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sbenthall / SHARKFin

Simulating Heterogeneous Agents with Finance
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Scaling the dividend process relative to the S&P500 #215

Closed sbenthall closed 1 year ago

sbenthall commented 1 year ago

We have two numbers for the S&P500, which are the historical mean and standard deviation of its price -- call these $\mu_P$ and $\sigma_P$.

I believe we've settled on how to derive the growth rate and standard deviation from these numbers.

Ultimately, the consumers are interested in the returns on the risky asset, which includes both the price and the dividend.

I believe that implies that the distribution of returns implied by the USUAL expectations is not the same as the distribution over changes to the price.

This is somewhat subtle, and I have code in #210 that makes these adjustments.

The problem I want to raise in this PR is that.... aren't the returns factored into the price of the S&P500, because of how the price is adjusted by the exchange to deduct the value of the dividends? I'm wondering if there's any holes in the logic here.

mesalas commented 1 year ago

paper on dividend and variation:

https://www.jstor.org/stable/pdf/24465694.pdf?refreqid=excelsior%3A46d10af3001edcaf36d3f7f5ffde9be0&ab_segments=&origin=&initiator=&acceptTC=1

sbenthall commented 1 year ago

As we discussed, I think that the relationship between the price and the dividend, and how it deteriorates as we depart from the LAP assumptions, should be something we write about in the paper.

@mesalas you convinced me that since in reality the price and dividend are not as related as they are in the LAP model, worrying too much about this point of model calibration is silly.

sbenthall commented 1 year ago

Closing, since we are no longer calibrating on the S&P500