Finance 381 Final Exam
One Chicago has just introduced a new single stock futures contract on the stock of Brandex, a company that currently pays no dividends. Each contract calls for delivery of 2,000 shares of stock in one year. The T-bill rate is 4% per year. If Brandex stock now sells at $250 per share, what should the futures price be?
$250 × 1.04 = $260.00
Jensen Measure
- Alpha of an investment - measure of abnormal return - must establish statistical significance via regression
Problems with Performance Measures
- Assume a fund maintains constant level of risk - Extremely bad for funds engaging in active asset allocation
Stock-Index Futures
- Available on DOMESTIC and INTERNATIONAL stocks - Several advantages over direct stock purchase such as lower transaction costs and easier to implement timing/allocation strategies
Foreign Currency: Forward Contracts
- CURRENCY MARKETS LARGEST IN THE WORLD - available from LARGE BANKS - FORWARD CONTRACTS used to hedge foreign currency transactions
Multi-Index model
- Fama-French - allows the estimation of alpha
Interest Rate Futures
- Major Contracts: Eurodollars, T-bills, T-notes, T-bonds - some foreign interest rate contracts ARE available - SHORT POSITION interest contracts benefit if Interest rates INCREASE - LONG POSITION interest contracts benefit if interest rates FALL
Interest Rate Futures: HEDGING
- Often requires CROSS-HEDGING: cross-hedging means hedging spot position with a futures contract that has a different underlying asset Ex: Hedge corporate bond by selling T-bond futures
Interest Rate Swaps
- One pays the other a fixed rate of interest in exchange for a variable rate of interest - NO PRINCIPLE EXCHANGED
Synthetic stock purchase
- Purchase of stock-index futures instead of actual shares - Allows frequent trading at low cost - Useful for foreign investments
Trading Strategies: SPECULATION
- SHORT if you believe the price will FALL - LONG if you believe price will RISE
Currency Swaps
- Two parties swap principle AND interest payments at a FIXED exchange rate - The firm may borrow money in whatever currency has the lowest interest rate and then SWAP payments into the preferred currency
Regulations
-Regulated by Commodity Futures Trading Committee (CFTC) - Exchange can set limits on one-day price changes
A single stock futures contract on a nondividend-paying stock with current price $195 has a maturity of one year. 1) If the T-bill rate is 4.2%, what should the futures price be? 2) What should the futures price be if the T-bill rate is still 4.2% and the maturity of the contract is three years?
1) $195 × 1.042 = $203.19 2) $195 × (1.042)^3 = $220.62
Suppose the yield on short-term government securities (perceived to be risk-free) is about 4%. Suppose also that the expected return required by the market for a portfolio with a beta of 1 is 12%. According to the capital asset pricing model: 1) What is the expected return on the market portfolio? 2) What would be the expected return on a zero-beta stock?
1) Since the market portfolio, by definition, has a beta of 1.0, its expected rate of return is 12%. 2) β = 0 means the stock has no systematic risk. Hence, the portfolio's expected rate of return is the risk-free rate, 4%.
Suppose the value of the S&P 500 Stock Index is currently $1,350. If the one-year T-bill rate is 3.1% and the expected dividend yield on the S&P 500 is 2.2%. What should the one-year maturity futures price be?
1,350 × (1 + 0.03 - 0.02) = $1,362.15
Alpha Capture
Construction of a positive alpha portfolio with all systematic risk hedged away
BASIS AND HEDGING: What is Basis?
Difference between futures price and spot price
open interest
Opened contracts not offset with reversing trade
futures price
the agreed-upon price to be paid on a futures contract at maturity
PASSIVE management
Diversified portfolio with NO security misplacing identification
Clearinghouse
Facilitates trading; may be intermediary between two traders
ACTIVE management
Forecasting broad markets and/or identifying mispriced securities to achieve higher returns
The current level of the S&P 500 is 1,200. The dividend yield on the S&P 500 is 2.0%. The risk-free interest rate is 1.0%. What should a futures contract with a one-year maturity be selling for?
Futures price = S0 (1+ rf − d)T = $1,200 × (1 + 0.010 − 0.020) = $1,188
Hedging
LONG: Endowment fund will purchase stock in 3 months; manager buys futures NOW to protect against rise in price SHORT: Hedge fund invests in long-term bonds' manager worries interest rates may increase, and SELLS futures
What system assists in rapid trade execution?
SuperDot
Classic market-timing strategy
Switch between T-bills and stocks based on market conditions - cheaper to buy T-bills then to shift stock market exposure by buying and selling stock-index futures
Maintenance origin
Value below which trader's margin may not fall; triggers margin call
single stock futures
a futures contract on the shares of an individual company
convergence property
the convergence of futures prices and spot prices at the maturity of the futures contract
marking to market
the daily settlement of obligations on futures positions
Based on current dividend yields and expected capital gains, the expected rates of return on portfolios A and B are 11% and 14%, respectively. The beta of A is .8, while that of B is 1.5. The T-bill rate is currently 6%, while the expected rate of return of the S&P 500 index is 12%. The standard deviation of portfolio A is 10% annually, while that of B is 31%, and that of the index is 20%. If you currently hold a market index portfolio, what would be the alpha for Portfolios A and B?
