Jensen's model proposes another risk adjusted
performance measure. This measure was developed
by Michael Jensen and is sometimes referred to
as the Differential Return Method. This measure
involves evaluation of the returns that the fund
has generated vs. the returns actually expected
out of the fund given the level of its systematic
risk (ßi). The surplus between the two returns
is called Alpha, which measures the performance
of a fund compared with the actual returns over
the period. Required return of a fund at a given
level of risk (ßi) can be calculated as:
ri = rf + ßi (rM - rf)
Where, rM is average market return during the
given period. After calculating it, alpha can
be obtained by subtracting required return from
the actual return of the fund.
Higher alpha represents superior performance
of the fund and vice versa. Limitation of this
model is that it considers only systematic risk
not the entire risk associated with the fund and
an ordinary investor can not mitigate unsystematic
risk, as his knowledge of market is primitive.
Alpha shows the fund’s performance relative
to the benchmark and can demonstrate the value
added by the fund manager. The higher the 'alpha'
the better the manager.
Alpha is a risk-adjusted measure
of the so-called "excess return" on
an investment. It is a common measure of assessing
an active manager's performance as it is the return
in excess of a benchmark index or "risk-free"
The alpha coefficient(αi) is
a parameter in the capital asset pricing model.
In fact it is the intercept of the Security
Characteristic Line (SCL). One can prove
that in an efficient market, the expected value
of the alpha coefficient equals
the return of the risk free asset:
E(αi) = rf.
Therefore the alpha coefficient can be used to
determine whether an investment manager has created
- αi< rf : the manager has destroyed value
- αi= rf : the manager has neither created
nor destroyed value
- αi > rf : the manager has created value
The difference (αi- rf ) is called Jensen's
The concept and focus on Alpha comes from an
observation increasingly made during the middle
of the twentieth century, that around 75 percent
of stock investment managers did not make as much
money picking investments as someone who simply
invested in every stock in proportion to the weight
it occupied in the overall market in terms of
market capitalization, or indexing. Many academics
felt that this was due to the stock market being
"efficient" which means that since so
many people were paying attention to the stock
market all the time, the prices of stocks rapidly
moved to the correct price at any one moment,
and that only luck made it possible for one manager
to achieve better results than another, before
fees or taxes were considered. A belief in efficient
markets spawned the creation of market capitalization
weighted index funds that seek to replicate the
performance of investing in an entire market in
the weights that each of the equity securities
comprises in the overall market..
In fact, to many investors, this phenomenon created
a new standard of performance that must be matched:
an investment manager should not only avoid losing
money for the client and should make a certain
amount of money, but in fact should make more
money than the passive strategy of investing in
everything equally (since this strategy appeared
to be statistically more likely to be successful
than the strategy of any one investment manager).The
name for the additional return above the expected
return of the beta adjusted return of the market
is called "Alpha".
A rational investor would not invest in an asset
which does not improve the risk-return characteristics
of his existing portfolio. Since a rational investor
would hold the market portfolio, the asset in
question will be added to the market portfolio.
Specific risk is the risk associated with individual
assets - within a portfolio these risks can be
reduced through diversification (specific risks
"cancel out"). Systematic risk, or market
risk, refers to the risk common to all securities
- except for selling short as noted below, systematic
risk cannot be diversified away (within one market).
Within the market portfolio, asset specific risk
will be diversified away to the extent possible.
Systematic risk is therefore equated with the
risk (standard deviation) of the market portfolio.
Since a security will be purchased only if it
improves the risk / return characteristics of
the market portfolio, the risk of a security will
be the risk it adds to the market portfolio. In
this context, the volatility of the asset, and
its correlation with the market portfolio, is
historically observed and is therefore a given
(there are several approaches to asset pricing
that attempt to price assets by modelling the
stochastic properties of the moments of assets'
returns - these are broadly referred to as conditional
asset pricing models). The (maximum) price paid
for any particular asset (and hence the return
it will generate) should also be determined based
on its relationship with the market portfolio.