Portfolio share with 'bad' assets

[Mv77]

Hi,

Working with the ConsPortfolioModel tool while trying to fix the CGMPortfolio remark, I noticed that the solution does not behave well when the risky asset is bad enough that the agent never wants to hold it (e.g. setting RiskyAvg = 0.8), and one works with continuous shares. The solution method in this setting fails because it finds no share satisfying the FOC so it goes to the line:

print('No optimal controls found for a=' + str(aNrmGrid[j]))

for every aNrm level, at every time period, and does not compute the consumption function.

I understand this case does not make much sense from a modeling point of view, but wanted to report the error nonetheless.

[mnwhite]

Yes, we need to handle that case-- I though I did, in fact. It can be done as an early step: compute E[Risky] and if it's no greater than Rfree, then ShareFunc should be constant at zero. Thanks for catching this. Stress testing / "dumb testing" is a good idea.

…

On Wed, Jul 1, 2020, 8:12 PM Mateo Velásquez-Giraldo < ***@***.***> wrote: Hi, Working with the ConsPortfolioModel tool while trying to fix the CGMPortfolio remark, I noticed that the solution does not behave well when the risky asset is bad enough that the agent never wants to hold it (e.g. setting RiskyAvg = 0.8), and one works with continuous shares. The solution method in this setting fails because it finds no share satisfying the FOC so it goes to the line: print('No optimal controls found for a=' + str(aNrmGrid[j])) for every aNrm level, at every time period, and does not compute the consumption function. I understand this case does not make much sense from a modeling point of view, but wanted to report the error nonetheless. — You are receiving this because you are subscribed to this thread. Reply to this email directly, view it on GitHub <#741>, or unsubscribe <https://github.com/notifications/unsubscribe-auth/ADKRAFPZKFV3D46S5QE4F6TRZPGGRANCNFSM4OOIILSA> .

[llorracc]

Mateo, Could you make a PR with the fix that Matt recommends? On Wed, Jul 1, 2020 at 8:26 PM Matthew N. White <[email protected]> wrote:

…

Yes, we need to handle that case-- I though I did, in fact. It can be done as an early step: compute E[Risky] and if it's no greater than Rfree, then ShareFunc should be constant at zero. Thanks for catching this. Stress testing / "dumb testing" is a good idea. On Wed, Jul 1, 2020, 8:12 PM Mateo Velásquez-Giraldo < ***@***.***> wrote: > Hi, > > Working with the ConsPortfolioModel tool while trying to fix the > CGMPortfolio remark, I noticed that the solution does not behave well when > the risky asset is bad enough that the agent never wants to hold it (e.g. > setting RiskyAvg = 0.8), and one works with continuous shares. The solution > method in this setting fails because it finds no share satisfying the FOC > so it goes to the line: > > print('No optimal controls found for a=' + str(aNrmGrid[j])) > > for every aNrm level, at every time period, and does not compute the > consumption function. > > I understand this case does not make much sense from a modeling point of > view, but wanted to report the error nonetheless. > > — > You are receiving this because you are subscribed to this thread. > Reply to this email directly, view it on GitHub > <#741>, or unsubscribe > < https://github.com/notifications/unsubscribe-auth/ADKRAFPZKFV3D46S5QE4F6TRZPGGRANCNFSM4OOIILSA > > . > — You are receiving this because you are subscribed to this thread. Reply to this email directly, view it on GitHub <#741 (comment)>, or unsubscribe <https://github.com/notifications/unsubscribe-auth/AAKCK76QYIJAMD55JS4MSZ3RZPH35ANCNFSM4OOIILSA> .

-- - Chris Carroll

[Mv77]

Sure, I can give it a go this afternoon.

[Mv77]

I'm getting started on this now.

The proposed solution is to -before solving- check if there is an equity premium, and if there isn't set the share to zero.

However, checking the code I see that you now allow income shocks and risky returns to be non-independent. This made me think: are there instances where it is optimal to have a positive share even if there is no premium? Maybe if the asset is a very good hedge against income shocks?

[mnwhite]

Yes, I was thinking about that, and the fact that future realizations of non-zero risky share might need to be computed for the "sticky portfolio" version of the model. Your intuition is correct that if asset returns and labor income are negatively correlated, then even a negative spread can result in non-zero share. Here's how to handle this robustly. In the step where it looks for bounds of the "first order condition crossing" in Share at some aNrm value (around line 790), if the value of the "FOC function" at s_t=0 implies that the agent would like to hold a negative share, choose s_t=0 and don't do the linear solve step. That is, if FOC_s[j,0] < 0, s_t should be zero and the stuff in the try/except block need not be done. Likewise, if FOC_s[j,-1] > 0, the agents wants to hold more than 100% of her wealth in the risky asset, so s_t = 1 for this a_t and the linear solving step can be skipped. Ideally, that try/except should not be there-- the code should always be able to find an appropriate solution to s_t \in [0,1] for any a_t. Man, I really thought I handled this.

…

On Thu, Jul 2, 2020 at 2:21 PM Mateo Velásquez-Giraldo < ***@***.***> wrote: I'm getting started on this now. The proposed solution is to -before solving- check if there is an equity premium, and if there isn't set the share to zero. However, checking the code I see that you now allow income shocks and risky returns to be non-independent. This made me think: are there instances where it is optimal to have a positive share even if there is no premium? Maybe if the asset is a very good hedge against income shocks? — You are receiving this because you commented. Reply to this email directly, view it on GitHub <#741 (comment)>, or unsubscribe <https://github.com/notifications/unsubscribe-auth/ADKRAFKL2MMB36MRGJMNAVDRZTFZDANCNFSM4OOIILSA> .