Constant Proportion Portfolio Insurance (CPPI) Lab

Model dynamic floor discounting, cushion leverage, cash-lock risk, gap crash events, and synthetic option replication.

Market Presets:

Steady Bull Market: Strong equity uptrend (+16% return, 15% vol) expands the cushion rapidly, maintaining maximum equity participation and capturing market upside.

Parameters

1000000
Total investment principal to protect.
90.0
Guaranteed capital level at terminal maturity.
4.0
Cushion leverage factor ($E_t = m \times C_t$). Gap risk threshold = $1/m$.
1.0
Duration until protected capital guarantee matures.
4.5
Bond discount yield for present value of floor.
12.0
Annualized expected equity return.
18.0
Annualized standard deviation of risky returns.
100.0
Upper boundary on portfolio equity exposure.
Floor PV ($F_0$)
$860,409
$F_T \times e^{-rT}$
Initial Cushion ($C_0$)
$139,591
$V_0 - F_0$
Gap Risk Buffer
25.0% Drop
Threshold: $1/m$
Final Value ($V_T$)
$1,098,420
ACTIVE / PROTECTED
Initial Equity Exposure
55.8% ($558k)
$m \times C_0$
CPPI Portfolio Return
+9.84%
Protected Strategy
Buy & Hold Asset Return
+13.40%
100% Unhedged Equity
Guaranteed Floor at Maturity ($F_T$): $900,000 Minimum Path Cushion: $62,400
Dynamic reallocation: Risky equity weighting scales with cushion expansion/contraction, while risk-free bond reserve preserves capital floor.
Theoretical terminal payoff comparison: CPPI exhibits convex synthetic call-option payoff behavior above the guaranteed capital floor ($F_T$).

Matrix 1: Floor Protection % vs Multiplier ($m$) on Initial Equity Exposure (%)

Matrix 2: Asset Volatility vs Investment Horizon on Cash-Lock Risk (%)

Institutional Theory: CPPI Mechanics & Risk Dynamics

1. Continuous-Time Dynamic Allocation

Introduced by Fischer Black & Robert Jones (1987) and Andre Perold (1986), CPPI constructs an asymmetric risk profile by continuously adjusting exposure between a risky asset and a risk-free bond. The protected floor $F_t$ is discounted to present value:

$$F_t = F_T \cdot e^{-r(T - t)}$$ $$C_t = \max(V_t - F_t, 0)$$ $$E_t = \min(m \cdot C_t, V_t \cdot \text{Cap})$$

where $F_T$ is the guaranteed capital floor at maturity, $C_t$ is the cushion, and $m$ is the leverage multiplier.

2. The Cash-Lock Trap

If an adverse market downturn drives portfolio value $V_t$ down to the discounted floor $F_t$, the cushion vanishes ($C_t \to 0$). Under the strict algorithm:

$$C_t = 0 \implies E_t = 0 \quad \text{and} \quad B_t = V_t$$

The portfolio is 100% liquidated into risk-free bonds, earning exactly $r$ until maturity. It is permanently locked out of any subsequent market recovery, crystallizing underperformance.

3. Gap Risk & Critical Crash Threshold

In discrete rebalancing (daily, weekly), a sudden gap crash can breach the floor before the portfolio manager can deleverage. The maximum instantaneous drop without floor breach is strictly:

$$\text{Max Tolerated Crash} = \frac{1}{m}$$

For example, with $m = 4$, a single-day drop exceeding 25% causes $V_t < F_t$. The product guarantor must inject capital to satisfy the terminal guarantee.

4. Synthetic Option Replication & Whipsaw Decay

Under continuous trading without gap risk, CPPI synthetically replicates a zero-coupon bond plus a Call option. However, CPPI is an explicit momentum strategy:

$$\text{Whipsaw Loss} \propto m(m - 1) \sigma^2$$

It mechanically buys equities after market rises and sells after market falls. In oscillating, range-bound markets, this "buy-high, sell-low" dynamic generates severe path-dependent decay.

Quantitative Mastery Quiz

1. For a CPPI strategy with a multiplier $m = 5$, what is the maximum single-interval asset drop that can be sustained without breaching the capital floor?

2. What defines the "Cash-Lock Trap" in portfolio insurance?

3. Why does CPPI perform poorly in high-volatility, sideways (choppy) markets?

4. What is the fundamental operational difference between CPPI and Option-Based Portfolio Insurance (OBPI)?

Frequently Asked Questions

CPPI is a dynamic asset allocation strategy introduced by Black and Jones (1987) and Perold (1986) that guarantees a minimum capital floor at maturity while capturing equity upside. It dynamically allocates capital to a risky asset equal to a leverage multiplier ($m$) times the cushion (the excess of portfolio value over the present value of the guaranteed floor).

The cash-lock trap occurs when an adverse market downturn causes portfolio value to fall to or below the discounted floor. In this event, the cushion drops to zero, forcing the algorithm to liquidate 100% of risky assets into risk-free bonds. The portfolio is locked into cash until maturity and cannot participate in any subsequent market recovery.

Gap risk is the danger that a sudden discrete crash occurs before the manager can rebalance. If the risky asset drops by more than $1/m$ between rebalancing intervals (e.g. 25% drop when $m = 4$), the portfolio value breaches the floor, leaving the strategy underfunded and exposing the product issuer to shortfall liability.

Option-Based Portfolio Insurance (OBPI) buys protective put options or zero-coupon bonds plus call options upfront, paying explicit option premiums that decay over time. In contrast, CPPI dynamically replicates convex call payoffs without paying upfront option premiums, but suffers path-dependent whipsaw decay in volatile, range-bound markets.

CPPI mechanically increases equity exposure as the market rises (expanding the cushion) and cuts equity exposure as the market falls (contracting the cushion). This buy-high, sell-low rule is an explicit trend-following (momentum) algorithm that thrives in persistent trends but suffers in mean-reverting, choppy regimes.

Related Risk & Portfolio Simulators

VIX Futures & Options Lab

Model mean reversion, term structure roll yield, and vol-of-vol.

Forward Volatility (FVA) Lab

Explore calendar variance replication and forward convexity drag.

Black-Litterman Portfolio Lab

Combine market equilibrium priors with subjective investor views.

OBPI Portfolio Insurance Lab

Model protective puts, 90/10 capital notes, and participation rates.