10/14 Chapter 11 - Managing TE
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1 Rauli Susmel Dept. of Finance Univ. of Houston FINA 4360 International Financial Management 10/14 Chapter 11 - Managing TE Last Lecture Managing TE Forwards/Futures Options Money Market (same as IRP) This Lecture We will review two cases: Receivables in FC and Payables in FC. Example 1: CASE I - Receivables in FC MSFT exports Windows to Switzerland for CHF 3M Payment due in 90 days. S t = 0.60 USD/CHF TE(in USD) = CHF 3M * 0.60 USD/CHF = USD 1.8M To manage TE, MSFT considers the following tools: forwards/futures, options, Money market instruments (used to replicate IRPT). MSFT also considers keeping the position open i.e., no hedging. Hedging Tools: Futures/Forwards/Options/Money Market Hedge/Do Nothing Data: Interest USD = 4.25%-5% Interest CHF = 4%-4.25% F t,90-day =.65 USD/CHF Put (X p = 0.64 USD/CHF; p p = USD.06) Call (X c = 0.63 USD/CHF; p c = USD.02) T = 90 days Possible scenarios for S t+90 (distribution for S t+90 based on the ED) S t+90 (USD/CHF) Probability Forward Hedge Sell Forward CHF Sell CHF forward at F t,90-day =.65 USD/CHF Amount to be received in 90 days = CHF 3M * 0.65 USD/CHF = USD 1.95M Note: No uncertainty. MSFT will receive USD 1.95M, regardless of S t+90.
2 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 0.60 USD/CHF (3) Deposit in US Bank at 5% MMH Calculations: Amount to be borrowed = CHF3M/( *90/360) = CHF M CHF M*0.60 USD/CHF = USD 1.781M = amt to be deposited in US Bank Amount to be received in 90 days = USD 1.781M (1+.05*90/360) = USD M Note: There is no uncertainty about how many USD MSFT will receive for CHF 3M. Note: There is no uncertainty about how many USD MSFT will receive for CHF 3M Compare FH vs MMH: MSFT should select the FH. MMH is dominated by FH. 3. Option Hedge -Buy CHF puts: X p = 0.64 USD/CHF, p p = USD.06/CHF Floor = 0.64 USD/CHF *CHF 3M = USD 1.92 M - Total premium cost Premium cost = CHF 3M * USD.06/EUR = USD.18M Opportunity Cost (OC) = USD.18M*.05*.25=USD.0025M Total premium cost = Premium cost + OC = USD.1825M Scenarios S t+90 (USD/CHF) Probability Exercise? Amount received (Net of cost, in USD) Yes 1.92M M = M No 1.95M M = M No 2.04M M = M E[Amount to be received in 90 days] =.2(1.7375)+.5(1.7675)+.3(1.8575) = M Notes: 1. An option establishes a worst case scenario. In this case, MSFT establishes a floor, a minimum amount to be received: USD 1.92M (or net USD ). 2. The opportunity cost (OC) is included to make a fair comparison with FH and MMH, which require no upfront payment. (OC=Time value of money!) Compare FH vs OH: FH seems to be better; but preferences matter. A risk taker may like the 30% chance of doing better with the OH. 4. No Hedge (Leave position open, that is, do nothing and wait 90 days) Scenarios S t+90 (USD/CHF) Probability Amount received (Net of cost) USD 1.82M USD 1.95M USD 2.04M E[Amount to be received in 90 days] = USD 1.947M
3 Compare FH vs NH: NH seems to be better. But, preferences matter (a very conservative manager might not like the 20% chance of the NH doing worse than the FH). Graph 11.1: General CF Diagram for all Strategies Payoff Diagram for MSFT Net Amount Received in t+90 No Hedge Put USD 1.83M Forw ard USD M S t+90 In general, the preference of one alternative over another will depend on the probability distribution of S t+90. If the probability of S t+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: CASE II - Payables in FC MSFT has payable in GBP for GBP 10M in 180 days. S t = 1.60 USD/GBP TE(in USD) = USD 16M MSFT decides to manage this TE with the following tools: Hedging Tools: Futures/Forwards/Options/Money Market Hedge/Do Nothing Data: Interest USD = 5%-5.25% Interest GBP = 6%-6.5% F t,180-day = 1.58 USD/GBP Put (X p = 1.64 USD/GBP; p p = USD.05) Call (X c = 1.58 USD/GBP; p c = USD.03) Distribution for S t+90 S t+90 (USD/GBP) Probability Which alternative is best? The hedge that delivers the least USD amount
