Cap - DOC by B2k03kwJ

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									10/14
Last class:
Managing TE
   Forwards/Futures
   Options
   Money Market (same as IRP)

Example: Receivables in FC
MSFT exports Windows XP to Swiss firm for CHF 3M Payment due in 90 days.
St = .60 USD/CHF
TE(in USD) = CHF 3M * .60 USD/CHF = USD 1.8M

Hedging Tools- Futures/Forwards/Options/Money Market Hedge/Nothing

Interest USD = 5%-5.25%
Interest CHF = 4%-4.25%
Ft,90-day = .61 USD/CHF
Put(X=.64 USD/CHF; P = USD .06)
Call(X=.63 USD/CHF; P = USD .02)
T = 90 days

1. Forward Hedge – Sell Forward CHF
      Sell CHF forward at Ft,90-day= .61 USD/CHF
      Amount to be received in 90 days = CHF 3M * .61 USD/CHF = USD 1.83M

Note: No uncertainty related to CHF CF

2. MMH (Replication of IRP) – borrow FC, convert to DC, deposit in domestic bank
   Today, we do the following:       (1) Borrow CHF at 4.25
                                     (2) Convert to USD at .6 USD/CHF
                                     (3) Deposit in US Bank at 5%
       MMH Calculations:
       Amt to be borrowed = CHF3M/(1+.0425*90/360) = CHF 2.9684M
       CHF 2.9684M* .60 USD/CHF = USD 1.781M = amt to be deposited in US Bank
       Amt to be received in 90 days= USD 1.781M (1+.05*90/360) = USD 1.8032M
Note: There is no uncertainty about how many USD MSFT will receive for CHF 3M

Compare 1 vs 2: MSFT should select the Forward Hedge

3. Option Hedge (Buy puts X=.64 USD/CHF)
   Floor= .64 USD/CHF *CHF 3M= USD 1.92 M - Total premium cost
   Premium cost = CHF 3M * USD .06 = USD .18M
   Opportunity Cost (OC) = USD .18M*.05*.25=USD .0025M

   Total premium cost = Premium cost + OC = USD .1825M
Scenarios
St+90 (USD/CHF)            Probability                           Exercise?   Amt rec. net of cost (in USD)
.60                        .2                                    Yes         1.92M - .1825M = 1.7375M
.65                        .5                                    No          1.95M - .1825M = 1.7675M
.68                        .3                                    No          2.04M - .1825M = 1.8575

E[Amount to be received in 90 days] = .2(1.7375)+.5(1.7675)+.3(1.8575) = 1.7885M

Note: The opportunity cost (OC) is included to make a fair comparison with FH and
MMH, which require no upfront payment.

Compare 1 vs 3: 1 seems to be better; but preferences matter. A risk taker may like the
30% chance of doing better with the OH.

4.      No Hedge (Do Nothing and wait for a 90 days)
Scenarios
St+90 (USD/CHF)      Probability                  Amt rec. net of cost
.60                  .2                                 USD 1.82M
.65                  .5                                 USD 1.95M
.68                  .3                                 USD 2.04M
E[Amount to be received in 90 days] = USD 1.947M

Compare 1vs4: 4 seems to be better.

Note: A conservative manager might not like the 70% chance of the FH doing no worse
than the No Hedge.

General CF Diagram
              Payoff Diagram for MSFT



Net Amount
Received in                             Put
                     No He dge
t+90




                                              Forw ard
USD 1.83M

USD 1.7375M

               .63 .64   .671                            St+90



In general, the preference of one alternative over another will depend on the probability
distribution of St+90. If the probability of St+90>.63 USD/CHF is very low, then the
forward hedge dominates.
Q: Where do the probabilities come from? We can estimate them using the empirical
distribution (ED).
Example: Payables in FC
MSFT has payable in GBP for GBP 10M in 180 days.
St = 1.6 USD/GBP
TE(in USD) = USD 16M

Hedging Tools- Futures/Forwards/Options/Money Market Hedge/Nothing

Interest USD = 5%-5.25%
Interest GBP = 6%-6.5%
Ft,180-day = 1.58 USD/GBP
Put(X = 1.64 USD/GBP; P = USD .05)
Call(X = 1.58 USD/GBP; P = USD .03)

Which option is best? The hedge that delivers the least USD amount

1. FH -buy forward GBP
    Amt to be paid in 180 days = GBP 10M*1.58 USD/GBP = USD 15.8M

2. MMH – borrow DC, convert to FC, deposit in foreign bank
    Today, we do the following:   (1) Borrow USD at 5.25
                                  (2) Convert to GBP at 1.6 USD/GBP
                                  (3) Deposit in US Bank at 6%
       MMH Calculations (we go backwards):
Amt to deposit = 10M/[1+(.06*180/360)] = GBP 9.708M
Amt to borrow = GBP 9.708M * 1.60 USD/GBP = USD 15.533M
Amt to repay = USD 15.533 *(1+.0525*180/360) = USD 15.94M
Compare 1 vs 2: 1 is better

3. Option Hedge -Buy GBP (call: establishes a ceiling, a cap on the GBP payables)
    Cap = GBP 10M*1.58 USD/GBP = USD 15.8M
    Total premium cost = Total premium + OC = 10M*USD .03*(1+.05*.5)= USD .31M

Scenarios
St+90 (USD/GBP)      Probability    Exercise?     Amt paid net of cost
1.55                 .3             No            USD 15.5M + .31M = USD 15.81M
1.59                 .6             Yes           USD 15.8M + .31M = USD 16.11M
1.63                 .1             Yes           USD 15.8M + .31M = USD 16.11M

     E[Amt to be paid in 180 days] = USD 16.02M
Compare 1 vs 3: 1 is better always. (Preferences do not matter.)

