Running a regression of stock returns against changes in exchange rates

 

Interpret the findings of the regression analysis
Estimate the degree of economic exposure based on the results from the regression analysis
You will do all of the above twice, first using some made-up data provided below; and a second time using an actual MNC you will select.
Instructions
Download the spreadsheet “Economic Exposure”. The file contains the following data over a 61month interval (these are data I made up for Part 1): Economic_Exposure.xlsDownload Economic_Exposure.xls

the stock price of a multinational company,
the value of the European Currency Unit (ECU), quoted $/ECU.
PART 1

Step 1: Use the price series for the company to calculate monthly returns. Note that 61 months of price data will generate 60 months of returns. Similarly, use the ECU series to calculate the monthly percentage changes in the dollar value of the ECU. Show the two series of changes in two separate columns next to the original prices and exchange rates.

Step 2: Regress the return on the company against the percentage changes in the ECU. Stated differently, the return on the company is the dependent (y-axis) variable and the change in the value of the ECU is the independent (x-axis) variable. Report the slope coefficient and its p-value, and the R-squared of the regression. The regression output should be shown in the Excel file.

Step 3: In one Word page, interpret the results as follows:

Provide an interpretation for each of the i) p-value of the estimated slope coefficient, ii) slope coefficient, and iii) R-squared
How does the value of the company change when the dollar depreciates?
How much economic exposure does the company have? Here you reach a conclusion based on your answers to 1 and 2 above.

 

Sample Solution

Analyzing Economic Exposure: Part 1 (Made-up Data)

Following the instructions, let’s analyze the economic exposure of the multinational company based on the provided data:

Step 1: Calculating Monthly Returns

We need to calculate the monthly returns for both the company’s stock price and the ECU value. Here’s the formula for calculating monthly returns (assuming data starts in cell A1):

Excel
= ((B2-B1)/B1)*100

a) Stock Return: Insert this formula in cell C2 (next to the price in cell B2) and copy it down for all subsequent months (60 months in total). This will give you the monthly percentage change in the stock price.

b) ECU Return: Use the same formula in cell D2 (next to the ECU value in cell C2) and copy it down for all months. This will give you the monthly percentage change in the ECU value (remember, a positive value indicates a depreciation of the dollar).

Step 2: Regression Analysis

Perform a linear regression in Excel with the following setup:

  • Dependent Variable (Y-axis): Stock Return (values in column C)
  • Independent Variable (X-axis): ECU Return (values in column D)

Run the regression analysis and record the following results:

  • Slope Coefficient: This value represents the change in the company’s stock return for every 1% change in the ECU value (positive or negative).
  • P-value of the Slope Coefficient: This value indicates the statistical significance of the slope coefficient. A low p-value (typically less than 0.05) suggests a statistically significant relationship between the variables.
  • R-squared: This value represents the proportion of the variance in the company’s stock return explained by the changes in the ECU value.

Step 3: Interpreting the Results (Write this in a separate Word document)

i) P-value:

  • A low p-value (e.g., less than 0.05) suggests a statistically significant relationship between the company’s stock return and the ECU value. This means that changes in the ECU value are likely influencing the company’s stock performance.
  • A high p-value (e.g., greater than 0.05) indicates a statistically insignificant relationship. In this case, ECU fluctuations might not be a significant factor affecting the company’s stock return.

ii) Slope Coefficient:

  • A positive slope coefficient indicates that the company’s stock return tends to move in the same direction as the ECU value. In other words, a depreciation of the dollar (positive ECU return) might lead to an increase in the company’s stock price (positive stock return).
  • A negative slope coefficient suggests the opposite. The company’s stock return might move against the ECU value. A depreciation of the dollar could lead to a decrease in the company’s stock price.

iii) R-squared:

  • A high R-squared value (closer to 1) indicates that changes in the ECU value explain a large portion of the variations in the company’s stock return. This suggests high economic exposure, meaning the company’s financial performance is significantly impacted by currency fluctuations.
  • A low R-squared value (closer to 0) suggests that ECU fluctuations have a minimal impact on the company’s stock return. This indicates low economic exposure.

Company’s Value Change with Dollar Depreciation:

Based on the slope coefficient, you can determine how the company’s value changes when the dollar depreciates (ECU value increases).

  • A positive slope coefficient signifies that the company’s value tends to increase with a depreciation of the dollar.
  • A negative slope coefficient suggests the company’s value might decrease with a depreciation of the dollar.

Economic Exposure:

The combined interpretation of the p-value, slope coefficient, and R-squared will help you estimate the degree of economic exposure.

  • A statistically significant positive relationship (low p-value, positive slope) with a high R-squared value indicates high economic exposure. The company’s performance is heavily influenced by currency fluctuations.
  • A statistically insignificant relationship (high p-value) or a low R-squared value suggests low economic exposure. Currency fluctuations have a minimal impact on the company’s performance.

Note: This analysis provides a starting point for understanding economic exposure. You’ll need to perform the calculations and interpret the results based on the specific data in the “Economic_Exposure.xls” file.

Next Steps:

Repeat steps 1-3 using real data from a chosen Multinational Company (MNC). This will allow you to assess the actual economic exposure of that specific company.

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