1. A PPLICATIONS OF F ORWARD AND F UTURES 1 Week 3

2. Christopher Ting A R ECAP OF F ORWARD AND F UTURES 2 ContractsForwardsFutures Custom; OTC traded Standardized; exchange traded Default RiskCounterparty default risk Clearinghouse guarantees against default. Margin Requirements Contract value generally paid at expiration. Margins and interim settlements are occasionally used to mitigate counterparty default risk Margin requirements and daily mask-to-market to settle gains/losses. Regulatory RequirementsEssentially unregulated. Regulated in U.S. at the federal level Transaction Data Generally unavailable to the public as transactions are private Reported to exchange and regulatory agencies Application/Preferred Risk Management Vehicle Interest rate resets on loans. Foreign currency risk Bond and equity portfolios Dealer transactions to offset Eurodollar swap/option interest rate trades

3. Christopher Ting M OTIVATION Why hedge? Companies can then focus on their main activities, for which presumably they do have particular skills and expertise. By hedging, they avoid unpleasant surprises such as sharp rises in the price of a commodity that is being purchased. What are the arguments against hedging? Shareholders are usually well diversified and can make their own hedging decisions It may increase risk to hedge when competitors do not Explaining a situation where there is a loss on the hedge and a gain on the underlying can be difficult 3

4. Christopher Ting Q UESTIONS TO BE A NSWERED When is a short futures position appropriates When is a long futures position appropriate Which futures contract should be used What is the optimal size of the futures position for reducing risk Mode of hedging Hedge-and forget Futures contracts versus forward contracts 4

5. Christopher Ting L ONG H EDGE, S HORT H EDGE, AND B ASIS f 1 : Initial Futures Price f 2 : Final Futures Price S 2 : Final Asset Price Hedge the future purchase of an asset by entering into a long futures contract Cost of Asset=S 2 – (f 2 – f 1 ) = f 1 + Basis 2 Hedge the future sale of an asset by entering into a short futures contract Price Realized =S 2 + (f 1 – f 2 ) = f 1 + Basis 2 Basis risk arises because of the uncertainty about the basis when the hedge is closed out. 5

6. Christopher Ting M EASURING E QUITY R ISK Equity portfolio risk: beta What is the beta of an equity index (proxy for market portfolio) chosen as the performance benchmark? How is the beta of an equity fund measured? 6 Measure of the direction and extent by which the equity portfolio and the index move together Variance of the return on market Risk level

7. Christopher Ting M ANAGING P ORTFOLIO B ETA Dollar beta of the portfolio market value of the portfolio p P p To modify the risk level of a portfolio, the target beta * should be set in such a way that the sum of the dollar betas of the existing portfolio and a specified number of futures contract N f. Dollar target beta dollar beta of the portfolio + N f dollar beta of 1 futures contract Number of contracts required 7 * P = p P + N f f f m multiplier Futures price

8. Christopher Ting H EDGING E XAMPLE S&P 500 cash value 1,000 S&P 500 futures price is 1,010 Value of Portfolio is $5,050,000 Beta of portfolio is 1.5 Beta of futures is 1.0 Multiplier of S&P 500 is 250 Risk-free interest rate = 4% Dividend yield on index = 1% What position in futures contracts on the S&P 500 is necessary to hedge the portfolio (i.e., * = 0) ? 8

9. Christopher Ting E XAMPLE : A DJUSTING PORTFOLIO BETA A manager of a $5,000,000 portfolio wants to increase the beta from the current of 0.8 to 1.1. The beta on the futures contract is 1.05, and the total futures price is $240,000. What is the required number of futures contracts to achieve a beta of 1.1? The appropriate strategy would be to take long position in 6 futures contracts. Taking a long position in index futures contracts will increase the beta and leverage up the position. 9

10. Christopher Ting T HE H EDGE ISN T P ERFECT (1) Rounding to the nearest whole contract gives rise to imperfect hedge. If the reference index (used to calculate the betas) increased in value by 2%; the value of the equity position increased by 1.6%; and the value of the futures price increased by 2.1 %. These values correspond exactly to what we would expect with the provided betas of 0.8 and 1.05. Had the leveraged position worked as desired (i.e., achieved an effective beta of 1.1), the value of the portfolio would have increased 1.1(0.02) = 2.2% to $5,110,000 = $5,000,000(1 + 0.022) In our example, where we leveraged up the beta with 6 contracts, the profit from the futures contract position is $30,240 = 6($240,000)(1.021)- 6($240,000) The profit from the equity position itself is $80,000 = $5,000,000(1.016) - $5,000,000 Therefore, the final value of the equity portfolio plus futures position is: $5,110,240 = $30,240 + $80,000 + $5,000,000 10

11. Christopher Ting T HE H EDGE ISN T P ERFECT (2) The return on the position is 0.022048 = ($30,240 + $80,000) / $5,000,000 The effective beta on the portfolio proved to be In this case, the discrepancy was due to rounding in the futures position. There is often other error from the fact that the portfolio and futures contracts are not perfectly correlated with the index. 11

12. Christopher Ting C LASS E XERCISE A fund has $400 million invested in a diversified portfolio of common stocks with a beta of 1.1 relative to S&P 500, which is at the level of 968.00. The six-month S&P 500 futures is trading at 998.00 and has a beta of 0.95. The dollar multiplier for the futures contract is 250. 1. To reduce the beta of the portfolio to 0.90, how many contracts should the fund manager trade (buy or sell)? 2. The S&P 500 index is down 3% at the futures expiration date. The portfolio is down 3.4%; the futures are trading at 969.56. What is the value of the overall position (stock portfolio + futures) and the effective beta? 12

