Problem Set on Pay Discrepancy- Beta Value - And Others
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SOME PROBLEMS TO PRACTISE WITH EXCEL 1. Predicting Sales on the basis of sales-force: The total monthly sales of a certain product (Y) is found to depend upon the number of sales professionals employed by the company (X) in that month. The following information is available: Y 125 340 286 400 225 269 300 175 375 X 27 53 41 59 33 34 49 31 56 Suppose the number of sales professionals employed by the company for the current month is 45. Predict the value of sales at the end of the current month 2. Planning Production Level A company sells swimsuits and has no clear indication of how the market will behave in future. But it has to predict demand and accordingly decide on quantity of production. Overestimation of demand will cause left over inventory and under-estimation will cause lost sales. The firm wants to find the optimum production quantity. Data on expected profit corresponding to a production level are calculated using observations from the past. Can you help the firm find the optimum production level? 3. Equal Pay for Equal Work A large firm employing thousands of workers has been accused of discriminating against its female managers. The accusation is based on a random sample of 100 managers. The mean annual salary of 38 female managers is $76,189, whereas the mean annual salary of the 62 male managers is $97,832. A statistical analysis reveals that the t-test of the difference between two means yields a p-value of less than 1%, which provides overwhelming evidence that male managers are paid more than the female managers. In rebuttal, the president of the firm points out that the company has a strict policy for equal work and that the difference may be due to other variables. Accordingly, he found and recorded the number of years of education and the number of years of experience for each of the 100 managers in the sample. Also recorded are the salary and gender (0=female, 1=male). The president wanted to know whether a regression analysis would shed some light on the issue. Can you help the president resolve this effectively? [The related excel data file “Pay discrepancy data - for students.xls” has been uploaded on the course web]. Do you need any other data to resolve it more effectively? 4. “Beta”-value of a Stock/ Portfolio The “beta” of a stock is a measure of risk associated with a stock. It measures the stock’s price “volatility” in relation to the rest of the market (i.e., how sensitive stock price is to market fluctuations). It measures how the stock’s price moves relative to the overall market. The “beta” value is calculated
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Transcript of Problem Set on Pay Discrepancy- Beta Value - And Others
8/3/2019 Problem Set on Pay Discrepancy- Beta Value - And Others
http://slidepdf.com/reader/full/problem-set-on-pay-discrepancy-beta-value-and-others 1/2
SOME PROBLEMS TO PRACTISE WITH EXCEL
1. Predicting Sales on the basis of sales-force:
The total monthly sales of a certain product (Y) is found to depend upon the number of salesprofessionals employed by the company (X) in that month. The following information is available:
Y 125 340 286 400 225 269 300 175 375 X 27 53 41 59 33 34 49 31 56
Suppose the number of sales professionals employed by the company for the current month is 45.Predict the value of sales at the end of the current month
2. Planning Production Level
A company sells swimsuits and has no clear indication of how the market will behave in future. But ithas to predict demand and accordingly decide on quantity of production. Overestimation of demand willcause left over inventory and under-estimation will cause lost sales. The firm wants to find the optimumproduction quantity. Data on expected profit corresponding to a production level are calculated usingobservations from the past. Can you help the firm find the optimum production level?
3. Equal Pay for Equal Work
A large firm employing thousands of workers has been accused of discriminating against its femalemanagers. The accusation is based on a random sample of 100 managers. The mean annual salary of 38female managers is $76,189, whereas the mean annual salary of the 62 male managers is $97,832. Astatistical analysis reveals that the t-test of the difference between two means yields a p-value of lessthan 1%, which provides overwhelming evidence that male managers are paid more than the femalemanagers. In rebuttal, the president of the firm points out that the company has a strict policy for equalwork and that the difference may be due to other variables. Accordingly, he found and recorded thenumber of years of education and the number of years of experience for each of the 100 managers in thesample. Also recorded are the salary and gender (0=female, 1=male). The president wanted to know
whether a regression analysis would shed some light on the issue. Can you help the president resolvethis effectively? [The related excel data file “Pay discrepancy data - for students.xls” has been uploadedon the course web]. Do you need any other data to resolve it more effectively?
4. “Beta”-value of a Stock/ Portfolio
The “beta” of a stock is a measure of risk associated with a stock. It measures the stock’s price
“volatility” in relation to the rest of the market (i.e., how sensitive stock price is to market fluctuations)
It measures how the stock’s price moves relative to the overall market. The “beta” value is calculated
8/3/2019 Problem Set on Pay Discrepancy- Beta Value - And Others
http://slidepdf.com/reader/full/problem-set-on-pay-discrepancy-beta-value-and-others 2/2
using regression analysis. The whole (Indian) market, which for this purpose, may be represented by
Sensex or Nifty, is assigned a beta of 1.
Collect data on (i) Daily closing price of a stock & (ii) Daily closing value of a Market Index over a timeperiod. Calculate Y = daily return for stock and X= daily return for Market Index. Regress Y on X and
get the equation: Y = α + βX. Slope is denoted by Greek letter β and pronounced as “beta”. It is the betaof the stock, it measures how sensitive is stock price to market fluctuations.
Beta = 1: stock price fluctuates as much as the marketBeta > 1: stock price fluctuates more than the marketBeta < 1: stock price fluctuates less than the market
The uploaded file “Axis bank-beta values-data for students” contains data on Axis Bank and Larsen &Toubro over the period 20 Nov 2008 to 17 Aug 2009. This file also contains data on BSE Bankex andBSE Capital Goods Index. Calculate the beta of these stocks for this period. Can one use the associatedmodels for forecasting purposes? Do they provide good fit to the data?
5. Energy Sales at WBSEDCL
Monthly data on WBSEDCL energy sales are given below, where units are MU = million units
unit=KiloWatt-Hour. Find the best regression model using time and seasonality.
