Active Portfolio Management 2

Summaries

Market equilibrium is the result of active portfolio management.

Separation Theorem: Optimal risky portfolio can be designed without considering the investors’ degree of risk-aversion. 2 steps to construct a portfolio:

1)      determine optimal risky portfolio

2)      determine % of risk-free asset by considering investors’ risk-aversion level

Active portfolio management has to redo 1) and 2) as the expectations and investor risk-aversion level change.

Treynor-Black Model:

1)      assume limited assets are mispriced (in the active management part)

2)      combine passive and active portfolios

a)      Construct a passive portfolio M (just equal to Market portfolio? Include the active portfolio stocks? Maybe doesn’t matter because this model assumes the number of mispriced asset is limited)

b)      Construct an active portfolio A.

a.      Alpha_i = expected return – return by CAPM = Ri – (R_rf + Beta * (R_m – R_rf))

b.      Recall from market model: Ri = a_i + b_i * R_m + error_i

c.      Assign weighting by alpha_i/sigma(error_i)^2

c)      Combine A and M and find CAL

d)      Partition with risk free asset according to investors’ requirement

Alpha_A = weighted sum of all alphas

Information Ratio:

Differences between the Sharpe ratios for P and M = (alpha_A / sigma(error_A))^2

Where alpha_A / sigma(error_A) is the information ratio (ex ante)

Compared to IR=(R_P – R_B)/sigma(R_P-R_B) which is ex post

*** The active profile is small. It has large unsystematic risk

If the prediction of alpha can be wrong, multiply the calculated alpha by R² ( the correlation square of historical alpha and predicted alpha)