Portfolio Models

Summaries

Market Model

R_i = alpha_i + beta_i * R_m + error_i

Also assume

1)      expected value of error_i is zero (non-systematic risk)

2)      error unrelated to market return

3)      error unrelated across asset

Therefore,

E(R_i) = alpha_i + beta_i * E(R_m)

Var(R_i) = beta_i^2 * Var (R_m) + Var(error_i)

Cov(i,j) = beta_i*beta_j * Var(R_m)

3n + 2 inputs need (2 are the market variance and expected return)

Macro-economic Factor Models

Ri = E(Ri) + S1 * F1 + S2 * F2 + error_i

S1, S2 are sensitivity factors

F1, F2 are economical factors (realized values – predicted values = surprises)

Error_i – firm-specific non-systematic risk

Priced risk – systematic risk, which cannot be diversified and will be compensated

*** Expectation value of F1 and F2 are zeros!

Fundamental Factor Models

Ri = E(Ri) + S1 * F1 + S2 * F2 + error_i

S1, S2 are Standardized sensitivities (e.g. (asset P/E – average P/E)/sigma_P/E)) – calculated directly, not by regression!

F1, F2 are factor returns – slopes of the cross sectional regressions (independent variables are the sensitivities and the dependent variables are the factor returns)

Arbitrage Pricing Model (APM)

Derived from arbitrage pricing theory (APT)

-          no arbitrage opportunities (gain profit by bearing no risk)

-          unsystematic risks are diversified away

APT equation

E(R_p) = R_rf + Sum(Beta * Lambda)

Each Lambda is a risk factor and Beta is the associated risk premium

Unlike in CAPM, there are many risk factors and not necessarily including the market risk factor