BitConnect and lending-platform Ponzis (2018)

BitConnect took bitcoin deposits into a “lending program” and credited interest of around 1% a day, said to come from a trading bot. Nothing was traded: interest and withdrawals were paid out of new deposits, and recruiters earned commissions down several levels of the investors they brought in. Credited balances compound, so the liabilities grow as

\[L_t = L_{t-1}(1 + i) + D_t - W_t, \qquad (1.01)^{365} \approx 38,\]

while the cash grows only with new deposits. Texas and North Carolina regulators ordered it to stop in January 2018, deposits dried up, and the platform closed within two weeks; the SEC later charged it with a two-billion-dollar fraud.

import matplotlib.pyplot as plt

import blockchainkit as bk
from blockchainkit.fraud.visualizers import plot_ponzi

Deposits grow, then stop at a regulator’s order

deposits = [100 * 1.03**day for day in range(120)] + [10.0] * 60
run = bk.fraud.simulate_lending_ponzi(deposits, daily_rate=0.01, withdrawal_rate=0.02)
print(f"collapsed on day {run.collapse}; raised {run.raised:,.0f}, paid out {run.repaid:,.0f}")
print(f"balances credited to investors at the end: {run.owed[-1]:,.0f}")
assert run.collapse is not None and 120 < run.collapse < 180
assert run.cash[-1] == 0 and run.owed[-1] > 0.5 * run.raised  # Owed, with nothing left.

fig, ax = plt.subplots(figsize=(9, 4))
plot_ponzi(run, ax=ax)
ax.set_xlabel("day")
ax.set_yscale("symlog", linthresh=100)
fig.tight_layout()

collapsed on day 149; raised 112,670, paid out 112,670
balances credited to investors at the end: 62,168

The referral pyramid

Each investor recruits two more, three levels deep, and every recruiter earns 7%, 3%, 2% and 1% on the deposits one to four levels below it.

sponsors, deposits_by = {}, {"root": 1_000.0}
level = ["root"]
for _ in range(4):
    nxt = []
    for parent in level:
        for k in range(2):
            child = f"{parent}.{k}"
            sponsors[child] = parent
            deposits_by[child] = 1_000.0
            nxt.append(child)
    level = nxt
commissions = bk.fraud.referral_commissions(sponsors, deposits_by)
by_depth = {}
for name, earned in commissions.items():
    by_depth.setdefault(name.count("."), []).append(earned)
averages = [sum(v) / len(v) for _, v in sorted(by_depth.items())]
print("average commission by depth:", [round(a) for a in averages])
assert averages == sorted(averages, reverse=True)  # The top of the pyramid earns most.

fig, ax = plt.subplots(figsize=(6, 4))
ax.bar(range(len(averages)), averages, color="#9333ea")
ax.set(xlabel="depth in the referral tree", ylabel="commission earned")
ax.set_title("Commissions flow to the top")
fig.tight_layout()

plt.show()

average commission by depth: [580, 420, 260, 140]

Exercise

With 1% daily interest and no withdrawals, how fast must daily deposits grow for the cash to keep pace with the credited balances? Compare with the breakeven growth of Ponzi’s own scheme.