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Assessing Exchange Rate Risk: Part I

Assessing Exchange Rate Risk: Part I. Forecasting Exchange Rates. The Truth is Out There. “There. Look at this. See? See? I'm right again. Nobody could've predicted that Dr. Grant would suddenly, suddenly jump out of a moving vehicle. ”.

noelle-mcdowell
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Assessing Exchange Rate Risk: Part I

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  1. Assessing Exchange Rate Risk: Part I Forecasting Exchange Rates

  2. The Truth is Out There...

  3. “There. Look at this. See? See? I'm right again. Nobody could've predicted that Dr. Grant would suddenly, suddenly jump out of a moving vehicle.” See, here I'm now by myself, uh, er, talking to myself. That's chaos theory. Three econometricians went turkey hunting. The first took a shot and missed to the left. The second missed to the right. The third shouted “We got it!!”

  4. Econometricians believe that there is “true” relationship between all things on our planet. If we run enough tests, we can eventually figure is out! More importantly, this relationship is stable and can be used for prediction

  5. Probability distributions identify the chance of each possible event occurring Probability Event -3 SD -2 SD -1 SD Mean 1 SD 2 SD 3 SD 65% 95% 99%

  6. Probability distributions are scaleable 3 X = Mean = 1 Variance = 4 Std. Dev. = 2 Mean = 3 Variance = 36 (3*3*4) Std. Dev. = 6

  7. Probability distributions are additive = + Mean = 1 Variance = 1 Std. Dev. = 1 Mean = 2 Variance = 9 Std. Dev. = 3 Mean = 3 Variance = 14 (1 + 9 + 2*2) Std. Dev. = 3.7 Cov = 2

  8. Suppose we know that your salary is based on your shoe size: The Truth Salary = $20,000 +$2,000 (Shoe Size) Salary Shoe Size Mean = 6 Variance = 4 Std. Dev. = 2 Mean = $ 32,000 Variance = 16,000,000 Std. Dev. = $ 4,000

  9. We could also use this to forecast: The Truth Salary = $20,000 +$2,000 (Shoe Size) If Bigfoot had a job…how much would he make? Salary = $20,000 +$2,000 (50) = $120,000 Size 50!!!

  10. Searching for the truth…. You believe that there is a relationship between shoe size and salary, but you don’t know what it is…. • Collect data on salaries and shoe sizes • Estimate the relationship between them Note that while the true distribution of shoe size is N(6,2), our collected sample will not be N(6,2). This sampling error will create errors in our estimates!!

  11. Slope = b a Salary = a +b * (Shoe Size) + error We want to choose ‘a’ and ‘b’ to minimize the error!

  12. We have our estimate of “the truth” T-Stats bigger than 2 are considered statistically significant! Salary = $45,415 + $1,014 * (Shoe Size) + error Intercept (a) Mean = $45,415 Std. Dev. = $1,650 Shoe (b) Mean = $1,014 Std. Dev. = $257

  13. Intercept (a) Shoe (b) $42,172 - $48,658 $509 - $1,520 The P-value tells you the probability that the coefficient is equal to zero

  14. Percentage of income variance explained by shoe size Error Term Mean = 0 Std, Dev = $11,673

  15. If we ever found “the truth”, it would look something like this!

  16. Using regressions to forecast…. 50 Salary = $45,415 + $1,014 * (Shoe Size) + error Mean = $45,415 Std. Dev. = $1,650 Mean = $1,014 Std. Dev. = $ 257 Mean = $0 Std. Dev. = $11,673 Salary Forecast Mean = $96,115 Std. Dev. = $17,438 Given his shoe size, you are 95% sure Bigfoot will earn between $61,239 and $130,991

  17. We’ve looked at several currency pricing models that have potential for being “the truth” Purchasing Power Parity % Change in e = Inflation – Inflation* Uncovered Interest Parity % Change in e = Interest Rate – Interest Rate* Covered Interest Parity % Change in e = Forward Premium/Discount Currency Fundamentals % Change in e = (%M - %M*) + (%Y - %Y*) + (i - i*) Technical Analysis % Change in e = Past Behavior of exchange rate Any combination of these could be “the truth”!!

  18. PPP and the Swiss Franc Note: PPP implies that a = 0 and b = 1

  19. For every 1% increase in US inflation over Swiss inflation, the dollar depreciates by 1.40%

  20. Obviously, we have not explained very much of the volatility in the CHF/USD exchange rate

  21. UIP and the Swiss Franc Note: UIP implies that a = 0 and b = 1

  22. For every 1% increase in US interest rates over Swiss interest rates, the dollar appreciates by 2.87%

  23. We still have not explained very much of the volatility in the CHF/USD exchange rate

  24. Using regressions to forecast…. (3 – 1.5) = 1.5 % Change in e = .55 – 2.87 * (i-i*) + error Mean = .55 Std. Dev. = .31 Mean = -2.87 Std. Dev. = 1.53 Mean = $0 Std. Dev. = 2.69 Given current interest rates, you are 95% sure that the % change in the exchange rate will be between -10.91% and 3.40%!! Salary Forecast Mean = -3.755% Std. Dev. = 3.58%

  25. Technical Analysis Uses prior movements in the exchange rate to predict the future

  26. A 1% depreciation of the dollar is typically followed by a .29% depreciation

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