Introductory Context
"The hedge ratio calculation integrates the portfolio's Nifty correlation (beta), the portfolio's total market value, the Nifty's current level, and the put option's lot size into a single formula. This calculation is performed once at each hedge entry and updated when the portfolio's value, beta, or Nifty's level changes significantly. "
The Basic Hedge Ratio Formula
Number of lots = (Portfolio Value × Portfolio Beta) / (Nifty Level × Lot Size). Where: Portfolio Value = current market value of the equity portfolio in rupees. Portfolio Beta = the portfolio's sensitivity to Nifty moves (beta of 1.0 means the portfolio moves approximately 1:1 with Nifty; beta of 0.85 means it moves 85 percent as much as Nifty). Nifty Level = current Nifty 50 index value. Lot Size = 75 units per Nifty lot.
Example: Portfolio value = Rs 60 lakh. Portfolio beta = 0.95. Nifty level = 23,500. Lot size = 75. Number of lots = (Rs 60,00,000 × 0.95) / (23,500 × 75) = Rs 57,00,000 / Rs 17,62,500 = 3.23 lots. Round to 3 lots for practical implementation (rounding down slightly under-hedges; rounding up slightly over-hedges). For most portfolios, the choice between rounding up or down for the fractional lot is less important than the beta estimate's accuracy.
Estimating Portfolio Beta
Portfolio beta is the weighted average of the individual holdings' betas relative to Nifty. For a 15-stock portfolio: beta = sum(weight_i × beta_i) for all 15 stocks. Individual stock betas are available from: (1) NSE's corporate filings and beta calculators. (2) Screener.in's fundamental analysis section. (3) Moneycontrol's stock analytics. (4) Manual calculation from 52-week or 3-year daily return regression.
Approximate beta ranges for common Indian stock categories: Large-cap financials (HDFC Bank, ICICI Bank, Kotak): 0.95 to 1.15. Large-cap technology (Infosys, TCS, Wipro): 0.70 to 0.90. Nifty 50 ETF: approximately 1.0. Midcap stocks: 1.1 to 1.4. Consumer staples (HUL, Nestle): 0.55 to 0.75. Pharmaceuticals: 0.65 to 0.85. Large-cap metals/energy (Tata Steel, ONGC, Reliance): 0.90 to 1.10. For a diversified large-cap portfolio: beta is typically 0.85 to 1.05. Using beta = 1.0 as the default approximation is acceptable when individual stock betas are not available -- it slightly over-hedges technology-heavy portfolios and slightly under-hedges banking-heavy portfolios.
Hedge Ratio Calculation Worked Example
Portfolio composition: Rs 10L HDFC Bank (beta 1.05), Rs 8L TCS (beta 0.80), Rs 7L Reliance (beta 0.98), Rs 6L Infosys (beta 0.75), Rs 5L ICICI Bank (beta 1.10), Rs 4L ITC (beta 0.70). Total: Rs 40L. Weighted beta = (10 x 1.05 + 8 x 0.80 + 7 x 0.98 + 6 x 0.75 + 5 x 1.10 + 4 x 0.70) / 40 = (10.5 + 6.4 + 6.86 + 4.5 + 5.5 + 2.8) / 40 = 36.56 / 40 = 0.914. Lots required = (Rs 40,00,000 x 0.914) / (23,500 x 75) = Rs 36,56,000 / Rs 17,62,500 = 2.07 lots ≈ 2 lots.
Partial Hedge Ratios - Deliberate Under-Hedging
Full hedge ratio (100 percent hedge) protects against 100 percent of Nifty's decline impact on the portfolio. The Rs 60 lakh portfolio with 3 lots of puts (from the earlier example) provides full hedge protection -- for every Nifty percentage point of decline, the portfolio's loss is fully offset by the put gain. A 50 percent partial hedge: 1.5 lots (approximately 1 lot in practice) reduces the portfolio's Nifty decline impact by approximately 50 percent -- accepting the other 50 percent as unhedged downside exposure in exchange for half the hedge cost.
The partial hedge rationale: most investors do not need or want full Nifty decline protection -- they simply want to limit the maximum drawdown from a catastrophic scenario. A 50 percent partial hedge at half the cost provides meaningful reduction of the worst drawdown scenarios without the full cost of 100 percent coverage. For most long-term equity investors whose portfolios can withstand a 15 to 20 percent decline but not a 40 to 50 percent crash, a 40 to 50 percent partial hedge with OTM puts provides the most cost-efficient structure.
Adjusting the Hedge After Portfolio or Market Changes
The hedge ratio must be recalculated and adjusted when: (1) Portfolio value changes significantly (more than 10 to 15 percent from the hedge entry level) -- a large increase in portfolio value requires additional puts; a large decrease reduces the required number of lots. (2) Portfolio composition changes (a major rebalancing that significantly alters the portfolio's beta) -- recalculate the weighted beta with the new holdings. (3) Nifty's level changes significantly (more than 10 percent from the entry level) -- the denominator changes, altering the required lots. The quarterly hedge roll (renewing the puts at each expiry) is the natural recalibration opportunity: at each roll, recalculate the hedge ratio using current portfolio value, current beta, and current Nifty level.
The hedge ratio calculation is the hedge's engineering specification. The strategy decision (what to hedge, at what level) is a portfolio management decision. The implementation details (how many lots, which strike, which expiry) are the execution. The hedge ratio calculation bridges the strategy decision to the implementation -- translating the abstract 'I want to protect my portfolio against a 15 percent decline' into the specific '2 lots of 21,150 PE at Rs 88 per unit' that implements that protection at the correct scale.
Recalculate the Hedge Ratio at Every Quarterly Roll
At each quarterly hedge roll date (when the existing puts expire and new ones are purchased): take 5 minutes to recalculate the hedge ratio with the current portfolio value and current Nifty level. If the portfolio has grown (from capital additions or market gains), the required lots increase. If Nifty has risen, the denominator increases and the required lots may decrease. Keeping the hedge ratio current ensures the protection level remains aligned with the portfolio's actual exposure rather than the exposure at the original hedge entry.