Sec. 8.2

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• Sec. 8.2 8.3
• Exchange Risk

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What is a Short Position?

• Liabilities gt 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.

• 1002Var(Ry) 1002Var(Rdm) 2(1002)Cov(Ry,Rdm)
  
• Var 1002(6005002(346.5)) 10021793
• SD Square Root of 10021793 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 .35820 or 56, so the variance of
  the portfolio is
• 1002(82)1002(202)2(1002)(56)
• 1002 82 2022(56)
• 1002644002(56)
• VAR 1002(576)
• SD100(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?