Success Measurement within the Investment [601418]

Success Measurement within the Investment
Management Process
A new approach by applying MPT
Jens Wingenfeld
Doctoral Studendt at University of Latvia, Riga
Faculty of Economics and Management
Hattersheim, Germany
[anonimizat]

Abstract—Investment Performance measurement plays a very
important role for any mutual fund both for the investor and
also for the Investment company as the issuer. Tradi tional
figures which describe performance and risk are consequently
offered in any Fact Sheet of a mutual fund. In Modern
Finance, success measurement is categorized in two
fundamental dimensions: a) Performance, and b) Risk. In this
context, the author ha s developed a new approach which
measures the contribution of an Investment Strategy or a
single asset of a portfolio lying on the efficient frontier within
the risk -return matrix in context of the Markowitz Model.
The following results are access to the f ramework of the
author´s research project of the Significance of Passive
Investment Strategies within the Mode rn Portfolio
Management Process respektively Modern Portfolio Theory
(MPT) .

Keywords -Investment Success Measurement, Efficient Portfolio,
Passive Investment
I. INTRODUCTION
Performance Measurement is an important aspect in
economics. The most convenient way to demonstrate
success is – like in any area of life – creating a clear number
(Wingenfeld, p. 80) . Referring to Markowitz (1952, p. 6),
two target dimensions are relevant and common for all
investors:

1. “They want “return” to be high. The appropriate
definition of “return” may vary from investor to investor.
But, in whatever sense is appropriate, they prefer more of it
to less of it.
=> “Performance ”

2. “They want this return to be dependable, stable,
not subject to uncertainty. No doubt there are security
purchasers who prefer uncertainty, like bettors at a horse
race who pay to take chances. …The techniques are for the
investor who, othe r things being equal, prefers certainty to
uncertainty.”

=> “Risk” II. TRADITIONAL SUCCESS MEASUREMENT N UMBERS
First of all, measurement parameters for the two
dimensions rate of return and risk of the single assets have
to be determined for comparing them an d for an evaluation
of combinations of diverse investment possibilities
(Hielscher, 1996, p. 54). Rate of return and risk have to be
operationalized to work with them in scientific models.
a) Rate of return
In general, the rate of return of a capital asse t is the
profit (residual) referred to the invested money. The discrete
rate of return is defined as


𝑟𝑡𝐷=𝑝𝑡−𝑝𝑡−1+𝑑𝑡
𝑝𝑡−1 

𝑟𝑡𝐷: discrete return of the asset within the time period t-
1 to t
𝑝𝑡: price of the assets at the time t
𝑝𝑡−1: price of the assets at the time t-1
𝑑𝑡: intermediate capital gains
t: period of valuation

For the calculation of the return of an asset via discrete
return, it is assumed one single interest yield at the end of
the evaluation period, whereas thi s period of time can be
different, e.g. one day, one month, or one year. Therefore,
the discrete return consists of a unique change of value of
the invested amount of money within the time period t -1 to t
(Poddig et al., 2009, p. 32).
The expected rate of return of a portfolio of assets is
simply a weighted average of the return of the individual
assets. The weight applied to each return is the fraction of
the portfolio invested in that asset. Thus, the uncertain
return of a portfolio is expressed by its ex pectancy value as
an expression for the rate of return which is realized over a

specific period of time. By an assumption of a discrete
distribution of the rates of return r, it follows

µ𝑖=∑𝑝𝑗∗𝑟𝑖𝑗𝑍
𝑗=1 (2)

where

µi: expectancy value of the rate of return of an asset i
rij: rate of return of the i -th asset by admission of the j –
th state of environment
pj: probability of occurrence of the j -th state of
environment
Z: number of possible states of environment

b) Risk
The quantification of uncertainty is also one of the
evolutionary breakthroughs in the theory of investments
during the last century (Qian, Hua, & Sorensen, op. 2007,
p. 3). Knight (2009, p. 15, the original was published in
1921 ) laid the groundwork with a quite intuitive definitional
distinction between uncertainty and risk :
(1) “Decision makers crudely operate in a of
random uncertainty”, and
(2) “Risk is a condition in which the decision
maker assigns formal mathematical
probabilities to specify the uncertainty.”