ALPHA for A: =.11 − [.06 +.8 × (.12 − .06)] = 0.2% ALPHA for B: = .14 − [.06 + 1.5 × (.12 − .06)] = −1.0%
Bogey
Benchmark portfolio comprised of THREE indexes with given weights - Bogey return represents return on unmanaged portfolio - Weights represent standard portfolio for typical risk tolerance of given type of client/fund in category
The S&P 500 Index is currently at 2,000. You manage a $6 million indexed equity portfolio. The S&P 500 futures contract has a multiplier of $250. If you are temporarily bearish on the stock market, how many contracts should you sell to fully eliminate your exposure over the next six months?
Each contract is for $250 times the index, currently valued at 2,000. Therefore, each contract has the same exposure to the market as $500,000 worth of stock, and to hedge a $6 million portfolio, you need:$6 million/$500,000 = 12 contracts
index arbitrage
Exploiting mispricing between underlying stocks and futures index contract - If futures price is too HIGH: SHORT futures and BUY underlying stocks - If futures price is too LOW: LONG futures and SELL underlying stocks Problems: - High Transaction Costs - Trades must be done simultaneously
it is now January. The current interest rate is 5.0%. The June futures price for gold is $1478.60, while the December futures price is $1,485. Assume the June contract expires in exactly 6 months and the December contract expires in exactly 12 months. Calculate the appropriate price for December futures using the parity relationship?
FDec = FJune × ( l + rf ) l/2 = $1478.60 × (1.050)1/2 = $1515.11 Arbitrage Opportunity!!! The listed futures price for December is too low relative to the June price. We could long the December contract and short the June contract to exploit the opportunity.
Spot-Futures Parity Theorem
Ff an asset can be purchased today and held until the exercise of a futures contract, the value of the future should equal the current spot price adjusted for the cost of money, dividends, "convenience yield" and any carrying costs
You purchase a Treasury-bond futures contract with an initial margin requirement of 20% and a futures price of $115,400. The contract is traded on a $100,000 underlying par value bond. If the futures price falls to $108,300, what will be the percentage loss on your position?
Margin = $115,400 × $0.20 = $23,080.00 Total $ loss = $115,400 - $108,300 = $7,100 Total % loss = $7,100/$23,080.00 = $30.76% loss
Cash Versus Actual Delivery: Taxation
Paid at year-end on cumulative profits/losses regardless of whether position is closed
Information Ratio
Ratio of alpha to the standard deviation of diversifiable risk.
Market Timing
Relative performance drives fund movement between risky portfolio and cash
Sharpe Ratio
Reward-to-volatility ratio; ratio of portfolio excess return to standard deviation. - used when choosing among competing portfolios that will NOT be mixed
A stock has an expected return of 6%. What is its beta? Assume the risk-free rate is 8% and the expected rate of return on the market is 18%.
SML of 6% = 8% + β(18% - 8%) ⇒⇒ β = -2/10 = -0.2
On January 1, you sold one March maturity S&P 500 Index futures contract at a futures price of 1,700. If the futures price is 1,800 on February 1, what is your profit or loss? The contract multiplier is $250.
Selling a contract is a short position. If the price rises, you lose money. Loss = (1,800 - 1,700) × $250 = $25,000
spread (futures)
Taking a long position in a futures contract of one maturity and a short position in a contract of a different maturity, both on the same commodity
The margin requirement on the S&P 500 futures contract is 10%, and the stock index is currently 1,200. Each contract has a multiplier of $250. How much margin must be put up for each contract sold?
The dollar value of the index is: $250 × 1,200 = $300,000 Therefore, the position requires margin of $30,000.
The multiplier for a futures contract on the stock-market index is $250. The maturity of the contract is one year, the current level of the index is 800, and the risk-free interest rate is 0.5% per month. The dividend yield on the index is 0.3% per month. Suppose that after one month, the stock index is at 820. Find the cash flow from the mark-to-market proceeds on the contract. Assume that the parity condition always holds exactly.
The initial futures price is: 800 × (1 + .005 - .003)12 = 819.4126 In one month, the futures price will be: 820 × (1 + .005 - .003)11 = 838.2215 The increase in the futures price is 18.809, so the cash flow will be: 18.809 × $250 = $4,702.22 ANSWER: $4,702.22
Forward Contract
an arrangement calling for future delivery of an asset at an agreed-upon price
Alpha Transport
establishing alpha while using index products both to hedge market exposure and to establish exposure to desired sectors
Treynor Measure
ratio of portfolio excess return to beta, used to evaluate portfolio that is part of larger portfolio with different managers
M^2 Measure
return difference between a managed portfolio leveraged to match the volatility of a passive index and the return on that index
Closing Out Positions
reversing the trade, take or make delivery, most trades are reversed and do not involve actual delivery
Basis Risk
risk attributable to uncertain movements in the spread between a futures price and a spot price
cash settlement
the cash value of the underlying asset (rather than the asset itself) is delivered to satisfy the contract
Short position
the futures trader who commits to delivering the asset
long position
the futures trader who commits to purchasing the asset
comparison universe
the set of portfolio managers with similar investment styles that is used to assess relative performance
Survivorship bias
upward bias in average fund performance due to the failure to account for failed funds over the sample period
