Portfolio Greeks & Hedging

In Level 1 you learned the Greeks one position at a time — delta, how much one option moves with its stock; theta, the daily rent on one contract. That was looking at your account through a keyhole.

This module opens the door. You will learn to add up the Greeks across every position you own: how much you gain or lose if the market rises $1, how much time decay costs or pays you each day, and how exposed you are if fear suddenly spikes. Then you will learn the main tool traders use to protect the whole account at once — buying index puts as insurance — with the honest math of what that insurance costs. Afterward, you will be able to answer three questions in under a minute: Which way am I betting, how big is the bet, and what happens to me in a crash?

From One Position to the Whole Account

Every Greek you learned in Options Part 2: Pricing & the Greeks — delta, theta, vega — can be added up across your positions. The sum is your net Greek: net delta is the deltas of everything you own added together, and the same goes for net theta (daily time decay) and net vega (volatility exposure).

Why bother? Because positions interact. A stock you own might gain when the market rises while a put you bought loses — and what matters is the total. Traders who only look at positions one at a time are constantly surprised by their own accounts; traders who look at the net numbers rarely are. Your broker usually shows these totals (look for a "position Greeks" or "portfolio" view) — and if it does not, you can add them by hand, exactly as this module shows.

Net Delta: How Many Shares You Really Own

Delta for a single option tells you its share equivalent. One contract with delta 0.40 behaves like 40 shares, because 0.40 × 100 shares = 40. Net delta does the same thing for your whole account in one stock: it tells you how many shares of exposure you really have, no matter how that exposure is packaged.

Here is a worked example. Say you hold four positions, all in the same fictional stock, XYZ, trading at $50:

Step by step: shares have delta 1 each, so 200 shares = +200. Each call contract adds 0.40 × 100 = +40, and three add +120. Each bought put subtracts 30, because puts gain when the stock falls. The call you sold counts negative — selling an option flips its Greeks to the other side.

Your net delta is +235. In dollars: if XYZ rises $1, your whole package gains about $235. If XYZ falls $2, you lose about $470. You do not own 235 shares — but your money behaves exactly as if you did.

One more number makes this real. Delta dollars = net delta × stock price = 235 × $50 = $11,750: your true directional exposure — the size of the bet — even if the cash value of your positions looks much smaller. Options let a little cash control a lot of exposure; net delta is how you see the real size.

Beta-Weighted Delta: Translating Everything Into SPY

Net delta works stock by stock. But what if you own five different stocks? Adding "+235 of XYZ" to "+80 of ABC" is adding apples to oranges — a $1 move in a sleepy utility stock and a $1 move in a wild tech stock are not the same event.

The fix is beta-weighted delta. Beta is a number comparing how jumpy a stock is versus the overall market: 1.0 means it tends to move about like the market, 2.0 about twice as much, 0.5 about half as much. Most brokers show each stock's beta next to its quote.

Beta-weighting translates every position into one common language: "how many shares of SPY does this behave like?" SPY is the ETF that tracks the S&P 500 — the market itself. The recipe, in plain words:

• Take the position's net delta in its own stock.
• Multiply by (stock price ÷ SPY price) — share counts are only fair once prices are equalized.
• Multiply by the stock's beta — its jumpiness adjustment.

Worked example. You hold a position in ABC, a fast-moving tech stock at $200, with beta 2.0. Its net delta is +40. SPY trades at $500.

• Step 1: 40 × ($200 ÷ $500) = 40 × 0.4 = 16.
• Step 2: 16 × 2.0 = +32.

Your ABC position behaves like owning 32 shares of SPY. Check it the common-sense way: if SPY drops $10 (a 2% market drop), a beta-2.0 stock tends to drop about 4% — $8 on a $200 stock — and 40 × $8 = $320 lost. Beta-weighted: 32 × $10 = $320. Same answer, one common yardstick.

Do this for every position, add the results, and you get one number for your whole account: your total market bet, in SPY shares. Multiply by SPY's price and you have your true market exposure in dollars — the number that tells you what a bad market week actually does to you.

Net Theta: Your Daily Rent Bill

In Level 1 you learned that a bought option charges you rent every day — theta — while a sold option collects that rent. Net theta adds it all up: it is what time itself pays you, or charges you, every single day, even if nothing moves.

Using positions like the ones above: your 3 long calls (theta −0.05 each) cost 0.05 × 100 = $5 a day per contract, or −$15 a day. Your 2 long puts (theta −0.04) cost $4 a day each, or −$8 a day. The call you sold (theta +0.06) pays you +$6 a day.

