Hedging and portfolio protection

OpeningThe three months after a big gain

This year your stock portfolio has grown from a cost of $160,000 to $200,000, an unrealized gain of $40,000. You're worried about the next three months, but you don't want to miss out if the rally keeps going.

You have two paths: sell 30%, or buy 3-month puts on the whole portfolio with the strike at 90% of the current price. Selling 30% realizes a $12,000 gain, and at a 15% long-term capital gains rate (an assumption) you owe $1,800 in tax. The puts cost 1.01% of the portfolio, or $2,021.

Selling 30% cuts gains and losses by the same proportion: at −30% you still lose $43,800. The puts lock the loss at $22,021 no matter how deep the fall, and at +15% you keep 93% of the gain. The cost is just as clear: at −10% the puts pay nothing, and you lose the premium on top. The $60,000 in cash from selling would earn about $600 in interest over three months; the table leaves that out.

This table is the whole chapter in miniature: every kind of protection has declines it pays out on and declines it doesn't. The sections below work through each one.

11.1Hedging versus trimming

Trimming cuts upside and downside by the same proportion. Hedging cuts only the downside, and the price is the premium.

Two tax traps

“Hedging doesn't trigger taxes” comes with conditions, and US tax law has specific rules for it:

• Constructive sale. If the hedge removes almost all the risk and return of the shares, as a very tight collar does (buy the 98 put, sell the 102 call), the tax law may treat you as having sold.
• Straddle rules. The shares and the options hedging them may be treated as a “straddle” position: losses on the hedge leg may have to be deferred, and buying a protective put on stock held less than a year may also affect how the holding period is counted.

The details of these rules are complex; when real amounts are involved, consult a tax professional. This chapter's approach: keep strikes some distance from the current price, and don't try to “lock everything in.”

When you should just trim

• The reason you bought no longer holds: what you need is to sell, and insurance can't fix a wrong call
• A single holding is too concentrated (say, 40% of the portfolio): hedging only postpones the problem
• In a tax-exempt or tax-deferred account: selling has no tax cost, so trimming is cleaner
• You can't afford ongoing premium: protection costing 3% a year will eat half your expected return

11.2Protective puts: the cost by strike and expiration

The closer the protection is to the current price and the shorter its term, the more it costs per year: rolling a 30-day at-the-money put every month costs 23% of the portfolio a year.

This chapter's skew assumption

In real markets, OTM puts carry higher IV than at-the-money options, OTM calls slightly lower (the skew from Chapter 6), and skew is steeper at short expirations. This chapter approximates that with a simple assumption:

Cost table

Set the current price at 100, so a put's price is a percentage of portfolio value. Annualized cost = price × 365 ÷ days, meaning “how much it would cost per year to keep rolling under the same conditions.”

Three takeaways:

• The shorter the term, the higher the annualized cost. At-the-money protection rolled monthly costs 23.1% a year; buying one year outright costs 5.2%. Time value decays with the square root of time (Chapter 5), so short-dated options lose the most each day.
• Each step further out of the money cuts the cost fast. At 91 days the at-the-money put costs 3.09%, the 90 just 1.01% and the 80 just 0.34%. The price is a deductible: the 90 put pays only for the part of the drop beyond 10%.
• Annualized costs are only comparable when they protect against the same risk. The 30-day 80 put annualizes to just 1.0%, cheaper than the one-year put's 1.5%. That doesn't make it a bargain: it pays only on “a 20% drop within a month,” which is far rarer than “a 20% drop within a year.”

A common middle ground in practice is 3–6 months and 5%–15% OTM: much cheaper than monthly at-the-money puts, and it starts paying out sooner than a far-OTM one-year put. Which one to pick depends on the decline you fear most (Section 11.4) and your budget (Section 11.6).

Buy long, sell early: when to roll

Time value decays fastest in the final weeks (Chapter 5). Since you'll keep rolling the protection anyway, you can hold only the “slow-decay” stretch of each option and sell it for a new one before it enters the steep part. Take the 90 put, assuming the market stays flat and the IV surface doesn't change:

For the same level of protection, the annualized cost falls from 4.05% to 2.07%, almost by half. There are two costs: you pay more cash up front (2.82% vs. 1.01%), and longer-dated options have more Vega, so a drop in IV means a bigger paper loss (and a rise in IV, the reverse). Also, as the market rises, the original strike drifts further from the current price, and you'll need to move the strike up to the new level; that step's cost isn't in the table.

11.3Collars: the price of “zero cost”

A zero-cost collar trades the upside above an OTM call for the protection of an OTM put. With skew, you sell more upside than you'd think.

