Asset Management
Lecture 9
Outline for today
Black-litterman model and sensitivity in
confidence
Treynor-Black vs Black-Litterman
Value of active management
The Black-Litterman Model
Step 1: Estimate the covariance matrix from
historical data
Step 2: Determine a baseline forecast
Step 3: Integrating the manager’s private
views
Step 4: Developing revised (posterior)
expectations
Step 5: Apply portfolio optimization
Sensitivity in confidence level
Confidence measured by standard deviation of view Q
Possible SD 0 0.0100 0.0173 0.0300 0.0600
Variance 0 0.0015 0.0003 0.0009 0.0036
E(RB|P) 0.0190 0.0148 0.0164 0.0152 0.0143
E(RS|P) 0.0140 0.0598 0.0424 0.0556 0.0643
Figure 27.5 Sensitivity of Black-Litterman Portfolio
Performance to Confidence Level (view is correct)
Treynor-Black vs Black-Litterman
TB BL
Maximization identical
The BL Model as Icing on the TB Cake
Suppose that you have two portfolios—one
for the US and one for Europe
The model would be run as two separate divisions
Each division would compile values of alpha
relative to their own passive portfolio
Portfolios need to be optimized separately
Relative performance of the two markets can be
expected to add information to the independent
macro forecasts for the two economies
The BL Model as Icing on the TB Cake
Use BL to include forecasts from comparative
economic and international finance analyses
Replace TB alpha with BL views
Example: assume only one stock in the active
portfolio
Alpha, beta, E(Rm), var(Rm), var(e)
The BL Model as Icing on the TB Cake
Use BL to include forecasts from comparative
economic and international finance analyses
Input list for BL model
R [ E ( RM ), E ( R A ) A E ( RM )]
A
P (0,1 )
A E ( RM )
PR' Q A
QE 0
D A
( ) Var( forecasting error )
2 u (t ) a0 a1a f (t ) (t )
2 ( D) 2 ( ) 2 (e) SCL : R(t ) a RM (t ) e(t ), t T
The BL Model as Icing on the TB Cake
Use BL to include forecasts from comparative
economic and international finance analyses
Calculate the conditional expected return will give
you the same results as from the TB model:
The realized abnormal return of time T
SCL : R(t ) a RM (t ) e(t ), t T
u (t ) R(t ) RM (t ) a(t ) e(t )
The precision of record, t
u (t ) a0 a1a f (t ) (t )
Adjust a (T ) a0 a1a f (T )
The BL Model as Icing on the TB Cake
The BL model could be viewed as a
generalization of the TB model
Differences?
Treynor-Black vs Black-Litterman
TB BL
Maximization identical
input Individual Views of relative
security analysis performance
target Security analysis Asset allocation
with adjustment where relative
of forecasts performance is
relevant.
Value of Active Management
Model for estimation of potential fees
Kane, Marcus, and Trippi (JPM, 1999)
The percentage fee, f, that investors would be willing
to pay for active services
f (S P S M ) / 2 A
2 2
Source of the power of the active portfolio
ai
the squared information ratios
2 (ei )
a
S P S M i 1 i
2 2 n
(ei ) Remember f is in addition to
2 what an index fund would
1 n ai
f
2 A i 1 (ei )
charge.
Concluding Remarks
The gap between theory and practice has
been narrowing in recent years
TB model is sensitive to large alpha values
BL model relies on the “confidence” level
which is often ambiguous.