T0 tt buy asset today s s t long forward 0 s t f

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t=0 t=T Buy asset today -S 0 S T Long forward 0 S T – F 0 Fin330 8
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Buy asset now vs. Long forward l Shift timing by lending or borrowing. l Timing of cash flows: t=0 t=T Buy asset today and borrow $ Long forward Fin330 9
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Buy asset now vs. Long forward l Shift timing by lending or borrowing. l Timing of cash flows: t=0 t=T Buy asset today and borrow $ -S 0 +S 0 =0 S T -S 0 e rT Long forward 0 S T – F 0 Fin330 10
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Buy asset now vs. Long forward l Which strategy generates a higher total payoff? l Both strategies have the same payoff at t=0 . l So we can just compare the payoffs at t=T : l Buy asset now: S T - S 0 e rT ; l Long forward: S T – F 0 . Fin330 11
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Arbitrage opportunities l Suppose that: S T - S 0 e rT > S T – F 0 F 0 > S 0 e rT l What could investors do? t=0 t=T Short-sell forward Borrow S 0 Buy and carry asset Total payoff Fin330 12
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Arbitrage opportunities l Suppose that: S T - S 0 e rT > S T – F 0 F 0 > S 0 e rT l What could investors do? t=0 t=T Short-sell forward 0 + F 0 -S T Borrow S 0 + S 0 -S 0 e rT Buy and carry asset - S 0 S T Total payoff 0 F 0 -S 0 e rT >0 Fin330 13
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Arbitrage opportunities l There would be an arbitrage opportunity in t=T (“money tomorrow”). l This is called “cash and carry” arbitrage : l buy the underlying asset and l short the offsetting forward contract. Fin330 14
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Arbitrage opportunities l Suppose that S T - S 0 e rT < S T – F 0 F 0 < S 0 e rT l What could investors do? t=0 t=T Long forward Short-sell the asset Lend money Total payoff Fin330 15
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Arbitrage opportunities l Suppose that S T - S 0 e rT < S T – F 0 F 0 < S 0 e rT l What could investors do? t=0 t=T Long forward Short-sell the asset Lend money Total payoff Fin330 16
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Arbitrage opportunities l Suppose that S T - S 0 e rT < S T – F 0 F 0 < S 0 e rT l What could investors do? t=0 t=T Long forward 0 S T -F 0 Short-sell the asset S 0 -S T Lend money -S 0 S 0 e rT Total payoff 0 S 0 e rT -F 0 Fin330 17
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Arbitrage opportunities l Suppose that S T - S 0 e rT < S T – F 0 F 0 < S 0 e rT l What could investors do?
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