Net theta = −15 − 8 + 6 = −$17 a day. Your account pays $17 a day in rent — about $85 over a 5-day week, roughly $340 over a 20-trading-day month, if prices sit still and nothing changes. Time is not free for option buyers; net theta is the meter running.

Neither sign is "good" or "bad" by itself. A net buyer expects negative theta — the price of big upside with limited risk. A net seller expects positive theta and accepts bigger risk in exchange. The mistake is not knowing which one you are.

Net Vega: Your Bet on Fear

Vega measures sensitivity to implied volatility (IV) — the fear-and-excitement gauge built into option prices, which you met in Options Part 2: Pricing & the Greeks. It tells you roughly how much a position gains or loses if IV changes by 1 point (say, IV going from 20% to 21%).

Long options have positive vega: when fear spikes and IV jumps, your options get more expensive even if the stock has not moved yet. Short options have negative vega: a fear spike makes the options you sold cost more to buy back.

Worked example. Say your account's net vega is +$120. IV rises 5 points during a scary week: you gain roughly 120 × 5 = +$600, before anything else changes. After an earnings report, IV collapses 5 points in the famous "IV crush": you lose roughly −$600, even if you guessed the stock's direction right.

Now flip it. A trader who mostly sells options might run net vega of −$200. A 5-point fear spike costs them roughly 200 × 5 = −$1,000. This is why net sellers respect vega: calm weeks pay them steadily, and one violent week can hand back months of rent. Net vega tells you, in advance, which kind of week you are built for.

The Concentration Trap: Five Positions, One Bet

Greeks are not the only hidden total. The other is concentration — how much of your money rides on one idea, even when it is spread across many tickers.

Picture an account holding: shares of a big chip-maker, calls on the same chip-maker, a semiconductor ETF, calls on a tech-heavy index fund, and shares of a second chip company. That looks like five positions. It is really one bet: "tech, and especially chips, go up." With $10,000 in each — $50,000 riding on one theme — a 10% drop in that theme costs about $5,000, not the $1,000 a truly separate position would suggest.

The test is simple: pick a bad headline for your biggest theme and ask, "How many of my positions lose money on this news?" If the answer is "almost all of them," you are not diversified — you own one bet in five costumes. Real diversification means positions that do not all move together: different industries, different kinds of assets, some that can even gain when others fall (like the index puts in the next section).

Hedging With Index Puts: Insurance for Your Account

A hedge is a position you take to lose money on purpose in good times, so that it gains money in bad times and softens the blow. The classic account-level hedge is buying put options on a market index ETF — usually SPY. If the whole market falls, your stocks lose — but your SPY puts gain, offsetting part of the damage. It works like homeowners insurance: you pay a premium every period, most periods it expires worthless and you are simply out the money — and you are not angry, because your house did not burn down. In the rare bad period, the payout is many times what you paid.

The full worked example. Your account is $60,000, invested in a diversified stock portfolio that moves roughly with the market. SPY trades at $600.

• Your market exposure in SPY terms: $60,000 ÷ $600 = 100 shares of SPY. One SPY put contract covers 100 shares — so 1 contract hedges the whole account.
• You buy a put with strike $570 — 5% below the current price. The gap between $600 and $570 is your deductible: like insurance that only pays after the first chunk of damage, this put only starts paying once SPY falls below $570.
• The premium is $6.00 per share, so one contract costs $6.00 × 100 = $600, with about 3 months until expiration.

What it costs. $600 per quarter. Renewed four times a year, that is $2,400 a year — 4% of your $60,000 account — spent purely on insurance. In a flat year, where the market ends exactly where it started, all four puts expire worthless and your account is $57,600 on hedging costs alone. That is the honest price of sleeping well — and it is also why, in a good quarter (SPY up 10%), your gain is +$6,000 − $600 = +$5,400, not the full $6,000. Anyone who quotes you a cheaper-sounding hedge is skipping one of these lines.

What it pays in a −10% drop. SPY falls 10%: $600 → $540.

Look at where the $3,600 comes from: the first 5% of the fall ($3,000) was your deductible — unprotected by design — plus the $600 premium. Your 10% loss became a 6% loss ($3,600 ÷ $60,000). The hedge did not make the crash painless. It made it survivable. (A put sold mid-crash is often worth more than the table shows, since fear spikes IV — count on the contract math, not the bonus.)