Collar = shares + long OTM put + short OTM call. The money from selling the call pays for the put; when the two are equal, it's called “zero cost.” It does have a cost: you just pay it in upside instead of cash.

Working out a zero-cost collar

The 91-day 90 put is worth 1.01% (IV 24%). You need a call strike whose price is also 1.01%. Under this chapter's skew, the answer is 107.9 (IV 16.4%): you give up the upside above 7.9% in exchange for protection below −10%.

Without skew, every strike has an IV of 18%, the 90 put is worth only 0.40%, and the zero-cost call strike is 113.9. Skew makes you give up 6 more percentage points of upside: the put is marked up and the call marked down, and both work against the collar buyer.

Asymmetric collars

“Zero cost” often pulls the cap in too close. Two common ways to loosen it:

• Pay a little for more upside. 95 / 110 costs a net 1.15%: protection starts at −5%, and you keep the upside up to +10%.
• Sell calls on only part of the holding. Buy the 90 put on the full amount and sell calls on only half the shares, and the zero-cost call strike drops to 104.5. Half the holding is capped at +4.5%; the other half has no cap. This suits times when you believe “the upside could be big.”

After a big rally: rolling the collar

You don't have to hold a collar to expiry. Suppose that 45 days after you open it, the market is up 10% (index at 110) and ATM IV has fallen to 15%. The 107.9 call is now in the money, worth 4.10; the 90 put is nearly worthless, at 0.12. Closing the whole collar costs 4.10 − 0.12 = 3.99; add the stock's +10, and you've netted about 6.0 over those 45 days.

Then open a new 91-day zero-cost collar at the new price: buy the 99 put (90% of 110), and the zero-cost call strike is 118.2. The new floor of 99 is only 1% below the original 100, which locks in most of the gain, and the new cap still leaves 7.4% of room above the current price. That's the rhythm of a rolling collar: when the market rises, shift the whole thing up and the floor rises with it.

11.4Put spreads and four approaches

A put-spread hedge protects against a “moderate” decline; the deeper the drop, the more it looks like no protection at all.

Put-spread hedge = shares + long higher-strike put + short lower-strike put. The 91-day 95 put is worth 1.76% and the 80 put 0.34%, for a net cost of 1.42% ($2,831). It pays in full between −5% and −20%, up to a maximum of 15%; below −20%, every extra 1% of decline costs you another 1%.

Why does selling the 80 put bring back so much? Skew again: the 80 put's IV is 30%, 12 points above at-the-money. You're selling the most expensive insurance in the market. If what you fear most is a 10%–20% pullback, this trade makes good sense; if what you fear most is a 2008-style crash, it isn't enough.

Put the four approaches on the same $200,000 portfolio (91 days, covering the notional 1:1):

• No hedge.
• Protective put: buy the 90 put, premium $2,021.
• Zero-cost collar: buy the 90 put, sell the 107.9 call.
• Put spread: buy the 95 put, sell the 80 put, cost $2,831.

How much to hedge: notional by beta

So far we've assumed a portfolio beta of 1. If the beta is 1.25 (tech-heavy, high-beta), the portfolio falls about 12.5% when SPY falls 10%, and the notional to cover is 200,000 × 1.25 = $250,000: about 320.5 shares at SPY 780, or 3.2 contracts. With the 91-day 702 put (90% of SPY, IV 24%, $7.88 per share), 3 contracts cost $2,365.

If SPY falls 20%, the 3 puts pay 300 × (702 − 624) = $23,400, while the beta-1.25 portfolio loses about $50,000. The protection covers only the part of the move below 702, and the portfolio has already lost about 12.5% before that. Also remember that all of this assumes beta holds steady: if the stocks in your portfolio fall further for reasons of their own, index puts won't pay any more.

Nor does the hedge ratio have to be 100%. Cover only half the notional ($100,000 of 90 puts) and the premium halves to $1,011; at −20% the portfolio loses −40,000 + 10,000 − 1,011 = −$31,011, and at −30% it loses −$41,011. The point of a half hedge is that it makes the “worst case” bearable while keeping the premium low enough that you'll stick with it year after year. There's no standard answer for the ratio. The best test is to ask yourself whether you'd panic-sell at that worst-case number.

The full numbers are in Case 1. For now, remember the logic of the choice: first answer “which kind of decline do I fear most,” then pick the structure.

• Afraid of a 10%–20% pullback: put spread
• Afraid of a crash and want to keep the upside: protective put
• Afraid of a crash and willing to cap the upside: collar

11.5VIX calls: crash hedges

VIX calls have the most explosive payoff in a crash, but they track VIX futures, so they cost more to hold and demand better timing than index puts.