13. Christopher Ting A DVANTAGES OF F UTURES Lower Transaction Costs – The use of futures contracts is preferable to liquidation/purchase of portfolio securities, especially over short time horizon. Asset Allocation Revisions – Futures allow managers to make asset allocation changes without disturbing the underlying portfolio. Transaction Time – Risk management strategies can be quickly initiated in response to a particular forecast, and quickly closed out should the outlook change. Contract Liquidity – Futures contracts are generally more liquid than a portfolios individual securities. 13

14. Christopher Ting D ISADVANTAGES Potentially Divergent Risk Management Outcomes – Betas can be unstable and are hard to measure. If a portfolios beta value does not capture the portfolios actual sensitivity to underlying sources of risk, then the hedging process will be inexact. As a result, the actual outcome may diverge from the desired outcome. Contract Liquidity – Futures are not exempt from liquidity problems. The liquidity of long-term futures is significantly lower than that of short-term futures. Entity Liquidity Needs – Although they require less capital to trade, futures cannot solve an investors immediate liquidity needs. For example, to meet an impending cash requirement, underlying securities still have to be liquidated. Leverage – Futures positions are leveraged; losses (or foregone gains) on purchases or sales of futures are potentially large in percentages. For this reason, some firms prohibit the use of these instruments. 14

15. Christopher Ting M ANAGED F UTURES Managed futures is a diverse collection of active hedge fund trading strategies that specialize in liquid, transparent, exchange- traded futures markets and deep foreign exchange markets Managed futures traders are commonly referred to as Commodity Trading Advisors or CTAs, a designation which refers to a managers registration status with the Commodity Futures Trading Commission and National Futures Association. Most CTAs trade equity index, fixed income, and foreign exchange futures. They dont simply take on systematic exposure to an asset class, or beta, but are attempting to add alpha through active management and the freedom to enter short or spread positions, which can result in totally different return profiles than the long-only passive indices. 15

16. Christopher Ting M ANAGED F UTURES G ROWTH IN A SSETS U NDER M ANAGEMENT 1980-2008 AUM ($billions) 16 Source: AlphaMetrix Alternative Investment Advisors, BarclayHedge Alternative Investment Database

17. B ARCLAY H EDGE S BTOP50 I NDEX 17 Dec 1987Feb 1991Apr 1995Jun 1999Aug 2003Oct 2007Dec 2011 Source: BarclayHedge Alternative Investment Database

18. Christopher Ting P ERFORMANCE OF M ANAGED F UTURES Maximum, Minimum, and Mean Rolling Return of Barclays Capital BTOP 50 Index Over Different Holding Periods (Jan 1987 through Dec 2008) 18 Rolling Rate of Return Months Source: AlphaMetrix Alternative Investment Advisors, Bloomberg

19. C ASE S TUDY 19

20. Christopher Ting O PTIMAL H EDGING WITH I NDEX F UTURES (1) An institutional investor holds a portfolio of Japanese stocks that has returns following closely that of the Nikkei 225 stock index returns S t+1 /S t, where S t+1 = S t+1 – S t. The value of the portfolio in yens is N S S t, i.e., N S shares of a stock called Nikkei 225. Multiplier of Nikkei 225 futures traded on SGX is ¥500. Value of the hedged portfolio with N f futures contracts is V t = N S S t – N f 500 f t P – F 20

21. Christopher Ting O PTIMAL H EDGING WITH I NDEX F UTURES (2) The change in portfolio value is V t+1 = N S S t+1 – N f 500 f t+1 P – F The investor minimizes the risk or variance of V t+1 by finding an optimal number N f such that the risk is minimum. Solving the first order condition with respect to N f leads to 21

22. Christopher Ting O PTIMAL H EDGE R ATIO o S : standard deviation of S, the change in the spot price during the hedging period o f : standard deviation of f, the change in the futures price during the hedging period o : the coefficient of correlation between S and f o h*: hedge ratio that minimizes the variance of the hedgers total position in the underlying and the futures. 22

23. Christopher Ting M INIMUM V ARIANCE H EDGE To hedge the risk of an index portfolio, the number of contracts that should be shorted is Beta of the index futures can be estimated with the following linear specification 23

24. Christopher Ting C ASE S TUDY (1) An asset management company has a long position of 500 lots in STI ETF. The volume-weighted average price per share is S$3.4567 when the STI ETF shares were purchased. Using a proprietary quant strategy, the fund holds the view that over the next 2 weeks, STI is expected to decline. To protect the funds value, the fund decides to use a futures contract to hedge. Naturally, the fund looks into STI futures traded on SGX. Question: What is the book value of the long position in STI ETF? Question: Should the fund perform a long hedge or a short hedge? 24

25. Christopher Ting C ASE S TUDY (2) Unfortunately, the liquidity of STI futures is almost zero. 25

26. Christopher Ting C ASE S TUDY (3) By contrast, futures on MSCI Singapore index are more liquid. 26

27. Christopher Ting C ASE S TUDY (4) Suppose the said 2 weeks start from November 9, 2010. Question: Which maturity month of SiMSCI should the fund use? Question: How many contracts should the fund cross-hedge with SiMSCI futures to achieve an optimal result? 27