A Tale of Two Futures: $ versus ¥ Nikkei 225 Index Futures

1. A Tale of Two Futures:$ versus ¥ Nikkei 225 Index Futures Christopher Ting

2. Learning Objectives • Define quanto • Understand inter-market spread trading strategy • Analyze the P&L of a short quanto position

3. Quanto • Quantos are derivatives where the payoff is defined using variables measured in one currency but paid in another currency • Example: futures contract providing a payoff of NT – K dollars ($) to the counterparty holding the long position. • Here, NT is the Nikkei 225 index value at maturity T and K is the futures price

4. Nikkei 225 Futures in USD and JPY • Contract Multiplier USD 5 for NKD; JPY 500 for NIY • Minimum Price Change (Tick) 5 index points • Final Settlement: Cash-settled to Special Opening Quotation of the Nikkei 225 Index on 2nd Friday of the contract expiry month • Last Trading Day 3:15 p.m. Central Time on the day preceding final settlement – usually the Thursday prior to 2nd Friday of the contract expiry month • Contract Months: Quarterlies for NKD; Quarterlies and Serials for NIY

5. Trading Hours (before 2011) • At 3:30 p.m. Singapore Time, T+1 session for Nikkei index futures opens • Simex: (multiplier 5, tick size 5 index points) • Osaka: Big (multiplier 5, tick size 10 index points) and Mini (multiplier 1, tick size 5 index points) • At 4 p.m. Singapore Time, NKD futures market opens • At 7 p.m. Singapore Time, NIY futures market opens

6. NKD: Dollar-Denominated Futures

7. NIY: Yen-Denominated Futures

8. Arbitrage Opportunity? At 14:02, NKD @ 10,800

9. Arbitrage Opportunity? At 14:02, NIY @ 10,735

10. Motivating Questions • Why was the market price of NKD 65 points higher than that of NIY on Jan 5? • Risk-free arbitrage opportunity? • Short NKD and long NIY? • The exchange rate on Jan 5, 2010 at 14:00 Central Time • Cash Market: ¥91.71 per $1 • Futures Market: front quarter JPY/USD futures (6J) price was 109,040, which was equivalent to ¥91.71 per dollar.

11. Follow-up Question • What should the futures price of NKD be relative to the futures price of NIY? • What should be the spread between these two futures prices?

12. NKD – NIY Spread • At time t=0, let N0 be the cash Nikkei index value, and the futures prices F$ and F¥ are • So the fair-value spread is F¥ = N0(1+ rT ) F$ = N0(1+ (r+ ns)T) = F¥ + N0  nsT F$ –F¥ = N0  ns T

13. Behavior of the NKD – NIY Spread • When cash market N goes up, dollar tends to strengthen (S increases) • In other words, when dollar strengthens (S increases), cash market N tends to go up. • Why? • Dollar strengthening means Yen depreciating, which will be helpful to export-oriented companies in Nikkei 225 index N, so N tends to go up. • Thus the correlation between the (percentage) change in N and the (percentage) change in S is positive.

14. Illustration • Suppose the correlation is 30%, the volatility of Nikkei 225 index return is 50%, and the volatility of the yen-per-dollar exchange rate is 15%. The index level is at 10,680 and the time to maturity is 3 months. • The spread is about 60 index points: 10,680  0.3  0.5  0.15  3/12 = 60.1

15. Money-Making Opportunity? • At maturity, T = 0, the NKD – NIY spread is zero. This is the time decay effect. • Since the NKD – NIY spread is positive, one can take a short position in this spread (i.e. sell NKD and buy NIY), and hold this spread position until maturity to benefit from the time decay. • Is it a good money-making opportunity?

16. Profit and Loss • At time t=0, sell short one NKD contract at a price of F$, and buy R number of NIY contracts at a price of F¥. • At maturity T, ST is the spot yen per dollar exchange rate • Let NT be the settlement price of the futures contract, which is based on the SOQ of cash Nikkei 225 index value. The position’s payoff at maturityis, in dollars –5  (NT – F$) + R  500  (NT – F¥) / ST

17. Profit and Loss (cont) • Suppose the ratio Ris chosen to be • Then the payoff is which is –5  (NT – F$) + 5  S0  (NT – F¥) / ST ¥ ¥  ¥

18. P&L Example: Normal • Same parameters as in the illustration, the spread is 60 points. Thus, gain from time decay is $5  60 = $300. • Suppose S0 = 90 yens per dollar. • So the ratio R is short NKD contracts and long 9 NIY contracts. • Suppose ST is 87 yens per dollar, i.e., dollar weakens, and the settlement is 800 points lower, i.e., NT – F¥ = –800 at maturity. • Then 5  (90 – 87)/87 = 15/87, and the P&L per NKD contract is –$15  800/87 + $300 = $116.09

19. P&L Example: Market Crashes • Suppose the market crashes, and ST is 85 yens per dollar, i.e., dollar weakens substantially, and the settlement is 2,000 points lower, i.e., NT – F¥ = –2,000. • Then 5 (90 – 85)/85 = 25/85, and the P&L at maturity is, for every NKD contract, –$25  2,000/85 + $300 = –$288.24

20. P&L Example: Market Rallies • Suppose the market rallies, and ST is 95 yens per dollar, i.e., dollar strengthens, and the settlement is 2,000 points higher, i.e., NT – F¥ = 2,000. • Then 5 (90 – 95)/95 = –25/95, and the P&L at maturity per NKD contract is –$25  2,000/95 + $300 = –$226.32

21. Bottom Line • When market is quiet, i,e., the markets neither crash nor rally, short quanto position will make money • But it will lose money if extreme conditions (either up or down) prevail. • Don’t be the next Nick Leeson!