T9: Systematic Risk and the Equity Risk Premium

Beta interpretation

β = 1: moves with market. β > 1: more volatile than market. β < 1: less volatile. β = 0: no systematic risk. β < 0: moves opposite to market (insurance).

Market portfolio beta

β of market portfolio = 1 always by definition.

Risk-free asset beta

β of risk-free asset = 0 always. Cov(rf, Rmkt) = 0.

CAPM formula

E(Ri) = rf + βi × (E(Rmkt) - rf). Risk-free rate + beta × market risk premium.

Overvalued vs undervalued

Compute (E(Ri) - rf) / βi for each stock. If > MRP → undervalued (above SML). If < MRP → overvalued (below SML).

Portfolio beta

βP = Σ wi × βi. Weighted average of individual betas. No cross terms needed.

SML vs CAL

SML: x-axis = beta, applies to all assets, identifies mispricing. CAL: x-axis = SD, applies to portfolio combinations with rf.

Efficient frontier rule

A portfolio is efficient if no other portfolio offers same return with less risk. Only upper boundary above MVP is efficient.

Negative beta stock

Expected return < rf. Investors accept lower return because stock provides insurance — performs well when market crashes.

Tangent portfolio rule

All rational investors hold the same risky portfolio (tangent portfolio) regardless of risk aversion. Only proportion in rf vs tangent differs.

Sharpe Ratio

(E(R) - rf) / SD(R). Measures return per unit of risk. The optimal CAL has the highest Sharpe Ratio.

Diversification cannot eliminate all risk

Even a perfectly diversified portfolio retains market risk. Diversification removes firm-specific risk only.