CHAPTER 10 Securities Futures Products Refinements

1
CHAPTER 10Securities Futures Products Refinements

• In this chapter, we extend the discussion of
  stock index futures. This chapter is organized
  into the following sections
• Stock Index Futures Prices
• Program Trading
• Hedging with Stock Index Futures
• Asset Allocation
• Portfolio Insurance
• Index Futures and Stock Volatility
• Index Futures and Stock Market Crashes

2
Stick Index Futures Prices

• In this section, the following issues are
  explored
• The empirical evidence on stock index futures
  efficiency.
• do stock index futures prices conform to the
  Cost-of-Carry Model?
• The effect of taxes on stock index futures
  prices.
• The timing relationship between stock index
  futures prices and the cash market index.
• Does the futures price lead the cash market
  index, or does the cash market index lead the
  futures?
• The seasonal impacts on stock index futures
  pricing.

3
Stock Index Futures Efficiency

• Recall that the success of an arbitrage
  opportunity can be affected by
• The use of short sale proceeds
• Transaction costs
• Dividend variability
• Every real market has a range of permissible
  no-arbitrage prices. This no-arbitrage band
  increases because of transaction costs and
  restrictions on short selling.
• Evidence suggests that the futures market was
  inefficient in the early days of trading but now
  it conforms well to the Cost-of-Carry Model.
• Figure 10.1 shows the result of a study by Modest
  and Sundaresan.

4
Stock Index Futures Efficiency

• Insert figure 10.1 here

• Notice how the observed price is almost always
  within the no arbitrage bounds and never deviates
  far from them.

5
Effect of Taxes on Stock Index Futures Prices

• Because futures prices are marked-to-market at
  year end for tax purposes, index futures
  contracts possess no tax-timing options.
• In the futures markets, tax rules require all
  paper gains or losses to be recognized as cash
  gains or losses each year.
• In the cash market, an individual can time his
  tax gains or losses.
• In an empirical study of the effect of the
  tax-timing option, Cornell concludes that the
  tax-timing option does not appear to affect
  prices.

6
Timing Effect on Stock Index Futures Prices

• The Day of the Week Effect in Stock Index Futures
• A great deal of evidence shows that returns on
  stocks differ depending on the day of the week.
  In particular, Friday returns are generally high.
  
• Leads and Lags in Stock Index Prices
• Leads and lags in stocks index prices refer to
  which market drives the other.
• Does the futures price lead the cash market
  index, or does the cash market index lead the
  futures market?
• The question of leads and lags has been explored
  in several studies, most of which find that
  futures prices lead cash market prices.

7
Program Trading

• In Chapter 9, we examine index arbitrage through
  program trading and how to engage in
  cash-and-carry and reverse cash-and-carry
  strategies to exploit pricing differences between
  the index and the index futures.
• Recall further from Chapter 9 that the futures
  price that conforms with the Cost-of-Carry Model
  is called the fair-value futures price.
• In this section, we determine the fair value of
  the December 2001 SP 500 stock index futures
  contract traded on November 30, 2001.

8
Program Trading

• Assume that the December 2001 futures contract
  closed at 1140 index points on November 30. The
  cash index price on this date was 1139.45. The
  value of the compounded dividend stream expected
  to be paid out between the 30th of November and
  December 21 totaled .9 index points. The
  financing cost for large, credit-worthy borrowers
  was approximately 1.90 annualized over a 365-day
  year (0.1093 over the 21 days from Nov 30 to Dec
  21). Suppose that the December 2001 futures price
  on November 30, 2001 had been 1143.00 instead of
  the actual 1140. Using this information, we can
  apply the Cost-of-Carry Model to determine the
  fair-value futures price
• F0,t 1139.45 (1 .001093) -.9 1139.80 index
  points
• Tables 10.1 and Table 10.2 show the transaction
  involved in a cash-and-carry and reverse
  cash-and-carry arbitrages.

9
Program TradingA Real World Example

• Table 10.1 shows how an arbitrage profit can be
  earned if the futures price is 1143.

By completing the arbitrage, the trader was able
to earn a 4.99 annualized return.
Since the financing cost was 1.9, an arbitrage
profit was earned.
10
Program TradingA Real World Example
Now suppose that the futures price is 1138. Table
10.2 shows how an arbitrage profit can be earned.
The investor is earning a 2.78 annualized return.
Since the financing cost is 1.90, an arbitrage
profit was earned.
11
Real-World Impediments to Stock Index Arbitrage

• The Cost-of-Carry Model needs to be refined to
  account for real-world impediments to arbitrage
  strategies.
• An empirical study conducted by Sofianos reports
  that
• Existence of arbitrage opportunities depends on
  the level of transaction costs. Lower transaction
  costs are associated with more frequent arbitrage
  opportunities.
• Arbitrageurs often use surrogate stock baskets
  containing a subset of the index stocks instead
  of trading all the stocks in the index.
• Arbitrageurs frequently establish (or liquidate)
  their futures and cash positions at different
  times.

