Hedging Strategy Design

Overview

Design systematic hedging plans for existing positions, covering linear hedges (futures / ETFs) and nonlinear hedges (options). Output hedge ratios, cost estimates, and execution plans. Core principle: hedging does not eliminate risk; it exchanges unknown losses for known costs.

Core Concepts

1. Beta Hedging (Futures / ETFs)

Principle: hedge portfolio systematic risk (beta) with index futures or ETFs while preserving single-stock alpha.

Hedge ratio calculation:

# 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)

China A-share beta hedging instruments:

Instrument	Code	Contract Multiplier	Margin	Suitable Scale
IF (CSI 300 futures)	IF2403	300 RMB / point	~12%	> 5 million RMB
IC (CSI 500 futures)	IC2403	200 RMB / point	~14%	> 3 million RMB
IM (CSI 1000 futures)	IM2403	200 RMB / point	~15%	> 3 million RMB
CSI 300 ETF (510300)	510300.SH	—	Unlevered	Any size

Note: stock-index futures have basis (spot-futures spread). Shorting futures when they trade at a discount brings extra return (basis convergence), while premium pricing adds extra cost.

2. Option Hedging Strategies

Protective Put

Hold the underlying + buy a put option

• Cost: option premium (typically 1-3% of underlying value per month)
• Protection range: fully protected below the strike price
• Applicable scenario: worried about a large drawdown but do not want to sell the position

China A-share example (50ETF options):

# 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

Collar

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

• Cost: close to zero-cost (the call premium offsets the put premium)
• Trade-off: gives up upside above the call strike
• Applicable scenario: willing to cap upside in exchange for free downside protection

Parameter selection guide:

Parameter	Aggressive	Balanced	Conservative
Put strike	ATM-5%	ATM-8%	ATM-10%
Call strike	ATM+8%	ATM+5%	ATM+3%
Net cost	Slightly positive	Near zero	Slightly negative (income)
Maximum downside loss	-5%	-8%	-10%
Maximum upside gain	+8%	+5%	+3%

Put Spread (Bear Put Spread Hedge)

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

• Cost: 30-50% cheaper than buying a naked put
• Protection range: only between the two strikes; no protection below the lower strike
• Applicable scenario: hedging against moderate drawdowns while being cost-sensitive

3. Tail-Risk Hedging

Far OTM put strategy:

# 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

VIX call strategy (US equities / options market):

# 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

4. Cross-Asset Hedging

Stock-bond hedge:

Stock/Bond Mix	Expected Volatility	Applicable Scenario
80/20	~15%	Bull market environment, small bond buffer
60/40	~10%	Classic allocation, suitable for most environments
40/60	~7%	Bear market environment, bond-led
Risk Parity	~8%	Volatility-balanced allocation

Note: stock-bond correlation is not stable. In 2022, US stocks and bonds both fell (rising rates), and the traditional 60/40 mix failed. In China, negative stock-bond correlation has been relatively more stable.

Stock-commodity hedge (equities + commodities):

• During rising inflation: commodities rise while equities come under pressure → commodities hedge inflation risk
• During falling inflation: equities rise while commodities come under pressure → equities drive returns
• Gold ETF (518880.SH): low correlation with China A-shares and effective for tail-risk hedging

5. Hedge-Ratio Calculation Methods

Comparison of three methods:

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

6. Hedging Cost Evaluation

Cost components:

Cost Item	Futures Hedge	Options Hedge	Cross-Asset Hedge
Direct cost	Margin usage + fees	Premium	Allocation to lower-yield assets
Opportunity cost	Basis cost (discount / premium)	Time decay (Theta)	Earn less in a bull market
Hidden cost	Roll cost	Volatility premium	Rebalancing transaction costs
Annualized estimate	2-5% (including basis)	3-8% (depends on IV)	1-3% (opportunity cost)

Cost-benefit decision framework:

# 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

Analysis Framework

Five-Step Hedging Design Process

1. Identify the risk: what kind of risk does the portfolio face? Systematic (beta) or idiosyncratic (single-name events)?
2. Choose the instrument: linear (futures / ETF) or nonlinear (options)? This depends on the risk shape and budget
3. Calculate the ratio: determine the number of hedge contracts or option lots
4. Evaluate the cost: what is the annualized cost, and is it acceptable?
5. Monitor and adjust: hedge ratios require dynamic adjustment (beta changes, options expire)

Risk Scenario → Hedge Instrument Mapping

Risk Scenario	Recommended Instrument	Cost Level
Systematic broad-market selloff	Short IF / IC futures	Low (margin)
Moderate drawdown (5-10%)	Collar / Put Spread	Low (zero-cost collar)
Black swan (>20% crash)	Far OTM put	Medium (continuous spending)
Rising rates	Short government bond futures (TF / T)	Low
Currency depreciation	FX forwards / options	Medium
Inflation upside surprise	Allocate to commodities / gold	Low (opportunity cost)

Output Format

## 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]

Notes

• China A-share index futures have trading restrictions (intraday opening limits, margin requirements), so actual usable size may be limited
• Option liquidity is concentrated in near-month and near-the-money contracts; deep OTM options have wide bid-ask spreads
• Beta is unstable: beta tends to be lower in bull markets and higher in bear markets (meaning the hedge is least sufficient when it is needed most)
• Collar strategies cap upside, so large rallies in the underlying can materially drag portfolio performance
• Tail hedging (far OTM puts) loses money most of the time and requires discipline to execute continuously; do not abandon it halfway because it "feels wasteful"
• Correlations in cross-asset hedges can change violently during crises (trending toward 1), failing exactly when they are needed most
• Hedge plans should be re-evaluated regularly (at least monthly) for beta and cost
• This framework is for research backtesting only, does not constitute investment advice, and does not involve live trading execution