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Sec. 8.2 – 8.3 Exchange Risk
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What is a Short Position? Liabilities > assets If you are borrowing Yen to buy $ denominated assets? Are you short or long? Who is long? Who is long on $? Who is short?
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What Happens if the Yen falls?
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Definition Foreign Exchange Risk = Variability in the value of an exposure that is caused by uncertainty about exchange rate changes.
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Risk Risk is a function of 2 variables Volatility of exchange rates Degree of exposure Degree of Risk Low = rate fixed, low exposure High = rate volatile, high exposure Consequences
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Calculation of Risk Degree of Exposure X Standard Deviation of Percent Change in Exchange Rates Notes Change Currency to Home Currency % Change allows us to compare across currencies
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Example Example: John has 200 Euros in receivables due in 6 months. Forward Exchange rate is 1.50$/Euro. Standard Deviation of Percent Change is10%. What is the Exchange Risk? Step 1 – Convert Exposure to home currency: 1.50$/Euro X 200 Euro = $300
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Example cont. Step 2 – Multiply Exposure by SD of % Change: $300 X 10% = $30 Probabilities: One SD, 68% probability the receivables will be worth between $270 - $330 Two SD, 95% probability the receivables will be worth between $240 - $360 Three SD, 99.7% probability the receivables will be worth between $210 - $390
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Example cont.
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Value at Risk The most we can lose over some period, given normal market conditions Usually 99% confidence level
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Example 2 Manny is expecting to receive 400 UK Pounds in 1 month. Forward exchange rate is 2.00$/Pound. Using Table 8-1, What will be the exchange risk? 2.00 $/Pound X 400 Pound = $800 Monthly Un-annualized SD = 2.66 SD = 800 X 2.66% = $21,28 68% Probability Manny will receive between $778.72 and $821.28
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Ex Risk with Multiple Currencies More Currencies = more complex Exposures and risks cannot simply be added together Must Consider correlation of movements in relation to home currency
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Calculation Risk = Sum of exchange Variances + Sum of Covariance of particular currencies Example: Variance of annual percentage changes in $/Yen is 600 percentage points, and Variance of $/DM is 500 percentage points. From Table 8-2, correlation is 0.624 and the covariance is 346.5. What is the exchange risk associated with $100 of Yen and $100 of DM?
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Calculations cont. 100^2Var(Ry) + 100^2Var(Rdm) + 2(100^2)Cov(Ry,Rdm) Var = 100^2(600+500+2(346.5)) = 100^2*1793 SD = Square Root of 100^2*1793 = 4234 cents or $42.34
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Review Problem 2 Suppose Sweta has $100 worth of accounts payable in C$ and $100 worth of accounts payable in A$, both due in 90 days, and want to know the SD of the portfolio of payables. She knows that the 90 day $/C$ % change is 8, the $/A$ % change is 20, and the correlation between the two is.35 What is SD of her portfolio?
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Review Problem 2 The covariance between percentage changes in $/C$ and $/A$ is.35*8*20 or 56, so the variance of the portfolio is: =100^2(8^2)+100^2(20^2)+2(100^2)(56) = 100^2 [8^2+ 20^2+2(56)] = 100^2[64+400+2(56)] VAR= 100^2(576) SD=100(24) Or $24, because the standard deviations are in percentage points
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Delta hedging The process in finance of setting or keeping the delta of a portfolio of financial instruments zero, or as close to zero as possible - where delta is the sensitivity of the value of a derivative to changes in the price of its underlying instrument. This is achieved by entering into positions with offsetting positive and negative deltas such that these balance out to bring the net delta to zero
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Mathematically Delta is the partial derivative of the instrument or portfolio's fair value with respect to the price of the underlying security, and indicates sensitivity to the price of the underlying. Therefore, if a position is delta neutral (or, instantaneously delta-hedged) its instantaneous change in value, for an infinitesimal change in the value of the underlying, will be zero
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Any Questions?
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