FORWARD AND Futures _II__answered by suchenfz

VIEWS: 8 PAGES: 30

									Agenda

   Financial Forward contracts
     Hedging   with forward contracts
     Finding “(Fair) Forward Price”



   Financial Futures contracts
     Hedging   with futures vs. forward contracts
     (Fair)Futures price?
Financial Forward Contracts:
          Pricing and Hedging
Type of hedging
   Perfect vs. imperfect hedging
   Short-hedging
     Suppose that your firm will export cars to a car dealer in a Russia. The
      Russian importer agreed to pays 200 million U.S. dollars in six months
        Today, fix the (buying) price of U.S. dollars six months later!
        Short position of 6-month won-dollar forward on 200 million U.S.
          dollars

   Long-hedging
     Due to the booming economy, Koreanair is expected to require
       additional 10 million gallons of aviation jet fuels in six months.
        Today, fix the (selling) price of Aviation jet fuels!
        Long position of six-month jet-fuel forward on 10 million gallons of
         aviation jet fuels
“Fair Forward Price”
   Forward contracting requires that contractors find
    “fair” forward price!
     What       that means by the “fair” price?
       The  forward price which both (well-informed and well-
          educated… very smart…. ) forward contractors can
          agree with.
         No pain, no gain for either contractors
         There are no free meals for either forward contractors
         …
         No arbitrage profits
               Don’t forget that you invest no money when you enter into forward contracts!
Example: Equity “Forward price”
   Equity Forward contracting
       A contract where you must buy(or sell) a underlying stock at maturity for
        a predetermined price(so-called “forward price”).

       You must decide
         Which stock e.g.) IBM, microsoft,….
         Number of stock e.g.) 10 shares 10,000 shares…
         The maturity e.g.) the second Thursday of June…
         How it will be settled
             e.g.) cash settlement vs. underlying delivery

           Most importantly and debatably, the equity forward price!
Equity “Forward price”
   How to decide how much you will pay (receive) by
    entering into a long (short) position of forward on
    stock?
     e.g.,   IBM stock forward contracts
       (Term  to maturity or) Time to Maturity: 1 year
       Suppose that current stock price is $10 and its underlying is
        1 share of IBM stock.
       Risk-free rate 3% and no dividend payment until maturity
       What should be its “(Fair) Forward price?”
     Replicating IBM forward contract
                   (synthetic forward contracts)

        A short position of IBM stock forward
                                              1 year later (t=1)
                                              IBM stock price:     $20

Today (t=0)                                   IBM forward: (- IBM stock + forward price)

IBM stock price =$10


IBM forward = $0
                                            IBM stock price:        $5

                                            IBM forward: - IBM stock + forward price)

        (Replicating portfolio)
             Short-sell 10 shares of IBM stock
             Put 10*$10=$100 into a bank account at 3% APR.

         Synthetic forward: $0              1 year later: (- IBM stock + $10.3)
Equity “forward price” formula without
dividend payment
   Forward price formula
       IBM    forward price = $10 ×


     Forward price (F0 )  Stock price today  S0   1  r 
                                                                  T




   How to replicate a long position of forward
    contract?
       (strategy)
              Borrow $10 at 3% APR for 1 year
              Buy one share IBM stock today and hold it for 1 year!
Arbitrage trading strategies
   Suppose that IBM forward price is $11. Is there an arbitrage
    opportunity? If so, what is the strategy?

   Suppose that IBM forward price is $10. Is there an arbitrage
    opportunity? If so, what is the strategy?

   Suppose that IBM forward price is $10.3. However, you also
    find that risk-free rate is 10%. Is there an arbitrage
    opportunity in the loan market? If so, show me the arbitrage
    strategy!
Arbitrage trading strategies
   Suppose that IBM forward price is $11. Is
    there an arbitrage opportunity? If so, what is
    the strategy?

The market price of IBM forward:                               $11
                                                                                     1
                                                                               0.03 
The theoretical (or “fair” or “no-arbitrage”) forward price: $10.3      10  1 
                                                                              
                                                                                     
                                                                                   1 



(Arbitrage strategy: “(Borrow and )Buy at lower price and sell at higher price!”)
Borrow 10 dollars at the interest rate of 3% and buy one share of IBM stock
  today
A Short position of IBM forward           (Arbitrage profits: $ 0.7 or 70 cents)
Arbitrage strategies
   Suppose that IBM forward price is $10. Is
    there an arbitrage opportunity? If so, what is
    the strategy?
The market price of IBM forward:                               $10
                                                                                     1
The theoretical (or “fair” or “no-arbitrage”) forward price:   $10.3           0.03 
                                                                        10  1    
                                                                                  1 



(Arbitrage strategy: “Buy at lower price and (Short-)sell at higher price!”)


Short-sell the IBM stock today at $10 and put $10 into a bank account at 3 %APR
A long position of IBM forward            (Arbitrage profits: $ 0.3 or 30 cents)
Arbitrage strategies
   Suppose that IBM forward price is $10.3. However, you also find that risk-
    free rate is 10%. Is there an arbitrage opportunity in the loan market? If
    so, show me the arbitrage strategy!
   (Arbitrage strategy:
           Borrow at a lower interest rate and Lend at higher interest rate! )
   Deposit $10 at 10%: –$10 today, $11 at maturity
                     1
                 r
    10.3  10  1     implies that interest rate should be 3% APR
                 1


   Short-sell a IBM stock:             $10 today, – IBM stock (IBM stock returned)
   Long position of IBM forward: $0 today, IBM stock – $10.3 at maturity
   –
Example: IBM forward with dividend payment

   Suppose that the underlying of IBM stock forward
    contract is 100 shares of IBM stock instead of 1
    share of IBM stock

   If there is a dividend payment of $1.03 per share
    1 day before the maturity, what should be the
    forward price?
Example: IBM forward with dividend payment

   Underlying: 100 shares of IBM stock
   Stock price today: $10 per share
   Risk-free rate: 3%APR
   Maturity: 1 year
   Dividend payment at maturity: $1.03 per share
   What should be its theoretical (or “fair” or “no-arbitrage forward price)?


