Arbitrage: when prices have to agree, or you get paid
Two portfolios with the same payoff in every state must have the same price. If they don't, you trade until they do, risk-free.
Method · Arbitrage
Intro
Arbitrage is a riskless profit — a trade that costs nothing today, can never lose, and pays you something. The rule: two portfolios that pay the same in every future state must cost the same today. When prices disagree, the gap is the trade. We’ll work one example: a stock vs. its forward.
✓ Intro · expand
Try first (productive failure)
Before the worked example: spend 60 seconds taking your best shot at this.
A guess is fine — being briefly wrong about a problem makes the explanation
land harder when you read it. This appears once per tutorial; skip
if you already know the trick.
60s
✓ Try first · expand
Worked example
A stock trades at $S = \$100$. A 1-year forward contract on the stock trades at $F = \$103$. The 1-year continuously-compounded risk-free rate is $r = 5\%$. No dividends, no transaction costs. What is the riskless arbitrage profit per share, expressed as today’s present value (in dollars, to 2 d.p.)?
✓ Worked example · expand
Practice 1 of 3Type a fraction, decimal, or expression — mathjs parses it.
✓ Practice · expand
Reflection
All three problems used the same recipe: <em>price the cash flow two independent ways, then trade the gap.</em> Why does the no-arbitrage assumption force $F = S e^{rT}$ in the first place — and which real-world frictions (borrowing spread, shorting cost, bid-ask) would have to exceed the gap before the arbitrage stops being free money?