Assessing Exchange Rate Risk: Part I Forecasting Exchange Rates.
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Post on 19-Dec-2015
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- Assessing Exchange Rate Risk: Part I Forecasting Exchange Rates
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- 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!! 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.
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- 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
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- Probability Event Mean Probability distributions identify the chance of each possible event occurring 1 SD 2 SD 3 SD -1 SD -2 SD -3 SD 65% 95% 99%
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- Mean = 1 Variance = 4 Std. Dev. = 2 Probability distributions are scaleable 3 X= Mean = 3 Variance = 36 (3*3*4) Std. Dev. = 6
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- Mean = 1 Variance = 1 Std. Dev. = 1 Probability distributions are additive + Mean = 2 Variance = 9 Std. Dev. = 3 Cov = 2 = Mean = 3 Variance = 14 (1 + 9 + 2*2) Std. Dev. = 3.7
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- Mean = 6 Variance = 4 Std. Dev. = 2 Mean = $ 32,000 Variance = 16,000,000 Std. Dev. = $ 4,000 Suppose we know that your salary is based on your shoe size: Salary = $20,000 +$2,000 (Shoe Size) Shoe Size Salary
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- We could also use this to forecast: Salary = $20,000 +$2,000 (Shoe Size) If Bigfoot had a jobhow much would he make ? Size 50!!! Salary = $20,000 +$2,000 (50) = $120,000
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- Searching for the truth. You believe that there is a relationship between shoe size and salary, but you dont know what it is. 1.Collect data on salaries and shoe sizes 2.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!!
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- Salary = a +b * (Shoe Size) + error a Slope = b We want to choose a and b to minimize the error!
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- Regression Results VariableCoefficientsStandard Errort Stat Intercept45415.651650.7627.51 Shoe1014.75257.213.94 Salary = $45,415 + $1,014 * (Shoe Size) + error We have our estimate of the truth Intercept (a) Mean = $45,415 Std. Dev. = $1,650 Shoe (b) Mean = $1,014 Std. Dev. = $257 T-Stats bigger than 2 are considered statistically significant!
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- Regression Results VariableP-valueLower 95%Upper 95% Intercept5.2E-10242172.3348658.97 Shoe9.12E-05509.401520.10 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
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- Regression Statistics Multiple R0.17 Standard Error11673.01 Observations500 Error Term Mean = 0 Std, Dev = $11,673 Percentage of income variance explained by shoe size
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- Regression Results VariableCoefficientsStandard Errort Stat Intercept20,0000Infinite Shoe2,0000Infinite Regression Results VariableP-valueLower 95%Upper 95% Intercept 0 20,000 Shoe02,000 Regression Statistics Multiple R0 Standard Error0 Observations500 If we ever found the truth, it would look something like this!
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- Using regressions to forecast. Salary = $45,415 + $1,014 * (Shoe Size) + error 50 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
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- Weve looked at several currency pricing models that have potential for being the truth Uncovered Interest Parity % Change in e = Inflation Inflation* Purchasing Power 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!!
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- Note: PPP implies that a = 0 and b = 1 PPP and the Swiss Franc
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- Regression Results VariableCoefficientsStandard Errort Stat Intercept.027.231.12 Inflation1.40.7421.89 Regression Results VariableP-valueLower 95%Upper 95% Intercept.910 -.49.43 Inflation.06-.0652.86 Regression Statistics R Squared.02 Standard Error2.69 Observations155 For every 1% increase in US inflation over Swiss inflation, the dollar depreciates by 1.40%
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- Obviously, we have not explained very much of the volatility in the CHF/USD exchange rate
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- Note: UIP implies that a = 0 and b = 1 UIP and the Swiss Franc
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- Regression Results VariableCoefficientsStandard Errort Stat Intercept.55.311.77 Interest Rate-2.871.53-1.87 Regression Results VariableP-valueLower 95%Upper 95% Intercept.07 -.061.18 Interest Rate.06-5.89.15 Regression Statistics R Squared.02 Standard Error2.69 Observations155 For every 1% increase in US interest rates over Swiss interest rates, the dollar appreciates by 2.87%
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- We still have not explained very much of the volatility in the CHF/USD exchange rate
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- Using regressions to forecast. =.55 2.87 * (i-i*) + error (3 1.5) = 1.5 Mean =.55 Std. Dev. =.31 Mean = -2.87 Std. Dev. = 1.53 Mean = $0 Std. Dev. = 2.69 Salary Forecast Mean = -3.755% Std. Dev. = 3.58% Given current interest rates, you are 95% sure that the % change in the exchange rate will be between -10.91% and 3.40%!! % Change in e
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- Technical Analysis Uses prior movements in the exchange rate to predict the future
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- Regression Results VariableCoefficientsStandard Errort Stat Intercept.12.21.57 Prior Change.29.073.86 Regression Results VariableP-valueLower 95%Upper 95% Intercept.56-.29.53 Prior Change.0001.14.45 Regression Statistics R Squared.09 Standard Error2.59 Observations154 A 1% depreciation of the dollar is typically followed by a.29% depreciation
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