Page 160 - Contributed Paper Session (CPS) - Volume 8

CPS2225 Retno Subekti et al.
2.2 Views Statement in Black Litterman
In many references, there are two types of views statement in BLM namely
relative views and absolute views. Relative view is the statement when
someone compare two or more assets related with the opinion of their return
in the future while absolute view is the statement about return prediction for
particular asset. It is clearly when we describe it in this following example.
A portfolio consists of 3 assets, namely A, B and C. Investors can state 3
views or more, but in this example only 2 views are used.
View 1: "I believe that asset A will return 1,75%"
View 2: "I convinced asset B will return 2% beyond C assets"
E(r) is an estimation of returns from investors, with these three assets, A, B
and C while two views are the investor ‘s opinion which can be expressed in
such linear combination of expected return.
E(r ) = 0,0175
A
E(r ) − E(r ) = 0,02
B
C
To transform it into linear combination, we need to define the link matrix or
the pick matrix, P so that equation can be written as follows,
1. E(r ) + 0. E(r ) + 0. E(r ) = 0,0175
C
B
A

0. E(r ) + 1. E(r ) − 1. E(r ) = 0,02
B
C
A

( )
1 0 0 0,0175
= [ ] () = [( )] = [ ]

0 1 −1 0,02
( )

Sometimes, it is possible to have an opinion for some of assets simultaneously,
such as when we believe that two assets will return outperformance two other
assets. For example, the statement about asset C and D will predict 1,5 %
outperform asset E and F. So, we can express
( )

( )

= [0.5 0.5 −0.5 −0.5] () = [ ] = [0.015]
( )

( )

In practice, we do not need to put the views in all assets in the portfolio,
at least we have one statement about the future return to work with Black
Litterman model. This is the unique of BL model because we can improve the
starting point which is equilibrium point with views/opinion.
The next question is how to write it in statistical words to describe the
combination process as same as fig.1. In (2), starting point for BL is neutral
equilibrium market which is CAPM and it is stated as a prior distribution while
views from investor is categorized as another information. The visualization of
the combination process is described in fig.1 and showed unclear explanation

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