073 How hedge funds use CAPM

The expected excess returns are proportional to β, β > 1

• Greater β = greater risk

The β of a portfolio = weighted sum of β of components:

• Where w_i is the weight of the i-th component of the portfolio

Example:

• You have information that IBM is going up
• But the same day the market goes down
• IBM goes down as well, but is better than the market

• Difference = alpha

• How to profit from it:
  • Long IBM
  • Short the market => short an index fund
  • Given that
    • β_ibm = β_market = 1.0
    • w_ibm = w_market = 0.5
  • r_ibm = w_ibm*β_ibm + w_ibm + α_ibm
  • r_market = w_market*β_market + w_market + α_market
  • r_ibm = 0.5*1 + 0.5*α_ibm
  • r_market =  − 0.5*1 + 0.5*α_market => we assume is 0
  • r_total = 0.5*α_ibm
  • We get r_total even when the market has gone down => we negated the market risk