Later, von Neumann and Morgenstern (2004)
formalized the specification of risk into microeconomic
theory, laying a foundation for rational decision making
under uncertainty with the concept of expected utility.
Fabozzi (2009, p. 21) defines risk as “hazard, peril,
exposure to loss or injury”, while Steiner et al. (2012, p.55)
describe it as deviation from planned conditions. Within
Modern Portfolio Theory, the term risk is defined as the
dispersion of outcomes around the expected value. It is a
further component for the common performance
measurement (two -dimensional performance measurement).
Hence, risk is to equate with random deviations of rates of
return. As a consequence, risk of a single asset can be
measured by the dispersion or the Standard Deviation of the
rate of return (Spremann, 1999, p. 204) . In case of a discrete
dispersion of the rate of return, the equitation for a single
asset is

𝜎𝑖2(𝑅𝑖)=∑𝑝𝑗(𝑟𝑖𝑗−µ𝑖)𝑁
𝑗=1 (3)

Due to the fact that Standard Deviation is the square root
of the Variance, one has
𝜎𝑖=√𝜎𝑖2 (4)

where

σi2: Variance of the future rate of return of asset i
σi: Standard De viation of future rate of return of asset
i

c) Risk in the portfolio -context
The risk that potentially can be eliminated
by diversification is called unique risk. Unique risk
stems from the fact that that many of the perils that
surround an individual company are peculiar to
that company and its immediate competit ors. But
there is also some risk which is unavo idable,
regardless of the degree of diversifikation. This
risk is generally known as market risk. Market risk
stems from the fact that there are other
economywide perils that threaten all businesses.
That is w hy stocks have a tendency to move
together and why investors are exposed to market
uncertainties, no matter how many stocks or assets
they hold (Brealy et. al, p. 162).
By employing Markowitz (1952) great
and fundamental research results, it is possible to
find a dominating combination of assets which are
preferable to invest in terms of risk and return.
This is the approach the author is going in the
following enhanced:

III. ENHANCEMENT FOR THE ASSET MANAGE MENT
INDUSTRIE
All the numbers s hown before are processed by Asset
Management Companies to solicit their investment
products. If these numbers are applied in a coherent and
forceful way, a sufficient explanatory power is guaranteed.
But the question is if it is possible to valuate investment
performance even in a more scientific way. Thus, within
Investment Industrie environment, the Markowitz model is
not applicated in this context forcefully . The author uses
MPT (Modern Portfolio Theory) to demonstrate if an
investment style or a single asse t is able to contribute an
above -averag e part to obtain such a portfolio or any of such
portfolios of assets which lie on the efficient frontier: As
Cohen, J. B. et al. (1973, p. 742) present, diverse data and
knowledge is required in order to determine th e composition
of efficient portfolio s. Table 1 shows this and contrasts it
with the approach of the author:

TABLE I. REQUIRED DATA FOR THE ANALYSIS

Required data Way of proceeding in the
study
1. Projections of the expected
rate of return, including
both current income and
capital gain or loss, to be
earned on each security
that might be considered
for inclusion in the
portfolio. Within the analysis, active
mutual funds and passively
managed Exchange Traded
Funds are covered in the
analysis. Historical returns, as
proposed as one possible way
of data gaining by Markowitz
(1952, p. 3) are employed. In
the case of active managed
mutual funds, the daily
published redemption price
contains e. g. dividends of the
shares within the fund. In the
case of ETF’s, arbitrage
mechanism ensures the same.
2. Estimates of the possible
range of error of rate of
return projection. The possible range of error of
rate of returns is illustrated by
the standard deviation or
volatility, which is calculated
on the basis of the variation
of the daily returns.
3. An indication of the
interrelationships
(covariances) of the error
ranges among securities. A covariance matrix that
illustrates the covariance
between any pair of fund is
generated
4. An indication of any
constraints placed upon
the por tfolio manager. Constraints are the following:
 Full investment
(100%): This means
that the amount of
the single weights of
the portfolio should
be 1 (budget
condition):
∑𝑤𝑖=1𝑁
𝑖=1
where
𝑤𝑖: weight of asset i
 No short sales: The
weight of any single
asset should be
greater or equal 0
𝑤𝑖≥0

The aim of the mathematical procedure in terms of
an optimization process, transferred with M S-Excel and its
Add-on “Solver”, is to demonstrate the contribution of an
investment strategy (the author concentrates in hi s work on
a passive Investment Strategy) within the efficent p ortfolios.
These are such portfolios which have a minimal risk at a
given return, or – vice versa – a maximum return at a given
Risk (Bruns, Meyer -Bullerdiek, p. 62). Ultimately, this is a
deduction of the economic princible in general . Figure 1
shows this principle of Finance :

Figure 1: The Efficient Frontier

A rational investor (“homo economicus”) is not
willing to invest in such portfolios which ly below the line
in figure 1 , because for any portfo lio below this line there
exist s at least another one which dominates them. The
approach of the author is now by employing this model to
investigate if a single asset or an investment strategy
(“Passive Portfolio M anagement ”) is a recommendable one:
This is the case if the calculation leads to the result that the
appropriate allocation for building portfolios lying o n the
efficient frontier lea ds to the conclusion that the
correspondent asse t is represented above average within
such a portfolio of assets.
One part of author´s current research resu lts are
demonstrated in figure 2 -4. Figure 2 shows the calculated 9
efficient portfolios lying on the efficient frontier with the
weighting of their certain assets:
For this particular period under investigation
(02.01.2001 – 31.08.2012 ), four assets are calculated to
build up portfolios lying on the efficient frontier (here the
passive product, active fund number 2, 3, and 5) . Active
fund 2 has the highest average weighting within these 9
portfolios with a share of about 47%. This fund also
constitutes the Maximum Return Portfolio (MRP). The ETF
and active fund number 3 do contribute a share of about
25%, and active fund 5 with a small contribution of about
3%. The active funds number 1, 4, 6, 7 and 8 are not
represented in one of the efficient portfolios. Figures 3
illustrates this graphically. Figure 4 shows an additional and
very interesting outcome: Thus an above -average admixture