12
Hedging with Stock Index Futures

• Recall from chapter 9 that a manager can
  determine the number of contract to trade by
  using the following equation

Where VP value of the portfolio VF value
of the futures contract ßP beta of the
portfolio that is being hedged
13
Hedging with Stock Index Futures
The risk of a combined cash and futures position
is equal to
Where
14
Hedging with Stock Index Futures

• The risk-minimizing hedge ratio (HR) is

Where COVSF the covariance between S and F
The easiest way to find the risk-minimizing hedge
ratio is to estimate the following regression
St the returns on the cash market position
in period t Ft the returns on the futures
contract in period t ? the constant
regression parameter ßRM the slope regression
parameter for the risk-minimizing hedge e an
error term with zero mean and standard
deviation of 1.0
15
Hedging with Stock Index Futures

• From the above equation, the negative of the
  estimated Beta is the risk-minimizing hedge
  ratio.
• Having found the risk-minimizing hedge ratio (
  -ßRM,), Compute the number of contracts to trade,
  using

16
Minimum Risk Hedging

• Assume that today, November 28, a portfolio
  manager has 10 million dollar invested in the 30
  stocks of the DJIA. The portfolio manager will
  hedge using SP 500 JUN futures contract.
• On Nov 27, the SP futures closed at 354.75. The
  future contract value is the index level times
  250.
• Compute the hedge ratio and determine the number
  of contract to purchase.
• Step 1 collect historical data
• In order to perform the analysis the portfolio
  manager collects historical data. The portfolio
  manager has collected 100 paired observations of
  daily returns data on her portfolio and the SP
  500 JUN futures contract. The data covers from
  July 7 to November 27.

17
Minimum Risk Hedging
Step 2 estimate the hedging beta using
The regression results are ßRM 0.8801 R2
0.9263

• Step 3 compute the futures position using

The estimated risk-minimizing futures position is
-99.24 contracts, so the portfolio manager
decides to sell 100 contracts.
18
Minimum Risk Hedging

• Step 4 evaluate the hedging results.
• Figure 10.2 illustrates the results.

• Insert Figure 10.2 here

The hedged portfolio maintained its value while
the un-hedged portfolio declined in value
substantially. Clearly, the hedge worked well.
19
Minimum Risk Hedging

• Using historical data or ex-ante (before the
  fact), the best ratio that the portfolio manager
  had was ßRM 0.8801.
• Using data after the fact or ex-post (data from
  Nov 28 to Feb 22), the best beta ratio that the
  portfolio manager had was ßRM 0.9154. This beta
  was calculated after the investment was made
  using data from Nov 28 to Feb 22.
• Figure 10.3 illustrates the differences in
  performance using ex-ante and ex-post data.

• Insert figure 10.3 here

While the ex-post hedge ratio is superior, the
ex-ante hedge is the best estimate that is
available at the time the decision must be made.
20
CAPM and Portfolio Beta

• Portfolio managers often adjust the CAPM betas of
  their portfolios in anticipation of bull and bear
  markets.
• Bull market increase the beta of the portfolio
  to take advantage of the expected rise in stock
  prices.
• Bear market reduce the beta of a stock portfolio
  as a defensive maneuver.
• From the CAPM, all risk is defined as either
  systematic or unsystematic.
• Systematic risk is associated with general
  movements in the market and affects all
  investments.
• Unsystematic risk is particular to a investment
  or range of investments.
• Diversification can almost eliminate unsystematic
  risk from a portfolio. The remaining systematic
  risk is unavoidable.
• A portfolio with zero systematic risk should earn
  the risk-free rate of interest.

21
CAPM and Portfolio Beta

• Portfolio managers can use hedging to eliminate
  only a portion of the systematic risk or they can
  use stock index futures to increase the
  systematic risk of a portfolio.
• Risk-Minimizing Hedge
• A risk-minimizing hedge matches a long position
  in stock with a short position in stock index
  futures in an attempt to create a portfolio whose
  value does not change with fluctuations in the
  stock market.
• To reduce, but not eliminate the systematic risk,
  a portfolio manager could sell some futures, but
  fewer than the risk-minimizing amount.
• To increase the systematic risk of the portfolio,
  a manager could buy some futures contracts.
• Figure 10.4 shows the price paths of two
  portfolios.

22
CAPM and Portfolio Beta

• The first portfolio is an unhedged portfolio. Its
  value starts with 10,000,000 and finished at
  9,656,090 in a period of declining markets. The
  second portfolio includes the same 10,000,000 of
  stocks from the first portfolio plus a long
  position of 52 futures contracts. This
  combination doubles the systematic risk of the
  portfolio. In this case, the value of the
  portfolio declined to 9,052,340 in the same
  period of declining markets.

