A protective put sets a floor under one stock for the price of the premium, and a collar sells a call to pay for it; the first lesson of this module covered both. Most people own several stocks, though, and a put on each one gets expensive fast. The usual answer is one hedge for the whole portfolio, bought as SPY puts. It costs a fraction of the stock-by-stock version, but it only pays when the market falls, not when one of your names falls on its own.
Beta turns your stocks into SPY
A stock's beta is how much it tends to move for each 1% move in the market. A beta of 1.5 means that when SPY falls 2%, the stock has typically fallen about 3%. It is measured from the past year of daily returns, so it is an average habit, not a promise.
To hedge with SPY you first restate each holding in SPY terms: dollars held times beta. That is called beta-weighting. Take a $250,000 portfolio of five stocks, $50,000 in each.
| Holding | Dollars | Beta | In SPY terms |
|---|---|---|---|
| Chip maker | $50,000 | 1.8 | $90,000 |
| Software | $50,000 | 1.4 | $70,000 |
| Bank | $50,000 | 1.2 | $60,000 |
| Retailer | $50,000 | 0.9 | $45,000 |
| Utility | $50,000 | 0.7 | $35,000 |
| Total | $250,000 | 1.2 | $300,000 |
The portfolio behaves like $300,000 of SPY, not $250,000. With SPY at $750, one put covers 100 shares, or $75,000 of SPY. So the hedge is $300,000 divided by $75,000: four SPY puts. Hedge by dollars alone and you buy three and a third, and the high-beta names run ahead of the protection.
Read the x axis as the index on a $100 scale. The holding has beta 1.5, so it counts as 1.5 units of the index, and one $95 put is what matching dollars buys. Below the strike the expiry line keeps falling at a third of the unhedged pace. Drag days down to see the position harden into its expiry shape.
The chart puts the problem on a $100 index. A holding with beta 1.5 moves like 1.5 units of the index, so a hedge sized to the dollars, one put per unit, leaves a third of the fall unhedged below the strike. Buy 1.5 puts and the line goes flat.
The beta-weighted hedge. Below $95 the expiry line goes flat, because the puts now gain as fast as the holding loses, provided the stock really moves 1.5 times the index. Raise volatility and the green line lifts below the strike before expiry: the puts are worth more when the market expects bigger moves.
SPY puts or a put on every stock
The other way is a put on each holding. Price both for 60 days, 5% below the market. SPY's implied volatility at that strike might be 15%; the five stocks might be 50%, 40%, 30%, 28% and 22%. On those numbers each SPY put costs about $4.04, so four cost about $1,600, or 0.65% of the portfolio. The five stock puts cost about $7,600, or 3%. The index hedge is nearly five times cheaper. Held to expiration, here is what each one pays.
| Scenario | Portfolio | SPY puts pay | Stock puts pay |
|---|---|---|---|
| Market falls 10%, each stock by its beta | -$30,000 | $15,000 | $17,500 |
| Market flat, the chip maker alone falls 30% | -$15,000 | $0 | $12,500 |
In a broad selloff the two hedges pay similar amounts, and the index one cost a fifth as much. In the second row the index hedge pays nothing at all. That gap is called basis risk: the risk that what you own and what you hedged with stop moving together. Your stocks can fall while SPY does not. Five names carry far more of that risk than fifty, because one bad report is a bigger share of the whole.
Why index vol sits below its stocks' vol
The index hedge is not cheap by accident. SPY's implied volatility sits well below the average of its stocks', and the reason is correlation, how closely two things move together. On any day some stocks rise while others fall, and inside an index those moves partly cancel. The index only moves as far as its stocks move together.
Take 500 stocks, each with 30% volatility. If they moved in perfect lockstep, the index would have 30% volatility too. If they moved completely independently, the index would have about 1.3%. Real stocks sit in between, and at a correlation of 0.3 the index comes out near 16.5%. That is why a single stock's IV is often two or three times SPY's. The catch for hedgers is that in a sharp selloff stocks tend to fall together, correlation jumps, and index vol rises faster than the stocks' own. Index puts get dear exactly when the tail risk arrives, so the time to buy them is before.
Choosing strike and expiry at a glance
The strike is the deductible. A put 5% below the market pays after the first 5% of the fall; one 10% below pays only after 10%, and at 15% vol for 60 days it costs about a seventh as much. Index skew is steep, so the further strike carries a higher IV than the at-the-money one, the skew from Module 11, which narrows that discount.
Expiry works on the square root of time. An at-the-money put with 90 days to run costs about 1.6 times one with 30 days, not three times, so the longer hedge is cheaper per day. Out of the money, short-dated puts are cheaper still, because the index rarely travels 5% in a few weeks. A common middle is two to three months, 5% to 10% out of the money, rolled to a new expiration with a month or so left. How big a hedge to carry against the rest of your risk is a sizing question, and Module 13 covers position sizing.
Put value on a $100 index by days to expiry, at the money and 5% and 10% below, all at 15% volatility. The at-the-money line climbs with the square root of time; the 10% put stays near zero for the first month. Drag volatility to 35, a single stock's level, and every line jumps: that is the price of hedging name by name.
The maths: beta-weighting and why index vol is lower
The hedge size is contracts = Σ(dollars × beta) / (SPY price × 100). For the portfolio above: (50,000 × 1.8 + 50,000 × 1.4 + 50,000 × 1.2 + 50,000 × 0.9 + 50,000 × 0.7) / (750 × 100) = 300,000 / 75,000 = 4.
Beta is correlation times relative volatility: beta = ρ × σ_stock / σ_index, where ρ is the stock's correlation with the index. A stock with 40% volatility and a 0.5 correlation to an index at 16% has a beta of 0.5 × 40 / 16 = 1.25. Data vendors estimate beta, correlation and volatility over their own windows, so live figures will not tie out exactly.
For an index of n equally weighted stocks, each with volatility σ and the same correlation ρ between every pair: σ_index = σ × √(ρ + (1 - ρ) / n). With σ = 30%, ρ = 0.3 and n = 500, that is 30 × √(0.3 + 0.0014) = 30 × 0.549 ≈ 16.5%. At ρ = 0.6, a selloff-level correlation, it is 30 × √0.6008 ≈ 23.3%: index vol up almost 7 points with no change in any single stock's vol. Run the formula backwards from index and stock IVs and you get the correlation the options market is pricing, called implied correlation.
Your turn
Open META in Price Context and read its Beta 1y. Work out how many SPY puts offset $100,000 of it, using SPY's price. Then open the SPY chain, price a put about 5% below the market, and set SPY's at-the-money IV beside META's.