RiskyAvg under the Usual conditions is way too high.

[sbenthall]

from sharkfin.expectations import UsualExpectations
from sharkfin.markets import MockMarket

ue = UsualExpectations(MockMarket())
ue.calculate_risky_expectations()
ue.risky_expectations()

Output:
{'RiskyAvg': 1.1474632135003242, 'RiskyStd': 0.18587207098922232}

[sbenthall]

Most likely due to this.

https://github.com/sbenthall/SHARKFin/blob/master/sharkfin/expectations.py#L116-L131

[sbenthall]

I've corrected some of my bad math.

Now the UsualExpectations are somewhat more reasonable:

{'RiskyAvg': 1.0916031021270372, 'RiskyStd': 0.09296520824951145}

But they are still too high for quarterly numbers.

I believe the reason for this is related to #215 . Namely:

• We have the rate of return and standard deviation of the S&P500 prices. We've been taking these as statistics on the price process.
• Backing up from that, we've been computing the parameters of the dividend process.
• Naturally, our computed expected value of returns will be higher than original S&P500 price process, because we are including a dividend. If our daily price-dividend ratio is 1000, then for 60 days in a quarter, there is a bonus of 6% returns from the dividend not included in the original S&P500 statistic. (On top of the ~1.038 quarterly return we would get from the unadulterated S&P500 process).

We have a few options at this point.

• Assume that the S&P500 process prices in returns, and so compute the dividend parameters that would make the Lucas return process match the S&P500. This will require doing some more math.
• Argue that while these expected values are high, they are due to unrealistic Lucas assumptions that we know not to be true. For example, dividends have lower standard deviation than would be predicted from price variation. So we just chalk this awkwardness up to the Lucas construction.

This also raises the "uninteresting" and inconvenient issue that in the real world, prices are systematically reduced when dividends are paid out.

What I'll do is push the quick fix for now (which gets us down from 1.15 quarterly to 1.09 quarterly), since the 1.09 figure might be easier for @alanlujan91 to work with on #205, and then raise this in a meeting.

[sbenthall]

Target: 1.012272234 quarterly return

[sbenthall]

https://www.investopedia.com/terms/e/epp.asp#:~:text=Theoretically%2C%20the%20premium%20should%20actually%20be%20much%20lower%20than%20the%20historical%20average%20of%20between%205%25%20and%208%25.