1. Statistical Functions in Excel

2. Sample Statistics versus Population Statistics  Population Statistics –Observations include all possible outcome –Degree of freedom = N  Sample Statistics –Observations are a representation –Degree of freedom = N-1

3. Excel Statistical Functions  Population Statistics –Standard deviation, variance, and covariance –STDEVP(x), VARP(x), COVAR(x,y)  Sample Statistics –Sample size: COUNT(x) –Standard deviation and variance –STDEV(x), VAR(x) –There is no Excel function for sample covariance Correct COVAR(x,y) for degree of freedom Sample covariance = COVAR() * N / (N-1) –Where N is sample size  Arithmetic Average –AVERAGE()  Correlation coefficient –CORREL(x,y)

4. Geometric Mean  Geometric mean  Geometric average return x 1 = (1 + r 1 )

5. GEOMEAN Function  Using Excel to compute geometric average return\ –A2:A100 contains monthly return, r.  GEOMEAN() returns the geometric mean  Three strategies: 1. Convert returns to 1+r -> B2:B100Y is 1+r.  Geometric average return = GEOMEAN(B2:B100) 2. Use the monthly return, r, and enter as an array.  Geometric average return = {GEOMEAN(1+ A2:A100)-1}. 3. PRODUCT() is also a useful function.  Geometric average return = (PRODUCT(B2:B100)^(1/N))-1

6. Homework 4 – Due July 10  Benninga: 7.3 –Download data file from course website –Compute population statistics, not sample statistics –Use Data Table to create the portfolios with varying percentages in the SP500  SHW3  Holden: Figure 9.1  SHW4