Risk & Portfolio

CPPI on 100 with a floor of 80 and a multiplier of 4: start with 80 in the risky asset. After +5% and +3% the exposure grows to 96 and the value to 106.9; after −10% the value is 96.2. Then a one-day −30% crash: exposure was 64.8, the loss is 19.4, and the value ends at 76.8 — below the 80 floor. CPPI protects the floor only if prices move smoothly enough to sell in time.

• The floor breaks in a gap larger than 1/m (here 25%); with a higher multiplier the crash needed is smaller.
• It sells after falls and buys after rises. When many follow the same rule, the selling feeds the fall — the Brady Commission pointed to portfolio insurance in the 1987 crash.
• After a fall it can lock into cash and miss the recovery: the cushion is gone.

value, floor, m = 100.0, 80.0, 4                          # CPPI: risky exposure = 4 x cushion
for move in [0.05, 0.03, -0.10, -0.30]:                    # the last day is a crash
    risky = min(m * (value - floor), value)
    value = value + risky * move
    print(f"{move:+.0%}  exposure {risky:5.1f}  value {value:5.1f}  floor {floor}")

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