Market Psychology

A fund returns +30%, +25%, −20%, −10% and +15%: 6.1% a year. Its investors put in 100, then 200 and 400 after the two good years, and take out 300 and 100 after the bad ones. Their money-weighted return is −3.1% a year, and they end with 247 for a net 300 put in. Same fund, opposite results; the difference is timing the flows. Dichev (2007) found this gap in market-wide data.

• “Smart” and “dumb” are labels for after the fact. Institutions herd and chase too; retail flows are not always wrong.
• Insider purchases are informative on average (Lakonishok & Lee 2001), insider sales much less so — many sales are for diversification or tax.
• Commercials in the COT report are mostly hedgers; their positions reflect hedging needs as well as views.

r = np.array([0.30, 0.25, -0.20, -0.10, 0.15])   # a fund's return each year, made up
flow = np.array([100, 200, 400, -300, -100])     # money investors put in (+) or take out (-) at each year's start

value = 0.0
for f, x in zip(flow, r):
    value = (value + f) * (1 + x)
fund = np.prod(1 + r) ** (1 / len(r)) - 1        # time-weighted: what the fund earned

cash = np.append(-flow, value)                   # the investors' own cash flows
roots = np.roots(cash[::-1])                     # money-weighted: the IRR of those flows
irr = [z.real - 1 for z in 1 / roots if abs(z.imag) < 1e-9 and z.real > 0]   # per-year rate

Assumes import numpy as np and import pandas as pd. Each snippet carries its own example numbers; the comments say which are made up.