Chapter 3: Hedging a portfolio with options
Hedging means buying insurance for the portfolio against a sharp drop. Puts on indexes are what institutions use most for this purpose.
| A $100,000 stock portfolio that moves with the S&P 500 index | SPY at $510 |
| Buy SPY puts at $480 (3 months to expiration) | Cost: $4.00 × 2 × 100 = $800 |
| If the market falls 20% (SPY about $408) | Portfolio loss: $20,000 · value of the two contracts: at least $14,400 |
| Net loss with the hedge | About $6,400 (20,000 − 14,400 + 800) instead of $20,000 |
| If the market rises | You lose only the cost of the insurance: $800 |
How is the value of the two contracts calculated in a drop?
At expiration, a Put with a 480$ strike is worth the gap between 480$ and the SPY price, if the price is lower. At 408$: (480 − 408) × 100 = 7,200$ per contract, and 14,400$ for two. Before expiration it is worth more, because some time value is left.
How many contracts do you need? Beta hedging
A portfolio doesn't always move with the index by the same amount. Beta measures that: a beta of 1.2 means the portfolio moves 1.2% for every 1% move in the index. The approximate number of contracts = portfolio value × beta ÷ (SPY price × 100). In the example with a beta of 1.2: 100,000 × 1.2 ÷ 51,000 ≈ 2.35, so two or three contracts.
Collar
It combines buying a protective put with selling a covered call on the same stock. The premium from the short contract pays for part or all of the insurance, and the price is a cap on profit if the market rises above the short contract's strike.
The real cost
Insurance is paid every period: $800 every three months comes to $3,200 a year, or 3.2% of the portfolio. That is why many people hedge partially, or only at certain times (before a big event or when implied volatility is cheap), instead of hedging all the time.
Summary
Hedging with puts limits the portfolio's loss in a crash in return for a fixed cost each period. The number of contracts comes from the portfolio's value and its beta, and a Collar lowers the cost in return for a cap on upside. So the question isn't “should I hedge?” but “how much do I pay for what protection, and when?” Permanent insurance on a small portfolio can cost more than it protects.
