A call option can turn a 12% rise in a stock into a 140% gain. The same option can turn a 3% rise into a 40% loss. This week you see how, and why your arena account doesn't trade them.
Learning objectives. After this week you can (1) define calls and puts and compute their payoffs; (2) find a call buyer's breakeven and maximum loss; and (3) tell hedging from speculation. This week is conceptual: the arena does not trade options.
Remember this: an option buyer can lose only the premium, and very often does.
1) What a derivative is
A derivative is a contract whose value comes from another asset. A call option gives its buyer the right, not the obligation, to buy a stock at a fixed strike price (K) until expiration. A put option gives the right to sell at the strike. The buyer pays the seller (the writer) a premium for that right. One contract covers 100 shares.
2) Payoffs at expiration
Call Payoff = max(S − K, 0) · Put Payoff = max(K − S, 0) · Profit = Payoff − Premium
S is the stock price at expiration; max(…, 0) means the payoff is never below zero. Stock at $100, you buy a call with K = $100 for a $5 premium:
| Stock at expiration | Payoff | Profit per share |
|---|---|---|
| $90 | 0 | −$5 (premium lost) |
| $100 | 0 | −$5 |
| $105 | $5 | $0 (breakeven = K + premium) |
| $112 | $12 | +$7 |
The worst case is the premium, but at $100 or below that is 100% of the stake.
3) Hedging vs. speculation
You own 100 shares at $50 and buy a put with K = $50 for $2. If the stock falls to $40, the shares lose $10 each but the put pays max(50 − 40, 0) = $10, so you lose only the $2 premium. That is a protective put: insurance. Hedging means taking a position that offsets a risk you already hold. The same put bought without the shares is speculation, a bet that the stock falls.
4) Why leverage eats beginners
$5,000 buys 50 shares of a $100 stock, or 10 calls (premium $5) on 1,000 shares. At $112 the shares make $600 (+12%) and the calls $7,000 (+140%). At $103 the shares make $150 while the calls lose $2,000 (−40%). Options also lose time value every day, so a buyer must be right about direction, size and timing. Studies find most retail option buyers lose money.
The arena is cash-only and long-only: every buy is paid from cash (no margin), you can sell only shares you own (no short selling), and there are no options. Its risk tools are diversification, bond ETFs, cash and position size. A sell limit order fills when the price rises to your limit, so it is not a stop-loss.
Quick self-check
(a) Put with K = $50, premium $2; the stock ends at $40. Payoff and profit per share? (b) Call with K = $100, premium $5; the stock ends at $103. Profit per share? (Answers: payoff $10, profit $8; $3 − $5 = −$2.)
Common mistakes
- Forgetting the premium. A call profits only above K + premium.
- Mixing up right and obligation. Writers can lose far more than they collected.
- Treating leverage as a strategy. It raises the stakes, not the odds.
This week in the arena
Paper-hedge your largest holding. Take its price from your Extrapoli quote, open the stock's free option chain on Yahoo Finance, and find the premium of a put with a strike near that price. Work out the premium as a percent of the share price: that is what a few weeks of insurance on that position would cost.