hedging-strategy

# 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:**

```python
# 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):**
```python
# 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:**

```python
# 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):**

```python
# 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:**

```python
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 =