Finding and sustaining Alpha is the wet dream of some mutual fund managers. If their investment approach would result in a sustainable alpha then it would mean that they generate money for their clients despite the fact that the stock market goes up and down.

1. The alpha of alpha seeking mutual funds
Chris De Corte
chrisdecorte@yahoo.com
March 28, 2017
1 Key-Words
Alpha, CAPM, Jensen.
2 Introduction
Finding and sustaining Alpha is the wet dream of some mutual fund managers. If their
investment approach would result in a sustainable alpha then it would mean that they generate
money for their clients despite the fact that the stock market goes up and down.
3 summary of formula’s from CAPM
The capital asset pricing model (CAPM) states that the return on an asset i can be expressed
in terms of the return on the market as follows [1]:
Ri = α + β · Rm + e (1)
where:
ˆ Ri = monthly return on the asset i
ˆ α = the intercept on the vertical axis
ˆ β = slope of the regression line
ˆ Rm = monthly return on the market
ˆ e = a random error term
1

2. 4 THE DATA AND THE CALCULATION
4 The data and the calculation
For the purpose of our calculation, we used as asset i the mutual fund listening to the name
”Vector Navigator” [4] and we compared it with the S&P [3] over the same period: from
October 2007 till March 2017. So, we used the return of the S&P as ”the market”. We
have put the 114 monthly starting values of our fund next to the market and calculated 113
monthly returns for both. Next, we let MS Excel draw for us graphs based on the data for
the total period and for the 8 individual full years and we let MS Excel calculate for us the
regression lines in each case. The regression line for the full period can be found in figure [1]
and the regression formula can be found in the upper right corner of the figure. In table [1],
we give an overview of the regression values for all the periods. For the one who wants to
recalculate all the details, a link to the MS Excel file is given in [5].
Figure 1: In this figure we compare the returns for the S&P (x-axis) with the returns of our fund
(y-axis) for 113 months and let MS Excel calculate a regression line resulting in an α and
a β.
2

3. 5 INTERPRETATION OF THE NUMBERS
Period β α + e
2008 0.1098 -0.0397
2009 0.3346 0.0171
2010 -0.0347 0.0159
2011 -0.058 -0.0049
2012 0.5148 0.0132
2013 -0.0446 0.0166
2014 0.5921 0.0097
2015 0.7499 0.0095
2016 0.7299 0.0001
Average 0.3215 0.00416
Total period 0.3431 0.0036
5 Interpretation of the numbers
The α+e from formula (1) for the total period comes to 0.0036. Although the random error e
is expected to be zero [1] but also the intercept α should be zero as any deviation from zero in
the alpha indicates that the share has at some time been inefficiently priced, which is unlikely
to persist [1]. But, we can be lenient to the idea of an alpha generating fund and appreciate
the work of the asset managers done and assume the best case scenario that the error e is
indeed 0. This would result in an α of 0.0036 or an excess return of 0.36%. But as the β is
only 0.343, it basically means that only 34% of your money is invested in the S&P and that
the remaining 66% of your invested money has been put on an interest bearing account with
a yield of only 0.36%! This sounds little and probably less than the risk free rate. Indeed,
according to [2]:
E(Ri) − Rf
β
= E(Rm) − Rf (2)
where:
ˆ E(Ri) = expected monthly return on the asset i
ˆ E(Rm) = expected monthly return on the market
ˆ Rf = risk free interest rate
3

4. 7 REFERENCES
From formula (2) follows:
E(Ri) = β · E(Rm) + Rf · (1 − β) (3)
Comparing formula (3) with formula (1), we get:
α + e = Rf · (1 − β) (4)
Filling in the values that we calculated previously, we get:
α + e = 0.0036 = Rf · (1 − β) = Rf · (1 − 0.3431) ≈ 0.66 · Rf (5)
or that:
Rf ≈ 0.00545 (6)
6 Conclusion
Seeking α might be the wet dream of some asset managers, the pursuit to it is most probably
another buzz word and only a good marketing stunt. In any case, according to formula (4),
the sought after excess return is most of the times less than the risk free interest rate and
hence there is no need to hire a fund manager to let him pursuit this for you.
7 References
1. Juta & CO, LTD ; Financial Management ; Carlos Correia, David Flynn, Enrico Uliana,
Michael Wormald ; pages 93-98.
2. Wikipedia. Capital asset pricing model.
3. finance.yahoo.com
4. www.vector.lu
5. www.researchgate.net/publication/315665320 calculating alpha for a fund
4