ø)

... and 1 file with indirect coverage changes

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[Mv77]

This is a pretty trivial PR and most of you are in Lausanne. Also, all tests pass and test coverage increases.

I'll merge without review.

[alanlujan91]

Can you confirm that the share limit applies to the 1 period solution and not just to the infinite horizon problem? I thought the share limit only existed in infinite horizon problem

[Mv77]

Hey, I think so. See below.

In any case we were computing that object even for LC calibrations (whether we're using it or not, which I'm not sure). And so time varying Rfree's resulted in errors.

Here's why I think the result applies:

As long as an agent has CRRA utility, no income, and decides on the share of wealth in stocks continuously, it is the case that $$v_t(m_t) = \Omega_t u(m_t)$$ for some possibly time-varying constant $\Omega$. This is true in infinite horizon and in finite horizon as long as every period satisfies that description (no income, etc) and the CRRA is constant.

So the portfolio problem is
$$\max_{s_t} E[\Omega_{t+1}u( a_t (R + s_t(\tilde{R} - R)))] = \Omega_{t+1}a_t^{1-\rho}\max_{s_t} E[u( R + s_t(\tilde{R} - R) )] )],$$
and I think we're using the FOC to the second problem to get the limiting share. If we interpret the limiting share as the share that would be optimal as assets become so large that income is irrelevant, it applies.

Does that sound right @llorracc ?