Optionality and Convexity

Optionality is the right but not obligation to act. Convex payoffs benefit from volatility rather than suffering from it. Understanding these concepts changes how you make decisions under uncertainty.

The future is uncertain. Most advice: reduce uncertainty. Better advice: position to benefit from uncertainty.

What Is Optionality?

An option is the right, but not the obligation, to do something.

A call option on a stock: you CAN buy at a fixed price. If the stock goes up, you exercise. If it goes down, you don't. You capture upside, avoid downside.

The key: asymmetric exposure. You benefit from good outcomes, are protected from bad ones.

Optionality exists beyond financial markets:

• Education gives you options on careers
• Savings give you options on opportunities
• Skills give you options on projects
• Relationships give you options on collaboration

The Value of Options

Options have value even if you never exercise them. Why? Because they capture upside while limiting downside.

More volatility = more option value. When outcomes are uncertain, options to act on favorable outcomes are worth more.

This is counterintuitive. Usually we think uncertainty is bad. But if you hold options, uncertainty is good—it increases the chance of outcomes worth exercising.

Convexity

A convex payoff benefits more from upside than it suffers from downside. The gains from positive outcomes exceed the losses from negative ones.

Graphically: a curved line that bends upward. Small inputs produce disproportionately large outputs on the positive side.

Examples:

• Venture capital: Most investments fail (capped loss). A few succeed massively (uncapped gain). Convex.
• Tinkering: Most experiments fail (small cost). A few produce breakthroughs (huge value). Convex.
• Writing: Most pieces get ignored (time lost). A few go viral (massive reach). Convex.

Concave payoffs are the opposite: downsides hurt more than upsides help. Selling insurance, taking on debt, making promises—all concave.

Strategy: Collect Options

Implications for decision-making:

Acquire Options Cheaply

Look for situations where you can get asymmetric exposure at low cost. Skills, relationships, small experiments—all cheap options on future possibilities.

Don't Exercise Early

Options have time value. Committing early forecloses alternatives. Delay commitment until information improves—unless waiting has significant cost.

Prefer Reversible to Irreversible

Reversible decisions preserve options. Irreversible decisions spend them. When uncertain, choose reversibility.

Create Optionality, Don't Just Optimize

Traditional planning optimizes for the most likely future. Optionality prepares for many futures. In uncertain environments, optionality beats optimization.

Anti-Fragility

Nassim Taleb extended this to "anti-fragility": systems that benefit from disorder.

• Fragile: Harmed by volatility. Glass, rigid plans, single points of failure.
• Robust: Unaffected by volatility. Stone, redundant systems, buffers.
• Anti-fragile: Benefited by volatility. Evolution, option positions, trial-and-error systems.

Convex payoffs are anti-fragile. They want volatility. They improve through stress.

Personal Applications

Career

Build skills that create options across domains. Avoid over-specialization that eliminates alternatives. Keep runway (savings) that lets you wait for good opportunities.

Projects

Run many small experiments rather than one big bet. Most will fail; some will succeed. The portfolio is convex even if individual bets aren't.

Relationships

Maintain diverse connections. Don't over-concentrate in one community or scene. Optionality in relationships means access to diverse opportunities.

Decisions

When uncertain, ask: "Does this create or destroy options?" Prefer the former. Avoid commitments that foreclose valuable alternatives.

The Cost of Optionality

Options aren't free. Maintaining them requires resources: time, money, attention. Sometimes committing fully outperforms hedging.

The question isn't "always maximize options." It's "what's the right balance of commitment and optionality given uncertainty levels and option costs?"

In stable environments with low uncertainty, commitment often wins. In volatile environments with high uncertainty, optionality wins.

— Decoded by DECODER