Question

Edgewood Co. has developed a regression model to forecast the percentage change in the value of the Mexican peso (et). The company believes the real interest rate differential (INT) and the inflation rate differential (INF) are the only factors that affect exchange rate movements. The following regression model was estimated with quarterly data for 15 periods.

                                         et =   0.001 - 0.9 INTt + 0.6 INF t-1 …………………………………………….(3)

                     

Given that INFt-1 was 1%, a probability distribution had to be developed for INTt as follows:

            

Probability                             20%                  50%                 30%

Possible Outcome                  -3%                  -4%                  -5%   

Find the expected value of the percentage change in the external value of the Peso, E (et) over the next month.

Answer 1

Solution :

Given Data

Pesos external value = 0.001 - 0.9 Interest (current time) + 0.6 Interest (previous time)

et = 0.001 - 0.09 [ Int(t) ] + 0.6 [ Inf(t-1) ]

Inf (t-1) = 1%

Therefore,

et = 0.001 - 0.09 [ Int(t) ] + 0.6 [0.01]

Expected value = Σ [ (x).P(x) ]

where x = outcome(s),

P(x) = probability of outcome(s) x's

Expected value of interest

[ Int(t) ] = (0.20)(-3%) + (0.50)(-4%) + (0.30)(-5%)

-0.6% + (-2%) + (-1.5%) = -4.1%

Putting values :

et = 0.001 - 0.09 [-4.1% ] + 0.6 [1%]

= 0.001 + 0.00369 + 0.006 = 0.01069

So, expected percentage change in peso external exchange rate (et) is 1.069%

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