Sizing a Hedge Without Guessing

A few plain rules of thumb keep hedging sane:

• Match the notional. Account value ÷ SPY price = your SPY share equivalent; ÷ 100 = contracts. $60,000 ÷ $600 = 100 shares = 1 contract. If the math gives 1.4 contracts, hedging with 1 is fine — partial insurance is normal.
• Buy time, not days. Insurance puts with 2–3 months or more until expiration decay slowly and are there when you need them. Puts expiring this week are not insurance — their theta rent is brutal and they are gone before most crashes finish.
• Set an annual budget and respect it. Decide in advance what insurance may cost per year — in the worked example, 4%, on the expensive side. A strike further below the price lowers the premium but raises your deductible: cheaper hedge, bigger first loss.
• Re-check after big moves. If your account grows to $90,000, one contract no longer covers it; if the market already fell hard, your old put may be deep in profit and your remaining exposure smaller. Resize to the account you have.

When NOT to Hedge

Insurance is a tool, not a religion. There are honest cases where hedging is the wrong move:

• Small accounts. On a $3,000 account, one $600 SPY put is 20% of everything you own, spent on a single hedge. That math never works. For small accounts, your hedge is position sizing — small risk per trade, cash kept aside, no single position big enough to sink you.
• Positions that are already defined-risk. A spread, or a bought option, already has a maximum loss you chose in advance. Insurance on top means paying twice against the same event.
• Trades measured in days. If a position will be closed this week by your plan, a 3-month index put is the wrong tool — it will barely move on your timeline while its premium is real money.
• Money you will not need for many years, where your written plan is to hold through storms and keep adding. Accepting full drops on purpose is legitimate — as long as it is actually your plan, written in calm weather, not a story invented mid-crash.

Common Mistakes at This Level

• Adding deltas across different stocks and calling it your exposure. Net delta is per stock. Cross-stock totals need beta-weighting, or the number is meaningless.
• Forgetting that sold options flip the sign. Every Greek of a short option counts negative. One missed minus sign misreads your whole account.
• Buying insurance during the crash. Fear makes puts expensive; a hedge bought in a panic often costs more than the protection is worth.
• Hedging with this week's puts. Weekly puts decay to zero in days. Insurance needs months of time, not hours.

• Believing five tech positions is diversification. Same theme, same direction, same bad day.
• Never re-sizing. Your account and the market both move. A hedge sized last year is a guess today.
• Counting the hedge as a profit center. The put is supposed to expire worthless most of the time. Judging insurance by whether it "made money" guarantees you cancel it right before you need it.

Chapter Summary

• Every Greek from Level 1 can be totaled across your account — net delta, net theta, net vega — and the totals, not the individual positions, are what you actually experience. Net delta is your share-equivalent exposure in one stock (net delta +235 means a $1 rise pays about $235); delta dollars (net delta × price) is the true size of the bet.
• Beta-weighted delta translates every position into SPY-share equivalents using price ratio and beta — one honest number for your whole market exposure.
• Net theta is your daily rent, and net vega is your exposure to fear itself: the first prices time passing, the second prices what an IV spike or IV crush does to your account per point. Either sign is fine — not knowing is not.
• Concentration hides risk: five positions on one theme are one bet, and they will all lose on the same day.
• Index puts are account insurance: a real, recurring cost (4% a year in the worked example) that turned a −10% market drop into a −6% account loss, deductible and premium included.
• Hedge in calm weather, buy months of time, size to your actual account — and skip hedging when your account is small or your positions already have defined risk.

Check Yourself

1. Your positions in one stock add up to a net delta of +235, and the stock rises $1. About how much does your account gain from that stock?
2. True or false: a net theta of −$17 means time decay pays your account $17 a day.
3. Your net vega is +$120, and implied volatility rises 5 points in a scary week. Roughly how much do your option positions gain from the volatility move alone?
4. In the hedging example, the SPY put had a $570 strike with SPY at $600. Why did the put pay nothing toward the first 5% of the market's fall?
5. Name one situation where buying an index-put hedge is usually a bad idea.

Show answers

Answers: 1) About $235 — net delta is your share equivalent, so a $1 move pays about $1 per unit of net delta. 2) False — negative net theta means your account pays about $17 a day in time decay. 3) About +$600 — vega is per IV point, so $120 × 5 = $600. 4) The gap between the $600 price and the $570 strike is the deductible: a put only has payoff value below its strike, so the first 5% of the decline is yours to absorb, plus the premium. 5) Any one of: a small account, where one premium is a huge share of the account (position sizing is the better hedge); positions already defined-risk, where you would insure the same event twice; or a trade you plan to close within days, which a months-long hedge cannot protect.