                F0  ( S  PV of dividend )  1  r 
                                                          T



                            1.03 
                   10               1  0.03  $9.27
                                                   1

                         1  0.3 
                                   1
                                    
Arbitrage opportunity strategy?
   Underlying: 100 shares of IBM stock
   Stock price today: $10 per share
   Risk-free rate: 3%APR
   Maturity: 1 year
   Dividend payment at maturity: $1.03 per share
   Suppose that IBM forward price is $10.



   Is there arbitrate opportunity?
   Show me the arbitrage strategy!
Currency forward contracts
   A contract where you must buy or sell foreign
    currencies at maturity for pre-determined price
    (forward exchange rate × amount of foreign
    currencies).
Example: foreign currency forward
   Suppose that Apple co. is scheduled to export
    iphone 4G to South Korea and it will receive 200
    million won in one month. The current won-dollar
    exchange rate is 1,160 won/$. Apple co. decide
    to engage in hedging the currency risk exposure by
    entering into won-dollar Non-deliverable
    forward(NDF) in the Hong Kong/Singapore offshore
    won/dollar NDF markets.
    (Korean risk-free rate 6% APR; U.S. risk-free rate 3%)
Example: foreign currency forward
   Apple co. receives 200 mil won in one month.
   Today’s exchange rate: 1,160 won/dollar
   Korean risk-free rate: 6% APR
   U.S. risk-free rate: 3% APR
   Suppose that the quoted forward exchange rate is 1,162.89 won/dollar and the
    underlying of the forward contract is 1 U.S. dollar.


   How to hedge against the risk?


   Is 1,160.80 won/dollar fair?
What is the “fair” forward foreign exchange rate?

   “Fair” forward exchange rate
    (= Theoretical forward exchange rate)

Forward foreign exchange rate
                                   1  domestic interest rate  T 
 current foreign exchange rate                                  
                                    1  foreign interest rate  T 


                                 1  rd  T   
                      F0  S0                
                                 1 r T      
                                      f       
“Theoretical (or “fair”) Forward price of financial
forward contracts

Forward contract type          Theoretical Forward price


Equity forward
                                 F0  S0  PV ( D)   1  rd  T 

Currency forward                              1  rd  T   
                                   F0  S0                
                                              1 r T      
                                                   f       
Bond forward
                                   F0  S0  PV (C)   1  rd  T 

Interest rate forward               ???? (We will study this later!)
( or Forward rate agreement)
Financial Futures contracts:
          Pricing and Hedging
“Futures Price”
   Futures prices are market prices quoted in
    exchanges.

     Likepublicly traded stock prices, futures prices are not
      decided through negotiations between individual
      traders but through market clearing
Currency Futures contracts
   Suppose that Apple co. is scheduled to export
    iphone 4G to South Korea and it will receive 200
    million won in three months (Suppose today is
    September 16th, 2010). The current won-dollar
    exchange rate is 1,160 won/$. Apple co. decide
    to engage in hedging the currency risk exposure by
    entering into won-dollar futures contracts traded in
    Korea Exchanges(KRX). Describe the hedging
    strategy! (Korean risk-free rate 6% APR; U.S. risk-
    free rate 3%)
Go to http://eng.krx.co.kr/m3/m3_3/m3_3_4/m3_3_4_1/UHPENG03003_04_01.html
Won-dollar futures maturing at the
  third Monday of November
“Fair (or theoretical)” Futures price
   Can we use the forward price formula for futures?
     In general, yes



   Does the forward price formula always work for the futures?
     No. Not always

     What are the factor which affects the use of forward price formula for
      futures?
        Correlation between interest rate movement and futures price
         matters!
        Positive(negative) correlation between interest rate and futures price
         implies that futures price is higher(lower) than forward price.
        However, on average, the impact of the correlations are not really
         significant. The forward price formulas are good guide lines for
         futures price too!
Marking-to-market example
       Gold futures!
       Initial futures price = $100, Initial margin requirement = $5, Maintenance
        margin requirement = $3
       Holding of short position of 10 contracts
Day              Beginning       Funds    Settlement    Future price    Gain/Loss    Ending
                   balance    deposited         price       change                  Balance
    0                   0           50       100.00               0            0        50
    1                   50                    99.20           -0.80            8        58
    2                   58                    99.00           -0.20            2        60
    3                   60                   101.00            2.00           -20       40
    4                   40                   103.50            2.50           -25       15
    5                   15          35       103.00           -0.50            5        55
    6                   55                   104.00             1.0           -10       45


                                                                   29
Hedging with futures
   Basis risk
     Unlike forward contracts, futures contracts are the contracts you can
      introduce or generate. By definition, you must pick up a type of futures
      contracts available in the futures markets.

       In many cases, you cannot find the futures contract with exactly same
        maturity with the risk exposure. In extreme cases, there is no futures
        contract on the equity or interest risk that you are exposed to.

       In order to hedge against your risk exposure, you may use a futures
        contract witch have high correlation with the exact futures contract you
        are looking for or with your risk exposure.
           In the previous example, we can use 1-month won-dollar futures instead of 3-
            month won-dollar futures (how?)
       Risk exposure due to using a derivative contract on a different
        underlying is called as “basis risk.”

								
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