of the passive investment management tool (ETF) most
notably is indicated for investors who are interested to build
a portfolio that lies on the left side of the efficient frontier
which means a portfolio with a preferably low risk. The less
volatility (i. e. risk) an investor is willing to undergo, the
more it is advisable to prefer a passive investment tool in the
portfolio. Therefore, the analysis revealed that in times with
much uncertainty referring to future – like the ongoing
worldwide economic crisis or the prevailing terrorist attacks
in France – a passive investment product can be a valuable
tool to stabilize a portfolio of diverse assets and to reduce
risk. This finding could not be an alysed with the help of
conventional success -measurement figures.

Figure 2: Result of an optimization process with MS -Excel

Figure 3 : Share of the searched Asset ithin the Efficient Portfolios

Figure 4 : Weighting of the certain assets within the Efficient Portfolios
ETF Akt. Fund 1 Akt. Fund 2 Akt. Fund 3 Akt. Fund 4 Akt. Fund 5 Akt. Fund 6 Akt. Fund 7 Akt. Fund 8 0.000169379
0.012001% 0.020031% 0.027728% 0.023329% 0.018441% 0.017488% 0.012930% 0.013597% 0.013934%
1.588858% 1.670286% 1.625167% 1.558859% 1.702970% 1.592832% 1.652690% 1.620240% 1.708140% 0.010790%
0.025245% 0.027899% 0.026412% 0.024300% 0.029001% 0.025371% 0.027314% 0.026252% 0.029177% 0
0.001349%
0.001349%
PortfolioTarget
Return/DayOptimization Risk ETF Akt. Fund 1 Akt. Fund 2 Akt. Fund 3 Akt. Fund 4 Akt. Fund 5 Akt. Fund 6 Akt. Fund 7 Akt. Fund 8Amount of
Weights
1 0.027728% 0.027728% 1.625167% 0.00% 0.00% 100.00% 0.00% 0.00% 0.00% 0.00% 0.00% 0.00% 100%
2 0.026379% 0.026379% 1.541599% 5.81% -0.00% 84.31% 9.87% 0.00% 0.00% 0.00% 0.00% 0.00% 100%
3 0.025030% 0.025030% 1.467625% 12.77% 0.00% 71.57% 15.65% 0.00% 0.00% 0.00% 0.00% 0.00% 100%
4 0.023682% 0.023677% 1.404043% 19.76% 0.00% 58.79% 21.45% 0.00% 0.00% 0.00% 0.00% 0.00% 100%
5 0.022333% 0.022333% 1.352995% 26.69% 0.00% 46.10% 27.21% 0.00% 0.00% 0.00% 0.00% 0.00% 100%
6 0.020984% 0.020980% 1.315159% 33.67% 0.00% 33.33% 33.00% 0.00% 0.00% 0.00% 0.00% 0.00% 100%
7 0.019635% 0.019635% 1.292195% 40.62% 0.00% 20.63% 38.76% 0.00% 0.00% 0.00% 0.00% 0.00% 100%
8 0.018287% 0.018287% 1.281090% 43.54% 0.00% 8.97% 38.84% 0.00% 8.65% 0.00% 0.00% 0.00% 100%
9 0.016938% 0.016938% 1.275508% 46.25% 0.00% 0.00% 34.03% 0.00% 19.73% 0.00% 0.00% 0.00% 100%
Portfolio 1: Maximum Return Portfolio
Portfolio 9: Minimum Variance Portfolio
Average Weighting to the Efficient Portfolios 1-9 25.46% -0.00% 47.08% 24.31% 0.00% 3.15% 0.00% 0.00% 0.00%Mean Value of Return
Standard Deviation
Variance

IV. CONCLUSION :
With the help of the author´s approach to measure
success within the Investment Industrie, a further tool to
measure the advantagenous of an asset was created. State -of-
the Art to valuate a portfolio or asset manager concerning his
decision -making process and his results is his track -record,
expressed by performance figures like discrete or continous
return. Alone, this dimension of success is not meanin gful,
because it does not describe the resulting risk an investor had
to bear. Therefore , all sophisticated investment companies
characterise their investment products using a risk -adjusted
success measurement figure. This is e. g. Sharpe Ratio or in
other words the Reward to Variability Ratio. By using the
author´s new success measurement tool, t here is provided a
powerful instrument for comparing diverse assets or
investment styles within a portfolio context. Future has to
show how this approach can be a standard success
measurement figure within Investment Management
Industry .

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