Question

Calculate the correlation between GM’s earning and the USD–ForeignCurrency(of your choice) exchange rate. According to your result, does the observed change in the exchange rate (e.g., USD appreciates against Euro) in a given year lead or lag the change in company’s earnings reported in a given year?

Answer 1

Assumption: Quarter - on - quarter earnings for GM have been considered for one year. Source: Macrotrends Financial Statements.

Line Item Considered: Net income

Exchange Rate: USD-INR (Indian Rupee) Exchange rates on quarter end dates have been considered, Source: Oanda Currency Converter

Year under consideration: 2019

Date	GM's Earnings (2019- Million USD - x)	USD- INR (y)	x-mean(x)	y-mean(y)	(x-mean(x))^2	(y-mean(y))^2	(x-mean(x))*(y-mean(y))
31-12-2019	2119	71.27	473.75	1.33	224439.06	1.7689	630.0875
30-09-2019	2381	70.34	735.75	0.4	541328.06	0.16	294.3
30-06-2019	2313	68.83	667.75	-1.11	445890.06	1.2321	-741.203
31-03-2019	-232	69.32	-1877.25	-0.62	3524067.6	0.3844	1163.895
Total (Column)	=6581	279.76	0	0	4735724.8	3.55	1347.08

Correlation between earnings and Exchange Rate:

Mean(x) = 6581/4 = 1645.25

Mean(y) = 279.76/4 = 69.94

Using the above formula-

r(x,y) = 1347.08/ sqrt(4735724.8*3.55) = 1347.08/4097.56 = 0.33

Thus, there is low correlation between GM's earnings and USD- INR Rate. Further, the exchange rate does appreciate through the year.

Does Exchange Rate Lead or Lag GM's Earnings-

Based on the chart for the four columns, the currency rate seems to lead the earnings for the year 2019 by a quarter. There is a steep fall in the chart observed from quarter 2-3. A similar fall is observed in quarter 3-4 in GM's earnings on the secondary axis.