• Explosive. When the market drops sharply, VIX often jumps, and nonlinearly. A small position in VIX calls can gain far more in a crash than index puts bought with the same money.
• The underlying is a future (Chapter 10, Section 10.8). In calm markets VIX futures usually sit above spot VIX and converge toward spot as expiration nears. If you buy a 20 call with spot at 14, the distance you actually have to cover is measured from the futures price, and the future itself is drifting down.
• The expiration dilemma. Front-month VIX calls respond most to a spike, but they expire quickly and have to be rolled again and again. Back-month futures move less in a panic, so back-month calls respond weakly too.
• Spikes are short. VIX mean-reverts strongly, and peaks often last only a few days. Without a monetization rule written in advance (Section 11.7), the gains can slip away while you hesitate.
• Basis risk. A rise in VIX doesn't mean your portfolio fell by a lot. In a slow, grinding bear market, VIX may rise only modestly and VIX calls won't help; index puts are more reliable there.

The safer way to use them is as a supplement to index puts, taking only a small slice of the tail-hedge budget and aimed specifically at “a sharp drop over a day or two.” When sizing, ask two questions first. If VIX futures jump sharply over a few days, roughly how much would these calls pay, and what share of the portfolio's loss over the same period would that cover? If there's no spike all year and they go to zero, what share of the tail-hedge budget is that? The answer to the second should be “a small slice.”

11.6The tail-hedge budget: buy insurance before the fire

Buy protection on a fixed budget of 1%–2% of the portfolio a year. It's cheaper than buying all at once in a panic, and easier to stick with.

Where 1%–2% comes from

There's no rigorous theory behind this number; it comes from a simple trade-off. The long-run excess return of stocks over cash is roughly a few percentage points a year (an assumption; it varies a lot from period to period). Spending 1%–2% a year on insurance still leaves most of that excess return. Beyond 2%–3%, the insurance itself eats most of the edge stocks have over cash, and you'd be better off simply holding less stock.

Under this chapter's assumptions (ATM IV 18%), here is the one-year put each budget buys:

• Budget 1%: strike about 74.9, 25% OTM
• Budget 1.5%: strike about 80.5, 19.5% OTM
• Budget 2%: strike about 84.8, 15% OTM

With the same 1.5% budget, if you wait until after a crash to buy, when ATM IV has risen to 32%, you can only get a put struck at 58.5: the premium is higher and the coverage lower. That's what “buy when IV Rank is low, not after the fire” means in numbers.

A twenty-year simulation

Below is a simulation over two hypothetical 20-year paths. Path A has two crashes (−35% in year 6, −24% in year 14); Path B has none. At the start of each year the budget buys a one-year put, with the strike solved at the IV of the time: ATM IV 18% in normal years, 32% if the previous year fell more than 15%.

You don't know in advance which path you're living on. So the point of a tail-hedge budget isn't “making money.” It does two things: it keeps you from panic-selling in a −35% year, and the cash the insurance pays out lets you rebalance and add at low prices. The simulation counts neither benefit, and they are the real return on protection.

How to spend the budget: laddering

Buying once a year bets all your protection on the IV at one moment and on one expiration date. A smoother approach is a ladder: each quarter, spend a quarter of the budget on one-year puts covering a quarter of the portfolio. After a year you always hold four puts with staggered expirations, and the strikes update to each quarter's market level. The annual spend is the same, but you won't overpay because IV happened to be high on one day, and you won't suddenly be left “naked” after a single expiration date.

11.7Monetization rules: after the protection pays off

Once your protection has made money, sell part of it. Otherwise, as soon as the market bounces and IV falls back, the paper profit vanishes quickly.

An example

You bought the 91-day 90 put for 1.01 (index at 100). Thirty days later the index has fallen 15% to 85 and ATM IV has risen to 34%. The put is now in the money, worth 7.16, 7.1 times its cost, with a Delta of −0.62.

Monetization rule: sell half, and roll the other half from the 90 put to the 80 put with the same expiration (IV 38.3%, price 2.83).

• Sell half: recover 0.5 × 7.16 = 3.58
• Roll the other half: 0.5 × (7.16 − 2.83) = 2.16
• Total cash recovered: 5.74 (5.7% of the original portfolio, 5.7 times the premium), and you still hold 0.5 units of the 80 put

On a rebound, the investor who held on watches 7.16 shrink to 1.02; the one who monetized keeps 5.86. If the crash continues, the one who monetized makes less (10.10 vs. 17.75) but still has the 80 put paying out. A monetization rule gives up part of the payoff in extreme cases in exchange for certainty in most cases.

