Statistics 701: CAPM from a statistical perspective

Summary so far

• Ponzironi 1: Bonferonni p-value = n * regular p-value.
• Ponzironi 2: Unseen crashes can be delt with by adding 3 of them to your data.
• Ponzironi 3: Correct for risk since variance matters.

Optimal investing

• long run growth rate = mean - variance / 2
• optimizing LRGR:
  • How leveraged should one be?
  • mean = alpha * (mean - RiskFreeRate)
  • varinace = alpha² variance
  • optimize a quadratic: -b/2a
  • Market details
    • If we put w fraction of wealth in market
    • mean is .07w
    • SD is (.22w)
    • Variance is (.22w)²
    • goal: maximize .07 w - .22²w²/2
    • optimize a quadratic: -b/2a = (-.07)/(-2*.22²/2) = 1.44
    • Slightly leveraged

  • optimum investment: alpha = (mean - RiskFreeRate)/variance
  • Units work out since everything is in returns

• Look at stock market
  • look at whole series (find annual mean and variance)
  • look at recient series
  • figure out optimal investment
  • compute LRGR and do it empirically

Last modified: Tue Oct 22 13:07:36 2002