This is the final exam for Asymmetry & Optionality. It pulls the whole course together: the shape of the payoff (value is probability times magnitude, the convex smile versus the concave frown), how a convex bet loses most of its rolls yet wins the war while a concave one prints pennies until the steamroller arrives, optionality as the right without the obligation and the antifragile/fragile/robust trichotomy, the barbell and Jensen’s inequality, and the closing heuristic — cut the downside, keep the upside open. Several questions look easy until you spot a hidden asymmetry: a “safe” streak that is really short optionality, a capped loss that isn’t actually capped, or variance masquerading as good convexity. Draw the payoff shape before you answer each one.
How this exam works
Read carefully — this exam is final. Each question appears one at a time. Once you submit an answer it is locked for good: there’s no going back, no retry, and no restart. Your score is hidden until the end, where you’ll see a pass/fail verdict. The pass mark is 70%. A few questions ask you to select all correct answers.
Asymmetry teaches you to replace one question with a better one before any risky decision. Which swap is correct?
Select an answer to continue.
Course Recap
Big picture
Asymmetry & optionality, in one picture
- Asymmetry & Optionality
- The shape of the payoff
- Value is probability times magnitude, so when payoffs are lopsided the magnitude wins; a convex smile caps the downside and leaves the upside open, while a concave frown caps the upside and leaves the downside open.
- Losing most bets, winning the war
- A convex bet loses a little on 80% of tries and wins big on 20% (EV 0.20 × 10 − 0.80 × 1 = +1.20), finishing far ahead, while the concave pennies-in-front-of-a-steamroller streak feels safe until fat tails make the ruinous loss inevitable.
- Optionality & antifragility
- An option is the right without the obligation, so payoff = max(0, price − strike) − premium caps the loss at the premium and keeps the upside open; fragile is short optionality (harmed by shocks), robust is unaffected, antifragile gains from volatility, and optionality is never free.
- Barbell & Jensen
- The barbell pairs a very safe base with small very risky convex bets and shuns the fragile middle that hides tail risk; Jensen says for a convex payoff the average of outcomes beats the outcome of the average, so volatility is fuel (0 or 10 squared averages 50, beating the average input 5 squared = 25).
- Cut the downside, keep the upside open
- Bound the loss before committing, run many small reversible experiments, and let winners run — while dodging the three traps: overpaying for optionality, a capped downside that is not really capped, and confusing mere variance with genuine convexity.
- The shape of the payoff
Key takeaways
Asymmetry rewires the first question you ask: not how often a bet wins but how big the win is versus the loss, because value is probability times magnitude and, when payoffs are lopsided, magnitude wins. Draw the shape — a convex smile caps the downside and opens the upside (lose a little often, win big rarely), a concave frown does the reverse (win a little often, lose everything rarely) — and you can be wrong 80% of the time and still finish far ahead, while a 99% win-rate sitting on an open-ended loss is a slow walk to ruin. Optionality is that smile manufactured on purpose: the right without the obligation, a small premium buying an open upside, which is why it is antifragile and loves volatility — and why fragility is just short optionality, and why the premium is never free. Put it to work with the barbell (very safe plus very risky, skip the fragile middle) and lean on Jensen’s inequality — for a convex payoff the average of the outcomes beats the outcome of the average, so spread is fuel. The whole latticework collapses to one rule: cut the downside, keep the upside open — bound your losses, run many small reversible experiments, let winners run, and watch for the three traps (overpaying for optionality, a capped downside that isn’t, and variance masquerading as convexity).