4 1. FH Buy forward GBP Amount 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 1.60 USD/GBP (3) Deposit in US Bank at 6% MMH Calculations (we go backwards): Amount to deposit = 10M/[1+(.06*180/360)] = GBP 9.708M Amount to borrow = GBP 9.708M * 1.60 USD/GBP = USD M Amount to repay = USD *( *180/360) = USD 15.94M Compare FH vs MMH: FH is better 3. Option Hedge Buy GBP calls: X c = 1.58 USD/GBP, p c = USD.03/GBP 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 S t+90 (USD/GBP) Probability Exercise? Amount paid (Net of cost, in USD) No USD 15.5M +.31M = USD 15.81M Yes USD 15.8M +.31M = USD 16.11M Yes USD 15.8M +.31M = USD 16.11M E[Amt to be paid in 180 days] = USD 16.02M Compare FH vs OH: FH is better always. (Preferences do not matter.) Note: Again, the option establishes a worst case scenario. In this case, MSFT establishes a cap, a maximum amount to be paid: USD 15.8M (or net USD 16.11M). 4. No Hedge leave position open; that is, do nothing and wait. E[Amt] = GBP 10M [1.55(.3)+1.59(.6)+1.63(.1)] = USD 15.82M Compare FH vs OH: FH 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 Intuition: The more the option is out of the money, the cheaper it is. The higher the cost, the better the coverage. Example: Revisit MSFT payables situation: MSFT has to pay GBP 10M in 180 days. Notation: X j = Strike Price (j = call; put) p j = Option premium (j = call; put) S t = 1.60 USD/GBP
5 Options available: X c = 1.56 USD/GBP, p c = USD.08, T=180 days (call) X c = 1.58 USD/GBP, p c = USD.07, T=180 days (call) X c = 1.63 USD/GBP, p c = USD.05, T=180 days (call) X c = 1.65 USD/GBP, p c = USD.04, T=180 days (call) X p = 1.58 USD/GBP, p p = USD.055, T=180 days (put) X p = 1.61 USD/GBP, p p = USD.095, T=180 days (put) 1. Out-of-the-Money (S t < X) Alternative 1: Call used: X c = 1.63 USD/GBP, p c = USD.05 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) Alternative 2: Call (X c =1.65 USD/GBP, p c = 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 (S t X) Call used: X c = 1.58 USD/GBP, p c = 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 c = 1.63 USD/GBP, p c = USD.05); sell Put (X p = 1.58 USD/GBP, p p = USD.055) Cost = GBP 10M*USD ( )/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 Notes: With a collar you get a lower cost (advantage), but you give up the upside of the option (disadvantage) there is always a trade-off! Zero cost insurance is possible sell enough options to cover the premium of the option you are buying.
6 CHAPTER 11 - 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 The raw data is in SGD/USD. First, we transform the data to changes (e f,t ). Excel produces a histogram. Below we show the raw changes (SGD/USD), and relative frequency for S t+30 (USD/SGD). Then, we get S t. Today, S t =0.65 USD/SGD e f,t (SGD/USD) Frequency Rel frequency St =1/.65*(1+e f,t ) St (USD/SGD) or less or
7 You can plot the histogram using excel to get the empirical distribution. Relative Frequency More Changes in USD/SGD (%) Relative Frequency M ore USD/SGD
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