• Insert figure 10.4 here

23
Asset Allocation

• In asset allocation, an investor decides how to
  allocate and shift funds among broad asset
  classes.
• Recall that for financial futures the cost of
  carry essentially equals the financing cost.
• In a full carry market, a cash-and-carry strategy
  should earn the financing rate, which equals the
  risk-free rate of interest. This can be expressed
  as
• Short-Term Riskless Debt Stock - Stock Index
  Futures
• A trader might create a synthetic T-bill by
  holding stock and selling futures
• Synthetic T-bill Stock - Stock Index Futures
• This is a synthetic T-bill rather than an actual
  T-bill. While the portfolio will mimic the price
  movements of a T-bill, no T-bills were purchased.
  This technique is useful for a trader that wishes
  to temporarily reduce the risk of a portfolio
  without selling stocks.
• A futures portfolio with no systematic risk has
  an expected return that equals the risk-free
  rate.
• Rearranging the second equation, a synthetic
  stock portfolio can be created.
• Synthetic Stock Portfolio T-bills Stock Index
  Futures

24
Portfolio Insurance

• For a given well-diversified portfolio, selling
  stock index futures can create a combined
  stock/futures portfolio with reduced risk.
• Portfolio insurance refers to a collection of
  techniques for managing the risk of an underlying
  portfolio.
• The goal of portfolio insurance is to manage the
  risk of a portfolio to ensure that the value of
  the portfolio does not drop below a specified
  level.
• It involves adjusting the number of futures
  contracts in the portfolio over time as the value
  of the portfolio changes.
• Dynamic hedging refers to implementing portfolio
  insurance strategies using futures. It requires
  continually monitoring the portfolio.
• While portfolio insurance can be desirable, it is
  not free.

25
Portfolio Insurance

• Assume that a stock index futures contract has an
  underlying value of 100 million. A trader wishes
  to insure a minimum value for the portfolio of
  90 million. Initially the trader sells futures
  contracts to cover 50 million of the value of
  the portfolio. Thus, in the initial position, the
  trader is long 100 million in stock and short
  50 million in futures, so 50 of the portfolio
  is hedged. Table 10.4 shows the basic strategy
  of portfolio insurance with dynamic hedging.

Notice that the value of the portfolio does not
drop below the 90 million floor, so the
insurance worked.
26
Implementing Portfolio Insurance

• Choosing the initial futures position depends on
• The floor that is chosen relative to the
  initial value.
• The lower the floor, the lower the portion the
  portfolio to be initially hedged.
• B. The volatility of the stock portfolio.
• The higher the volatility of the stock portfolio,
  the higher the proportion of the portfolio to be
  initially hedged.
• Adjustments to the futures position depends upon
  
• The floor that is chosen relative to the
  portfolio value.
• New information about the volatility of the
  stock price.
• Higher the volatility leads to larger futures
  positions.

27
Index Futures and Stock Market Volatility

• Has stock market volatility increased since the
  introduction of stock index futures trading?
• 1. Stock index futures have been alleged to
  cause market volatility due to index
  arbitrage and portfolio insurance practices.
• Evidence suggest that worldwide financial
  volatility has generally decreased.
• Even if proven that stock index futures trading
  did increase stock market volatility, is that
  bad?
• In an efficient market, the price quickly adjusts
  to reflect new information.
• Price volatility results from the arrival of new
  information in the market.
• Economists often interpret volatile prices as
  evidence of functioning efficient market.

28
Index Arbitrage and Stock Market Volatility

• 2. Critics argue that index arbitrage may lead
  to dramatic volatility in the market and
  disrupted trading.
• Recall that in index arbitrage, traders search
  for discrepancies between stock prices and
  futures prices.
• When the discrepancies are large enough to cover
  the transaction costs, index arbitrageurs enter
  the market to sell the overpriced side and buy
  the underpriced side.
• This action may put large orders on the market at
  critical times.

29
Portfolio Insurance and Stock Market Volatility

• 3. Portfolio insurance can also contribute to
  potential order imbalances that might affect
  stock prices.
• Assume a large drop in stock prices. This will
  cause the following chain reaction
• Future prices will fall.
• Portfolio insurers will place large numbers of
  orders to sell index futures.
• Critics argue that the large sell orders from
  portfolio insurers might temporarily depress
  futures prices below the price justified by the
  Cost-of-Carry Model, creating disruptive chain
  reactions.

30
Index Futures and Stock Crashes

• October 19, 1987 Stock Market Crash
• Dow Jones value drops by 22.61
• Heavy trading volume brought trade processing to
  a virtual halt.
• The inability of cash markets to handle the
  incredible order flow contributed to the market
  turmoil.
• The Cascade Theory was introduced from the Brady
  Report.
• The Cascade Theory was described as a vicious
  cycle cause by index arbitrage and portfolio
  insurance.

31
Index Futures and Stock CrashesCascade Theory
32
Index Futures and Stock Crashes

• Figure 10.6 shows the spread between the cash and
  futures using Chicago time.

• Insert figure 10.6 here

Figure 10.6 indicates that on October 19, 1987
the stock and futures basis did respond to the
information that was available.