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id: options-vs-stocks title: Options vs. Stocks summary: A rigorous comparison of stocks and options across ownership, risk, leverage, time decay, and capital efficiency. outlook: neutral tags:

• beginner
• foundations
• comparison

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Learning goals

By the end of this lesson you should be able to:

• Explain the fundamental difference between ownership (stocks) and rights (options).
• Quantify leverage and compute percentage returns for both.
• Understand why time decay is a risk for options but not for stocks.
• Compare capital requirements, risk profiles, and probability of profit.
• Make informed decisions about when to use stocks vs options.

The core difference: ownership vs. rights

This is the most important distinction in finance:

• Stock: you own a fractional piece of a company. You have voting rights, dividend entitlements, and infinite time horizon.
• Option: you own a contract about that stock. You have the right to buy or sell at a fixed price, but only until expiration.

Capital requirements (the leverage equation)

Let's be precise about capital efficiency.

Stock purchase:

• 100 shares at $S_0 = 100$ costs $10,000

Call option:

• 1 contract (100 shares) with premium $C_0 = 5$ costs $500

Both give exposure to 100 shares, but the capital differs by 20×.

This ratio is called notional leverage:

$$\text{Notional Leverage} = \frac{100 \times S_0}{C_0 \times 100} = \frac{S_0}{C_0}$$

For our example: $100 / 5 = 20×$ leverage.

Leverage cuts both ways (the math is symmetric)

Consider a 10% stock move:

Stock position:

• Investment: $10,000
• Stock rises 10% to $110
• Profit: $1,000
• Return: 10%

Call option (strike 100, premium $5):

• Investment: $500
• Stock rises 10% to $110
• Option value: $\max(110 - 100, 0) = 10$ (at expiration)
• Profit: $(10 - 5) \times 100 = 500$
• Return: 100%

The option delivered 10× the percentage return on a 10% stock move.

But if the stock falls or stays flat, the option can lose 100% while the stock loses much less.

Time decay: the silent option killer

This is where stocks have a permanent advantage.

Stocks have no time decay:

• Hold for 10 years with no price change → same value
• No urgency, no expiration pressure

Options decay every day:

• Even if the stock does nothing, options lose value
• This is theta decay
• Decay accelerates near expiration

The math of time decay

Theta is measured in dollars per day. A typical ATM option might have:

• At 90 DTE: $\theta \approx -0.03$ per day
• At 30 DTE: $\theta \approx -0.05$ per day
• At 7 DTE: $\theta \approx -0.12$ per day

This is why short-dated options are dangerous for beginners—time works against you faster.

Risk profile comparison (be precise)

Let's compare four scenarios for a $10,000 risk budget:

Long stock (100 shares at $100)

• Max loss: $10,000 (stock goes to$0)
• Max gain: unlimited
• Break-even: $100
• Time pressure: none

Long call (20 contracts at $5 each)

• Max loss: $10,000 (all options expire worthless)
• Max gain: unlimited
• Break-even: $105
• Time pressure: constant decay

Long put (20 contracts at $4 each) + cash

• Max loss: $8,000 (puts expire worthless)
• Max gain: ~$190,000 (if stock goes to$0)
• Break-even: $96
• Time pressure: constant decay

Stock + protective put (100 shares + 1 put at $4)

• Max loss: $900 ($500 below strike + $400 premium)
• Max gain: unlimited minus $400 premium
• Break-even: $104
• Time pressure: on the put only

Probability of profit (PoP) differs structurally

Stocks only require the price to rise above your purchase price.

Options require the price to move beyond the strike by more than the premium.

Example with $S_0 = 100$:

• Stock PoP ≈ 50% (price needs to go up)
• ATM call PoP ≈ 40% (price needs to exceed strike + premium)
• OTM call PoP ≈ 20-30% (price needs even bigger move)

This is not a flaw—it's the trade-off for leverage.

Dividends and corporate actions

Stockholders receive:

• Dividends (cash payments)
• Voting rights
• Stock splits (more shares)

Option holders receive:

• Nothing directly
• Options are adjusted for splits, but not for dividends
• Early exercise may be optimal before dividend dates

When to prefer stocks

Choose stocks when:

• You want long-term ownership without time pressure
• You want dividends and voting rights
• You are comfortable with larger capital commitment
• You want simpler risk management

When to prefer options

Choose options when:

• You need defined risk (max loss = premium)
• You want leverage with fixed maximum loss
• You have a short-term thesis (days to weeks)
• You want to structure specific payoffs (hedging, income, targeted bets)

Common beginner mistakes

1. Treating options like stocks: holding too long, ignoring decay
2. Ignoring leverage risk: betting too big because options are "cheap"
3. Wrong time horizon: buying short-dated options for slow-moving theses
4. Forgetting total cost: comparing single option price to stock price instead of notional

Optional math: return comparison formulasRead more

Stock return:

$$R_{\text{stock}} = \frac{S_T - S_0}{S_0}$$

Long call return:

$$R_{\text{call}} = \frac{\max(S_T - K, 0) - C_0}{C_0}$$

Leverage ratio (approximate):

$$\text{Leverage} \approx \frac{\Delta}{\text{option price} / \text{stock price}} = \frac{\Delta \times S_0}{C_0}$$

Where $\Delta$ is the option delta (sensitivity to stock price).