1. FORWARD AND FUTURES CONTRACTS èObligation to buy or sell an asset at a future date at a price that is stipulated now èSince no money changes hands now, contract value should be zero èFutures contracts distinguished from forwards by standardization and marking- to- market, but in our analysis we will treat the two contracts as if they were the same

2. NO-ARBITRAGE SPOT-FORWARD PRICING RELATIONSHIP F 0T = forward price on underlying asset to be delivered at T S 0 = spot price of underlying asset Assume: underlying asset makes no cash payments between now and T

3. WHAT IF IT DOESN’T HOLD? If F 0T > S 0 (1+r f ) T : Borrow S 0 Buy underlying asset Sell underlying asset for future delivery If F 0T < S 0 (1+r f ) T : Sell underlying asset short Invest in riskless asset Buy underlying asset for future delivery

4. EXAMPLE: 1 and 2-PERIOD ZEROS

5. T-BILL SPOT FUTURES ARBITRAGE

7. Long Bill (due 12/22) discount = 4.48 Price = (1-.0448(139/360))mil = 982,702.22 Short Bill (due 9/22) discount = 4.13 Price = (1-.0413(48/360)) =.99449333

8. T-BILL SPOT FUTURES ARBITRAGE Futures (due 9/22) Quote = 95.38 discount = 100-95.38 = 4.62 Price = (1-.0462(91/360))mil = 988,321.67 ¬Buy 1 mil face val. long bills: 982,702.22 ­Buy 988,321.67 face value short bills:.99449333(988321.67) = $982,879.31 ®Buy 1 mil face 91 day bills for delivery 9/22: 988,321.67

9. SPOT-FORWARD PRICING (Underlying asset has cash payout) Discrete-time version  = cash flow payout rate (e.g., dividend yield)

10. Application: COVERED INTEREST ARBITRAGE

11. SPOT-FORWARD PRICING (Underlying asset has cash payout) Continuous-time version  = instantaneous cash flow payout rate (e.g., dividend yield)

12. EXAMPLE: STOCK INDEX ARBITRAGE 8/5 S&P 500 index spot = 457.09 futures = 459.8 (12/16 delivery - 129 days from now) 129-day T-bill yield = 4.774% S&P div. yld. = 2.83%

13. STOCK INDEX ARBITRAGE (cont.)

14. CALENDAR SPREADS We have two futures contracts on the same asset but with different delivery dates, near (n) and far (f) How should the contracts be priced relative to one another?

15. TWO INVESTMENT STRATEGIES (see Problem 7, Chapter 8)

16. SAME PAYOFFS, SAME VALUE

17. PUT-CALL INTEREST RATE PARITY