CPPI and Portfolio Insurance

Constant Proportion Portfolio Insurance (CPPI) is a way to put a floor under a portfolio using nothing but a trading rule, no options required. The promise is appealing: pick a value you never want to fall below, say 80% of today's wealth, and CPPI mechanically manages your risky-versus-safe allocation so that, in the absence of a sudden gap, you can't breach it. It's the do-it-yourself version of Tail-Risk Hedging, insurance built from rebalancing instead of from bought puts.

The trick rests on one number, the cushion: how far your portfolio currently sits above the floor. When the cushion is fat you can afford to take risk; when it's thin you must pull risk off the table. CPPI turns that intuition into an exact rule.

The rule

Define the floor $F$ (the minimum value you'll protect) and the cushion $C = V - F$, where $V$ is your current portfolio value. Then hold an amount in the risky asset equal to a fixed multiplier $m$ times the cushion:

$$E = m \times C = m \,(V - F),$$

with the rest parked in a safe asset (cash or short bonds). Here $E$ is the dollar exposure to the risky asset, $m$ is the multiplier (a constant, typically 3 to 6), and $C$ is the cushion. As the portfolio rises, the cushion grows and you buy more risk; as it falls toward the floor, the cushion shrinks and you sell risk, so that if the cushion ever reached zero you'd be fully in the safe asset and the floor would hold.

Worked example

Start with $100, a floor of $80, and multiplier $m = 4$. The cushion is $100 - 80 = 20$, so you hold $4 \times 20 = 80$, i.e. $80, in risky assets and $20 in cash.

Now the market falls 10%. Your risky sleeve drops from $80 to $72, so the portfolio is $72 + 20 = 92$. The new cushion is $92 - 80 = 12$, and the target risky exposure is $4 \times 12 = 48$. You currently hold $72 of risk, so you sell $24, cutting exposure right into the decline. Fall another 10% and the cushion shrinks again, you sell more, and your risky exposure marches toward zero as you near the floor. The rule sells low, on purpose, to protect the floor.

Conversely, if the market had risen 10%, the risky sleeve grows to $88, the portfolio to $108, the cushion to $28, and the target exposure to $4 \times 28 = 112$, so you'd buy more risk. CPPI is momentum-like: it adds risk into strength and cuts it into weakness.

Multiplier, gap risk, and the option connection

The multiplier is a bet on the worst single-day move. CPPI's floor is safe only if the market can't fall more than $1/m$ before you rebalance. With $m = 4$, a drop bigger than $25\%$ in one gap, before you can trade, pushes the portfolio through the floor, "gap risk." Higher $m$ means more upside participation but a thinner safety margin. This is the fundamental limit: CPPI insures against gradual declines, not overnight crashes.

Where it fits

CPPI sits alongside Drawdown Control (which de-risks based on distance below a peak rather than above a floor) and Vol Targeting (which scales exposure by volatility). All three are rule-based risk overlays that trade rather than hedge. CPPI's distinctive feature is the hard floor and the linear exposure-to-cushion rule, elegant and transparent, provided you respect its one true enemy: the gap you can't trade through.