4. No Hedge –do nothing.
       E[Amt] = GBP 10M [1.55(.3)+1.59(.6)+1.63(.1)] = USD 15.82M
Compare 1 vs 4: 1 is better; but preferences matter.
Options hedging (with different X)
With options it is possible to play with different strike prices –different insurance
coverage.

Key:   The more the option is out of the money, the cheaper it is.
       The higher the cost, the better the coverage.

Revisit MSFT payables situation: MSFT has to pay GBP 10M in 180 days.
Notation: X = Strike Price
           P = Option premium
St = 1.60 USD/GBP
Call(X= 1.56 USD/GBP, P= USD .08, T=180 days)
Call(X= 1.58 USD/GBP, P= USD .07, T=180 days)
Call(X= 1.63 USD/GBP, P= USD .05, T=180 days)
Call(X= 1.65 USD/GBP, P= USD .04, T=180 days)
Put (X= 1.58 USD/GBP, P= USD .055, T=180 days)

1. Out-of-the-Money (St < X)
Call(X=1.63 USD/GBP, P=USD .01)
       Cost = Total premium = GBP 10M * USD .05/GBP = USD 500K
       Cap = worst amount to be paid = 1.63 USD/GBP * GBP 10M = USD 16.3M
       (Net cap = USD 16.8)
Call(X=1.65 USD/GBP, P=USD .04)
       Cost = GBP 10M * USD .005/GBP = USD 400K
       Cap = 1.65USD/GBP * GBP 10M = USD 16.5M => Net cap = USD 16.9M

Note: The tradeoff is very clear: The higher the cost, the better the coverage.

2. (Closest At-the-money) In-the-money (St  X)
Call(X= 1.58 USD/GBP, P= USD .07)
        Cost = Total premium = USD 700K
        Cap = USD 15.8M => Net cap = USD 16.5M

Compare to Out-of-the-money:         Advantage: Lower cap.
                                     Disadvantage: Its cost.

Companies do not like to pay high premiums. Many firms finance the expense of an
option by selling another option. A typical strategy: a collar (buy one option, sell another)

3. Collar (buy one call, sell one put. In general, both are OTM)
Buy Call(X=1.63 USD/GBP, P=USD .05); sell Put(X= 1.58 USD/GBP, P= USD .055)
        Cost = GBP 10M*USD (.05-.055)/GBP = USD -50K
        Cap = 1.63 USD/GBP * GBP 10M = USD 16.3M
        Floor = Best case scenario = 1.57 USD/GBP*GBP 10M = USD 15.7M
        => Net cap = USD 16.25; Net floor = USD 15.65M
Note: With a collar you get a lower cost (advantage), but you give up the upside of the
option (disadvantage).

Note 2: Zero cost insurance is possible => sell enough options to cover the premium of
the option you are buying.
BONUS COVERAGE: Getting probabilities from the Empirical Distribution
Firms will use probability distributions to make hedging decisions. These probability
distributions can be obtained using the empirical distribution, a simulation, or by assuming a
given distribution. For example, a firm can assume that changes in exchange rates follow a
normal distribution. Here, we present an example on how to use the empirical distribution.

Example: We want to get probabilities associated with different exchange rates. Let’s
take the historical monthly USD/SGD exchange rates 1981-2009. The raw data is in
SGD/USD. First, we transform the data to changes (ef,t). Excel produces a histogram.
Below we show the raw changes (SGD/USD), and relative frequency for St+30
(USD/SGD). Then, we get St. Today, St =.65 USD/SGD


                                                              St            St
   ef,t (SGD/USD)       Frequency       Rel frequency   =1/.65*(1+ef,t) (USD/SGD)
-0.0494 or less            2             0.0058           1.462         0.6838
    -0.0431                2             0.0058           1.472         0.6793
    -0.0369                1             0.0029           1.482         0.6749
    -0.0306                3             0.0087           1.491         0.6705
    -0.0243                6             0.0174           1.501         0.6662
    -0.0181                20            0.0580           1.511         0.6620
    -0.0118                36            0.1043           1.520         0.6578
    -0.0056                49            0.1420           1.530         0.6536
     0.0007                86            0.2493           1.540         0.6495
     0.0070                52            0.1507           1.549         0.6455
     0.0132                41            0.1188           1.559         0.6415
     0.0195                29            0.0841           1.568         0.6376
     0.0258                5             0.0145           1.578         0.6337
     0.0320                7             0.0203           1.588         0.6298
     0.0383                5             0.0145           1.597         0.6260
     0.0446                0             0.0000           1.607         0.6223
  0.0508 or +              3             0.0058           1.617         0.6186
You can plot the histogram using excel to get the empirical distribution.
                                 0.4
                                0.35
   Relative Frequency

                                 0.3
                                0.25
                                 0.2
                                0.15
                                 0.1
                                0.05
                                  0
                                       More      -5        -3      -1       0        1     3      5
                                                         C ha nge s in US D / S G D (%)



                                 0.4
                                0.35
           Relative Frequency




                                 0.3
                                0.25
                                 0.2
                                0.15
                                 0.1
                                0.05
                                   0
                                       M o re   0.6185        5
                                                         0.631 0.6445     0.651   0.6575 0.6705 0.6835

                                                                   USD/SGD

								
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