Option-Based Portfolio Insurance (OBPI) Lab

Q: What is Option-Based Portfolio Insurance (OBPI)?

Option-Based Portfolio Insurance (OBPI) is a static or semi-static hedging strategy introduced by Leland and Rubinstein (1976) that establishes a guaranteed capital floor at maturity using financial options. It is structured either as a Protective Put (holding the underlying asset plus an OTM/ATM put option) or as a Capital Protected Note (holding a zero-coupon bond that matures to the floor plus call options to capture equity upside).

Q: How does a 90/10 Capital Protected Note structure work?

In a 90/10 structured note, the investor allocates the discounted present value of the guaranteed floor (e.g., $90 discounted by risk-free interest rates) into a zero-coupon government bond that grows to $90 at maturity. The remaining capital (the option budget) is used to buy call options on the underlying equity index, enabling partial or leveraged equity participation without exposing the guaranteed floor to market downside.

Q: What determines the Equity Participation Rate (Alpha) in OBPI?

The equity participation rate is determined by the ratio of available call budget to the call option price: Alpha = (Call Budget / Call Price) * (Spot Price / Initial Portfolio Capital). It increases with higher risk-free interest rates (which discount the zero-coupon bond and expand the call budget) and longer horizons, but decreases with higher implied volatility (which inflates option premiums).

Q: Why is OBPI path-independent compared to CPPI?

OBPI payoffs depend strictly on the underlying asset's terminal price at maturity (ST) and the option strike (K), making the outcome path-independent. Unlike Constant Proportion Portfolio Insurance (CPPI), OBPI is immune to cash-lock traps and whipsaw decay during intra-horizon market drawdowns, because the options and zero-coupon bonds are held to maturity without forced mechanical liquidation.

Q: What is the primary drawback of Option-Based Portfolio Insurance?

The primary drawback of OBPI is the explicit upfront option premium and continuous time decay (Theta bleed). If the underlying market trades sideways or rises modestly, the option premium expires worthless, acting as an upfront performance drag. Additionally, in low interest rate environments, the zero-coupon bond discount is negligible, leaving very little capital to purchase call options.

Model protective puts, 90/10 capital protected notes, equity participation rates, and Black-Scholes theta decay.

Market Presets:

Standard 90% Capital Protection: 90% floor over 1 year at 4.5% risk-free rate. Provides strong bond discount cushion to fund ATM calls with ~75% equity participation.

Parameters

Portfolio Capital ($V_0$) 1000000

Total investment principal to protect.

Protection Floor ($F_T$ %) 90.0

Guaranteed capital level at terminal maturity.

Horizon ($T$ Years) 1.0

Time until option expiry and bond maturity.

Risk-Free Rate ($r$ %) 4.5

Zero-coupon bond yield and discount rate.

Dividend Yield ($q$ %) 1.5

Continuous underlying equity dividend yield.

Asset Volatility ($\sigma$ %) 18.0

Black-Scholes implied option volatility.

Option Strike ($K$ % of Spot) 100.0

Moneyness of call and protective put options.

Floor at Maturity

$900,000

Guaranteed $F_T$

Participation Rate

76.4%

Equity Upside ($\alpha$)

Call Budget (90/10)

$139,591

$V_0 - F_T e^{-rT}$

Protective Put Cost

5.82%

Of Protected Asset

Bond Cost (PV)

$860,409 (86.0%)

Zero-Coupon Bond

ATM Option Prices

C: $9.42 | P: $5.82

Per $100 Spot Unit

Daily Theta Decay

-$142 / day

Portfolio Time Bleed

Synthetic Delta

0.452

Effective Equity Δ

Portfolio Vega

$2,840 / 1% σ

Vol Sensitivity

Put-Call Parity

Valid (Diff < $0.01)

$S e^{-qT} + P = K e^{-rT} + C$

Terminal payoff comparison: OBPI guarantees the minimum floor ($F_T$) on market crashes while capturing equity upside governed by participation rate $\alpha$.

Daily mark-to-market progression over 252 trading days: In a flat market, the option premium bleeds away via Theta decay, converging to the bond floor.

Impact of market environment: Higher interest rates expand the call budget by discounting the bond, while higher implied volatility raises call prices and shrinks participation.

Matrix 1: Floor Protection % vs Risk-Free Rate ($r$) on Equity Participation Rate (%)

Matrix 2: Asset Volatility ($\sigma$) vs Horizon ($T$) on Protective Put Cost (% of Asset)

Institutional Theory: OBPI Derivatives Mechanics

1. Dual Formulations & Put-Call Parity

Introduced by Hayne Leland & Mark Rubinstein (1976), Option-Based Portfolio Insurance (OBPI) can be structured in two mathematically equivalent formats via European Put-Call Parity:

$$\text{Protective Put} = S_t e^{-q(T-t)} + P(K, T)$$ $$\text{Capital Protected Note} = F_T e^{-r(T-t)} + \alpha \cdot C(K, T)$$ $$S_0 e^{-qT} + P(K, T) = K e^{-rT} + C(K, T)$$

where $F_T = K$ is the guaranteed floor, $r$ is the risk-free rate, $q$ is the dividend yield, and $\alpha$ is the participation rate.

2. The 90/10 Structured Note & Participation Rate

In retail and institutional capital-guaranteed structured notes, the issuer invests the present value of the guaranteed floor into a zero-coupon bond and uses all remaining capital to purchase call options:

$$\text{Call Budget} = V_0 - F_T e^{-rT}$$ $$\alpha = \frac{\text{Call Budget}}{C(K, T)} \cdot \frac{S_0}{V_0}$$

When interest rates are high ($r \uparrow$), the bond costs less, leaving a larger budget for calls and driving participation $\alpha$ above 100%.

3. Path Independence vs. CPPI

A critical advantage of OBPI over Constant Proportion Portfolio Insurance (CPPI) is path independence. Because option contracts settle strictly on terminal spot $S_T$:

$$V_T = \max(S_T, K) \quad \text{or} \quad F_T + \alpha \max(S_T - K, 0)$$

OBPI is completely immune to the cash-lock trap and whipsaw decay. An investor cannot be shaken out of their equity exposure during temporary flash crashes.

4. The Cost of Insurance: Theta Bleed & Vol Drag

The core disadvantage of OBPI is the explicit cost of option premiums and continuous time decay (Theta bleed):

$$\Theta_{\text{call}} = -\frac{S e^{-qT} \sigma \phi(d_1)}{2\sqrt{T}} - r K e^{-rT} \Phi(d_2) + q S e^{-qT} \Phi(d_1)$$

If the underlying market trades sideways or rises moderately, option values decay toward zero, representing an unrecoverable insurance cost.

Frequently Asked Questions