Mix of Risk Free and Risky Portfolio

E(r_c) and σ_c

E(r_c) = r_f + y*[E(r_p) - r_f]

σ_c = y*σ_p

CAL = Capital Allocation Line

Slope (tradeoff of risk and return)

S = [E(r_p) - r_f ]/

σ_p

Portfolio A Dominates Portfolio B if

E(r_a) ≥ E(r_b)

σ_a ≤ σ_b

E(r_c) = r_f + ([E(r_p) - r_f]/σ_p) * σ_c

                                  ^            ^

                             _{Intercept     Slope}

Curves that contain different portfolios that the investor is indifferent between (portfolios with equivalent utility levels)

y^*=

[E(r_p) - r_f ] / Aσ_p²

This is the optimal percentage to invest in the risky portfolio

2 Advantages of passive strategy over active

1. Significantly cheaper than active
2. Free Rider Benefit

1. They're undiversified (biased toward big/popular stocks)
2. They're top heavy (weighted toward largest stocks)
3. They're chasing performance (weighted toward winners)
4. You can do better