Stat 101: Finance and covariance

• Admistrivia:
  • Read sections 4.6 and 4.7 tonight!
  • Homework problem from book page 177, 4.104 doesn't sum to 1. change last entry from .01 to .02

• Mean and variance of a portfolio of two real stocks
  • E(Sears) = .0016, SD(Sears) = .0745, Var(Sears) = .0055
  • E(Penney) = .0018, SD(Penney) = .0714, Var(Penney) = .0051
  • porfolio = (Sears + Penney)/2
  • E(portfolio) = .0017, SD(portfolio) = .0658, Var(portfolio) = .0043

• Correction factor is called covariance
  • formula: Var(aX + bY) = a² Var(X) + b² Var(Y) + 2 ab Cov(X,Y)
  • Cov(X,Y) = SD(X) * SD(Y) * corr(X,Y)
  • Draw some pictures
  • Corr(Sears,Penney) = .63, check formula
  • Notice: portfolio is still an advantage

• What is the worst for a portfolio? Could Variance be larger than either one? Answer = no.

• Derive covariance from var(X+Y)
  • Z = X - E(X)
  • W = Y - E(Y)
  • Var(X+Y) = Var(Z + W)
  • Var(Z + W) = E(Z + W - 0)²
  • Var(Z + W) = E(Z²) + 2 E(ZW) + E(W²)
  • Var(X + Y) = Var(X) + Var(Y) + 2 E(ZW)
  • Var(X + Y) = Var(X) + Var(Y) + 2 E(ZW)

• Full normalization
  • Z = (X - E(X))/SD(X)
  • Correlation is covariance for normalized data

• Example from table

Last modified: Mon Oct 25 10:09:37 EDT 1999