Hedging Strategy Design

# Minimum-variance hedge ratio
hedge_ratio = beta_portfolio * (portfolio_value / futures_value)

# Example: hold a 10 million RMB China A-share portfolio, beta = 1.2
# CSI 300 futures (IF) contract value = index level × 300
# IF level = 4000, contract value = 4000 × 300 = 1.2 million
# Required number of short contracts = 1.2 × (1000 / 120) = 10

# Beta estimation method
import numpy as np
# OLS regression: portfolio_returns = alpha + beta * index_returns + epsilon
beta = np.cov(portfolio_returns, index_returns)[0][1] / np.var(index_returns)

Hold the underlying + buy a put option

# Hold 1 million shares of 50ETF (about 2.7 million RMB)
# Buy 100 contracts of 50ETF put 2700 (strike 2.700)
# Premium ≈ 0.05 RMB/share × 10000 shares/contract × 100 contracts = 50,000 RMB
# Cost ratio = 50,000 / 2,700,000 ≈ 1.85%
# Protection effect: losses are capped once ETF falls below 2.700

Hold the underlying + buy an OTM put + sell an OTM call

Buy a higher-strike put + sell a lower-strike put

# Buy deep OTM puts (delta ≈ -0.05 ~ -0.10)
# Characteristics: expires worthless most of the time, but pays off massively during black swans

# Parameters
otm_put_strike = current_price * 0.85  # 15% OTM
cost_per_month = portfolio_value * 0.003  # about 0.3% / month
expected_payoff_in_crash = portfolio_value * 0.10  # ~10% payoff in a severe selloff

# Cost management: ongoing spend of about 3.6% / year, profitable only in tail events
# Taleb-style hedge: lose small amounts often, make large gains occasionally

# Buy OTM VIX calls (strike = current VIX + 10)
# If VIX jumps from 15 to 40, call value explodes
# Naturally negatively correlated with an equity portfolio

# China A-share substitutes:
# China has no VIX futures, so alternatives are:
# 1. Buy OTM 50ETF puts (similar tail protection)
# 2. Go long volatility: buy a straddle
# 3. Allocate to gold ETF (518880.SH) as a safe-haven asset

import numpy as np
from scipy import stats

# Method 1: OLS regression (simplest)
slope, intercept, r, p, se = stats.linregress(hedge_returns, portfolio_returns)
hedge_ratio_ols = slope

# Method 2: Minimum variance
covariance = np.cov(portfolio_returns, hedge_returns)[0][1]
variance_hedge = np.var(hedge_returns)
hedge_ratio_mv = covariance / variance_hedge

# Method 3: EWMA (exponentially weighted, more sensitive)
lambda_param = 0.94  # RiskMetrics default
ewma_cov = pd.Series(portfolio_returns * hedge_returns).ewm(alpha=1-lambda_param).mean()
ewma_var = pd.Series(hedge_returns**2).ewm(alpha=1-lambda_param).mean()
hedge_ratio_ewma = ewma_cov / ewma_var

# Selection guidance:
# Static hedge (monthly rebalance) -> OLS
# Dynamic hedge (weekly rebalance) -> EWMA
# Theoretical analysis -> minimum variance

# Is the hedge worth it?
hedge_cost_annual = 0.04           # 4% annualized
expected_loss_without_hedge = 0.15 # 15% expected max loss without hedge
prob_of_loss = 0.25                # 25% probability

expected_loss = expected_loss_without_hedge * prob_of_loss  # = 3.75%

# If hedge_cost > expected_loss -> hedge is relatively expensive
# If hedge_cost < expected_loss -> hedge is cost-effective
# Here 4% > 3.75%, so the hedge is marginally expensive, but it may still be worth it because of tail risk

## Hedging Plan — [Portfolio Name]

### Portfolio Overview
- Portfolio size: [X ten-thousand RMB]
- Portfolio beta: [X.XX] (vs [benchmark index])
- Main risk: [systematic / sector concentration / tail]

### Hedging Plan
- Instrument: [short IF futures / Collar / Put Spread / ...]
- Hedge ratio: [X.XX]
- Number of contracts / option lots: [N]
- Hedge coverage: [X%] (full / partial hedge)

### Cost Evaluation
- Direct cost: [X ten-thousand RMB / year]
- Annualized cost ratio: [X%]
- Margin / premium usage: [X ten-thousand RMB]

### Scenario Analysis
| Market Move | PnL Without Hedge | PnL With Hedge | Hedge Effect |
|---------|-----------|-----------|---------|
| Down 10% | -X | -X | Reduce loss by X |
| Down 20% | -X | -X | Reduce loss by X |
| Up 10% | +X | +X | Give up X of upside |

### Execution Notes
- Entry timing: [specific time / condition]
- Rebalance frequency: [monthly / quarterly / event-driven]
- Exit condition: [risk resolution criterion]