Slide strategic financial management l02

STRATEGIC FINANCIAL MANAGEMENT BASIC STATISTICS KHURAM RAZA First Principle and Big Picture Summarizing Data The problem that we face today is not that we have too little information but too much Making sense of large and often contradictory information is part of what we are called upon to when analyzing companies  Data Distributions  Summary Statistics Data Distributions  Frequency distribution  Discrete distribution  Continuous distribution  you can summarize even the largest data sets into one distribution and get a measure of  What values occur most frequently and  The range of high and low values Summary Statistics The information that gives a quick and simple description of the data  Measures of Central Tendency  Mean Minimum Height: 6.2  Quintiles Average Height : 6.68  Measures of Dispersion Maximum Height : 7.3  Variance Average Change Per Day : 0.03  standard deviation  Relative Measures of Variation  Coefficient of Variation (CV)  Standardized Variable (Z-Score) Mean  The mean is the average of the numbers: a calculated "central" value of a set of numbers  To calculate: Just add up all the numbers, then divide by how many numbers there are  Example: what is the mean of 2, and 9? Add the numbers: + + = 18  Divide by how many numbers (i.e we added numbers): 18 ÷ = So the Mean is n X i X1  X    X n  X  i 1 n n Quintiles For individual observations/discrete frequency distribution, the i th quartile, j th decile and k th percentile are located in the array/discrete frequency distribution by the following relations Qi  i(n  1) th observation in the distribution, i 1, 2, j(n  1) th observation in the distribution, j 1, 2, ,9 10 k(n  1) Pk  th observation in the distribution, k 1, 2,,99 100 Dj  Variance & Standard deviation  The variance and the closely-related standard deviation are measures of how spread out a distribution is  variance measures the variability (volatility) from an average or mean Variance Standard Deviation Variance & Standard deviation Mr •  X has eight eggs Each egg was weighed and recorded as follows: 60 g, 56 g, 61 g, 68 g, 51 g, 53 g, 69 g, 54 g Mean = ∑X/n 472/8 =59 Variance = ∑(x- )2/n 320/8 = 40 S.D = √(x- )2/n √40 = 6.32 gram Comparing Standard Deviations Data A 11 12 13 14 15 16 17 18 19 20 21 Mean = 15.5 S = 3.338 20 21 Mean = 15.5 S = 0.926 20 21 Mean = 15.5 S = 4.567 Data B 11 12 13 14 15 16 17 18 19 Data C 11 12 13 14 15 16 17 18 19  The smaller the standard deviation, the more tightly clustered the scores around mean  The larger the standard deviation, the more spread out the scores from mean 02:57:50 PM 10 Coefficient of Variation (CV)  S   100% CV   X   Can be used to compare two or more sets of data measured in different units or same units but different average size 02:57:50 PM 11 Use of Coefficient of Variation  Stock A: – Average price last year = $50 – Standard deviation = $5 S $5 CVA   100%  100% 10% $50 X  Stock B: – Average price last year = $100 – Standard deviation = $5 S $5 CVB   100%  100% 5% $100 X 02:57:50 PM Both stocks have the same standard deviation but stock B is less variable relative to its price Standardized Variable 02:57:51 PM 13 Performance evaluation by z-scores The industry in which sales rep Mr Atif works has mean annual sales=$2,500 standard deviation=$500 The industry in which sales rep Mr Asad works has mean annual sales=$4,800 standard deviation=$600 Last year Mr Atif’s sales were $4,000 and Mr Asad’s sales were $6,000 Which of the representatives would you hire if you have one sales position to fill? 02:57:51 PM Performance evaluation by z-scores Sales rep Atif Sales rep Asad XB= $2,500 XP =$4,800 S= $500 SP = $600 XB= $4,000 XP= $6,000 ZB XB  XB  SB ZB  4,000  2,500 500 ZP 3 XP  XP  SP ZP  6,000  4,800 600 Mr Atif is the best choice 02:57:51 PM 2 Relationships in the Data When there are two series of data, there are a number of statistical measures that can be used to capture how the two series move together over time 10000 9000  Covariance  Correlations  Regressions 8000 7000 6000 Sales COGS Selling Exp Admin Exp 5000 4000 3000 2000 1000 100 200 300 400 500 600 700 800 900 1000 Covariance Covariance indicates how two variables are related A positive covariance means the variables are positively related, while a negative covariance means the variables are inversely related The formula for calculating covariance of sample data is shown below The covariance between the returns of the S&P 500 and economic growth is 1.53 Since the covariance is positive, the variables are positively related—they move together in the same direction Correlation  Correlation is another way to determine how two variables are related In addition to telling you whether variables are positively or inversely related, correlation also tells you the degree to which the variables tend to move together  The correlation measurement, called a correlation coefficient, will always take on a value between and – 1:  If the correlation coefficient is one, the variables have a perfect positive correlation  If correlation coefficient is zero, no relationship exists between the variables  If correlation coefficient is –1, the variables are perfectly negatively correlated (or inversely correlated) Correlation  A correlation coefficient of 66 tells you two important things:  Because the correlation coefficient is a positive number, returns on the S&P 500 and economic growth are positively related  Because 66 is relatively far from indicating no correlation, the strength of the correlation between returns on the S&P 500 and economic growth is strong Regressions A regression uses the historical relationship between an independent and a dependent variable to predict the future values of the dependent variable Businesses use regression to predict such things as future sales, stock prices, currency exchange rates, and productivity gains resulting from a training program Y=a+bX Slope of the Regression Intercept of the Regression Regressions