The other direction: moving up after a rally

Monetizing handles declines; rallies need a rule too. Say you bought a one-year 90 put (2.82), and three months later the market is at 110. The old put is now 18% from the current price and worth only 1.42; a new one-year 99 put (90% of 110) costs 3.10. Selling the old one and buying the new one costs a net 1.68, about 1.5% of the new portfolio value. That money raises your protection floor from 90 to 99. A common rule: once the market is up 10% or more from where you bought, move the strike up, and count the cost against that year's tail-hedge budget.

Rules written in advance

• When the protection is worth 3–5 times its cost, or its Delta goes past −0.6, sell half first
• Roll the rest to a lower strike or a longer expiration, recovering cash while keeping tail protection
• Monetizing while VIX is spiking and the term structure is inverted beats waiting until VIX has come back down
• Put the cash from monetizing into a rebalancing plan: buying stock back at low prices is one of the real sources of return on protection

The rebalancing arithmetic is worth doing. If the 5.74 you recovered goes back into stock with the index at 85, and the index later returns to 100, that money earns an extra 5.74 × (100 ÷ 85 − 1) = 1.01, roughly the premium you paid in the first place. The payout in the decline, plus the gain from using that payout to buy low, is the full return on protection.

Neither the 3–5× threshold nor the −0.6 threshold is theoretically optimal. A Delta past −0.6 means the put is moving more and more like a short stock position: the advantage from convexity is shrinking, and you're holding volatility at its most expensive. The thresholds give you a rule to follow when emotions run highest. You can adjust the numbers to your own style, but write them down on the same day you buy the protection.

11.8Stock replacement: deep-in-the-money LEAPS

Sell the stock and buy deep-in-the-money long-dated calls (LEAPS), and you keep about 90% of the directional exposure while capping your maximum loss at the premium.

Example: you hold 200 shares of a $150 stock, worth $30,000. Instead, you buy 2 one-year calls struck at 110 (IV 30%; a single stock, so skew is ignored here):

• $46.56 each, Delta 0.906; 2 contracts are equivalent to 181 shares
• Cost $9,312, freeing $20,688 in cash, which earns about $844 in interest over a year at 4%

What's inside the time value

Put–call parity lets you take the call apart:

The interest component is roughly offset by the interest the freed-up cash earns, so what you're really paying for is the 110 put: stock replacement equals “shares + a protective put 27% OTM.”

If the stock doesn't move, the replacement loses $468, about the value of the two puts; at 180 it makes $468 less; below 110, the loss is capped at $8,468.

When stock replacement makes sense

• The position has an unrealized loss or only a small gain, so selling costs almost nothing in tax (while steering clear of the wash-sale rule)
• In a tax-exempt or tax-deferred account, selling creates no current tax
• You still like the stock but want a hard limit on the worst case, without paying for puts every quarter
• IV is low: the “implied put” inside the LEAPS is cheaper

11.9Adjusting portfolio beta with options

Without touching your holdings, you can use index options to bring portfolio beta from 1.25 down to 0.75. But option Deltas change, so the beta you set will drift.

Using the beta weighting from Chapter 4: a $200,000 portfolio with beta 1.25 and SPY at 780 is equivalent to 200,000 × 1.25 ÷ 780 = 320.5 shares of SPY. A target beta of 0.75 corresponds to 192.3 shares, so you need −128.2 shares of SPY Delta. The options are 91-day, with IV from this chapter's skew assumption.

“After −5%” assumes SPY instantly drops to 741 and ATM IV rises to 24%; “after +5%” assumes it rises to 819 and ATM IV falls to 15%. A few ways to read the table:

• Buying puts: more defensive the further it falls. As the market drops, the puts' Delta grows and portfolio beta falls from 0.74 to 0.37, exactly the direction you want. The catch is cost: $6,857 a quarter, 3.4% of the portfolio.
• Selling calls: more defensive the further it rises. You collect cash, but in a decline the calls' Delta shrinks and beta climbs back to 0.90, so the protection weakens just when you need it most. In a rally beta is pushed down to 0.38, and you get no share of the gains however far it rises.
• The collar is the most stable. The long put and the short call have Gamma of opposite sign, which cancels out, so after ±5% beta stays around 0.7, at almost zero cash cost.

Check regularly after adjusting. You can write the rule as: when effective beta drifts more than ±0.15 from target, readjust the number of contracts. Remember two more things. Beta itself is estimated from historical data, and in a crash, correlations between stocks rise and beta changes. And index options can't hedge stock-specific risk: if one stock in your portfolio blows up on earnings, SPY puts won't help.

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