Asset Management Lecture 6

Outline for today Treynor Black Model M2 measure of performance Sensitivity to return assumption Tracking error

Treynor Black Model The optimization of a risky portfolio using a single-index model is know as the Treynor Black model (or diagonal model)

Optimizing procedure

Treynor Black Model

Table 27.1 active portfolio management with 6 assets

M 2 Measure Developed by Modigliani and Modigliani Create an adjusted portfolio P* with T-bills and the managed portfolio P so that SD[r(P*)]= SD[r(M)] Example: Volatility of r(P)=1.5*volatility of r(M) P*=2/3P+1/3T With the same SD, you can now compare the performance

M 2 Measure: Example Managed Portfolio: return = 35%standard deviation = 42% Market Portfolio: return = 28%standard deviation = 30% T-bill return = 6% Hypothetical Portfolio: 30/42 =.714 in P (1-.714) or.286 in T-bills r(P*)=(.714) (.35) + (.286) (.06) = 26.7% Since this return is less than the market, the managed portfolio underperformed

M 2 Measure: Example σ E(r) PM T σ(P)σ(M) P* M2

M 2 Measure: Example σ E(r) P M T σ(P) σ(M) P* M2

M 2 Measure Simplification for calculation

Table 27.1 active portfolio management with 6 assets

Target price and alpha on June 1, 2006

The Optimal Risky Portfolio with the Analysts’ New Forecasts

The Optimal Risky Portfolio (W A < 1)

Drawback of the model Extreme sensitivity to expected return assumptions The results often run against investor intuition Such quantitative optimization processes are rarely employed by managers What about putting some constraints to this model?

Tracking error Portfolios are often compared against a benchmark Tracking error Benchmark Risk: SD of Tracking error

The Optimal Risky Portfolio with the Analysts’ New Forecasts

Tracking error Set weight in the active portfolio to meet the desired benchmark risk For a unit investment in the active portfolio For our example: For a desired benchmark risk Assume that the desired benchmark risk is Wa(Te)=0.0385/ Wa(Te)=0.43

Constrained benchmark risk