1

APPLICATIONS OF FORWARD AND FUTURES

Week 3

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A RECAP OF FORWARD AND FUTURES

Contracts Forwards FuturesCustom; OTC traded Standardized;

exchange tradedDefault Risk Counterparty 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 Requirements Essentially 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 portfoliosDealer transactions to offset Eurodollar swap/option interest rate trades

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MOTIVATION

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 decisionsIt may increase risk to hedge when competitors

do notExplaining a situation where there is a loss on the

hedge and a gain on the underlying can be difficult

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QUESTIONS TO BE ANSWERED

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 hedgingHedge-and forgetFutures contracts versus forward contracts

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LONG HEDGE, SHORT HEDGE, AND BASIS

f1 : Initial Futures Price

f2 : Final Futures Price

S2 : Final Asset Price Hedge the future purchase of an asset by entering

into a long futures contract Cost of Asset=S2 – (f2 – f1) = f1 + Basis2

Hedge the future sale of an asset by entering into a short futures contract

Price Realized =S2 + (f1 – f2) = f1 + Basis2

Basis risk arises because of the uncertainty about the basis when the hedge is closed out.

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MEASURING EQUITY RISK

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?

2

),(

m

mpp

rr

C

Measure of the direction and extent by which the equity portfolio and the index move together

Variance of the return on market

Risk level

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MANAGING PORTFOLIO BETA

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 Nf.

Dollar target betadollar beta of the portfolio + Nf dollar beta of 1 futures

contract

Number of contracts required

mfP

Nf

pf

*

* P = p P + Nf f f m

multiplier

Futures price

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HEDGING EXAMPLE

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) ?

30010,1250

000,050,5

0.1

5.1

fN

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EXAMPLE: ADJUSTING 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.

95.5000,240$000,000,5$

05.18.01.1

fN

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THE HEDGE ISN’T PERFECT (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

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THE HEDGE ISN’T PERFECT (2)

The return on the position is0.022048 = ($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. 

1024.1020.0

022048.0value index of change %

value portfolio of change % betaeffective

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CLASS EXERCISE

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?

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ADVANTAGES OF FUTURES

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 portfolio’s individual securities.

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DISADVANTAGES Potentially Divergent Risk Management Outcomes – Betas

can be unstable and are hard to measure. If a portfolio’s beta value does not capture the portfolio’s 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 investor’s 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.

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MANAGED FUTURES “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 manager’s registration status with the Commodity Futures Trading Commission and National Futures Association.

Most CTAs trade equity index, fixed income, and foreign exchange futures. They don’t 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.

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MANAGED FUTURES GROWTH IN ASSETS UNDER MANAGEMENT 1980-2008

AUM ($billions)

Source: AlphaMetrix Alternative Investment Advisors, BarclayHedge Alternative Investment Database

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BARCLAYHEDGE’S BTOP50 INDEX

0 50 100 150 200 250 3000

1000

2000

3000

4000

5000

6000

7000

8000

9000

Dec 1987 Feb 1991 Apr 1995 Jun 1999 Aug 2003 Oct 2007 Dec 2011

Source: BarclayHedge Alternative Investment Database

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PERFORMANCE OF MANAGED FUTURES

Maximum, Minimum, and Mean Rolling Return of Barclays Capital BTOP 50 Index Over Different Holding Periods (Jan 1987 through Dec 2008)

Rolling Rate of Return

Months

Source: AlphaMetrix Alternative Investment Advisors, Bloomberg

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CASE STUDY

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OPTIMAL HEDGING WITH INDEX FUTURES (1)

An institutional investor holds a portfolio of Japanese stocks that has returns following closely that of the Nikkei 225 stock index returns St+1/St , where St+1 = St+1 – St .

The value of the portfolio in yens is NS St, i.e., NS shares of a “stock” called Nikkei 225.

Multiplier of Nikkei 225 futures traded on SGX is ¥500.

Value of the hedged portfolio with Nf futures contracts is Vt = NS St – Nf 500 ft P – F

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OPTIMAL HEDGING WITH INDEX FUTURES (2)

The change in portfolio value isVt+1 = NS St+1 – Nf 500 ft+1 P – F

The investor minimizes the risk or variance of Vt+1 by finding an optimal number Nf such that the risk is minimum.

Solving the first order condition with respect to Nf leads to

11122

12

1 ,5002500 ttfStftSt fSNNfNSNV CVVV

1

11*

500,

t

ttSf f

fSNN

VC

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OPTIMAL HEDGE RATIO

o sS : standard deviation of DS, the change in the spot price during the hedging period

o sf : standard deviation of Df, the change in the futures price during the hedging period

o r : the coefficient of correlation between DS and Df

o h*: hedge ratio that minimizes the variance of the hedger’s total position in the underlying and the futures. f

S

S

f

N

Nh

**

500

f

SS

f

fSS

t

ttSf

NNf

fSNN

500500500,

21

11*

VC

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MINIMUM VARIANCE HEDGE

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

mf

PN f *

111

t

t

t

t

t eff

SS

t

t

tt

t

t

t

ttS

t

tt

t

t

t

tttS

t

ttSf f

P

ff

f

ff

SS

SN

ff

f

ff

SS

fSN

f

fSNN

500500

,

500

,

500

,

1

11

12

11

1

11*

V

C

V

C

VC

t

t

t

t

t

t

ff

ff

SS

1

11 ,

V

C

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CASE STUDY (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 fund’s 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?

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CASE STUDY (2)

Unfortunately, the liquidity of STI futures is almost zero.

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CASE STUDY (3)

By contrast, futures on MSCI Singapore index are more liquid.

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CASE STUDY (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?