chapter 6 prediction of investor’s investment...
TRANSCRIPT
178
CHAPTER 6
PREDICTION OF INVESTOR’S INVESTMENT DECISION IN
MUTUAL FUNDS USING FUZZY LOGIC
6.1 INTRODUCTION
Mutual Funds are becoming an effective way for investors to participate
in financial markets. An investor must learn to analyze and measure the risk and
portfolio returns. The fund performance is mainly impacted by characteristics such
as the size of an asset; turnover ratio’s and fee structure. Lenders’ highest priority
lies in understanding the relation between fund performances as also the above
characteristics. Currently the lenders depend upon investment advisors for their
financial planning. Moreover, no customized tools are available for investment
decision. Therefore, a fund planner tool called Techno-Portfolio Advisor is proposed
in the present study. The highlights of the proposed tool are (a) it helps the investors
to understand the critical relations and support mutual funds selection across the
Asset Management Companies (AMCs) in India. (b)Its design is based on the fuzzy
inference rules by considering the investor preferences like investment amount, age,
objective and rate of returns from the investments. (c)The optimal funds for
achieving the investor goal are evaluated based on the quantitative data available
from the historical NAV from SEBI/AMFI/AMCs. (d) The tool has a two pronged
benefit – for the investor community to choose the right fund scheme and achieve
the investment goals as well.
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Mutual funds allow a group of investors to pool their money together and
invest. The fund’s manager invests the funds’ assets, typically by buying stocks or
bonds, or by a combination of the two as shown in Figure 6.1. The benefits of
mutual funds to investors are many. First of all, it is very difficult for an investor
with only Rupees 5000 to invest in a diversified basket of market or financial
instruments. But any small lender can easily accomplish a diversified portfolio by
investing through diversified mutual fund(s). Secondly, unlike the underlying assets
that may have limited liquidity in the market, mutual funds can be very easily
traded. Thirdly, by combining their cash together, investors in mutual funds have an
access to a professional management, fourthly, investors experience lower
transaction costs. As a result, this sector has witnessed a tremendous growth in the
past two decades.
Figure 6.1 Concept of Mutual Fund
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A mutual fund is a professionally managed investment scheme that pools
money from many investors and invests it in stocks, bonds, and other securities.
Currently, the global value of all mutual funds totals more than $US 26 trillion.
There are various mutual fund schemes like Income, Growth, Equity, Balanced,
Sector, Tax Saving Schemes, Equity Linked, Infra Structure, Gilt Funds etc., with
different objectives and different investment pattern of funds, which confuse the
minds of investors – what to choose, where to choose. The advertisements and other
modes of communications being undertaken by various fund operators (Asset
Management Companies) put the investors into a state of confusion regarding the
selection of suitable scheme. There might be some false advertisements, schemes
involving hidden costs and clear stated objectives material provided as caveats. All
these put the investors into a trouble in their decision making. The awareness level
about various schemes as per age, income, risk taking ability, period of investment,
expected return, taxation, are generally not up to the expected level among the
investors.
The work is limited to three open-ended funds, three each in the equity,
tax planning & the sector funds respectively of selected AMCs (Franklin Templeton,
ICICI and HDFC) to the availability of NAV data for the past two years (2011-
2012). The objective of this work is to analyze the financial performance of selected
mutual fund schemes through Sharpe Ratio, Treynor Ratio, Jenson Ratio etc. using
inference rules and list the investment amounts in each scheme to achieve investor
target amount. Mutual funds are an integral part of the stock market and the
investment avenue for large number of investors in the recent years. There are a
number of investment opportunities available to an investor. Each of these
investments has its return features along with own risks. The main focus of this
research is to find out the risk and return features and study the performance of the
funds and compare it with the market return. The proposed work gains the
admiration and support from professionals in the finance field; they embrace it as a
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potential investment analysis for portfolio managers, financial planners, and
investors.
Based on the literature study, it is found that so far some researches deal
with statistical tools or quantitative tools to analyze the performance of the mutual
fund. All researches use one or two methods to compare the mutual funds of one or
two schemes only. Some researches focus only on a particular fund and enumerate
its advantages and disadvantages. But a research focused on comparing the similar
type of open ended schemes in different AMCs is quite rare.
Funds vary in size and cash holdings. They have different fee structures:
some funds charge loads while others do not. Some funds managers try to time the
market and trade more often, while some others tend to hold a more long-term view
and trade less. However, researchers examining the relation between fund
performance and fund properties are yet to produce conclusive findings.
A method is proposed in the present study to help domain professionals
to analyze the critical relations and take decisions in fund selection. The main focus
of this research is to analyze the risk, return parameters of the top performing
equity- small / midcap, tax planning and sector funds based on various measures, to
compare the performance of fund returns with the market returns, to analyze the
stock selecting ability and the market timing ability of the fund managers of the top
performing funds. Hence this research has been taken to fill the gap to compare
selected three schemes and three AMCs by using different statistical and ratio
analysis. Besides, there is no tool for directing investors in choosing the optimal
funds for their investment goals. Hence the proposed tool, Techno Portfolio Advisor
guides the investors in achieving their target amounts by their preferences such as
goal, return rate, inflation rate, target amount, age.
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The investment portfolio is a combination of securities owned by a given
investor. Securities are investment opportunities (investment instruments,
investment vehicles, stocks), traded easily on a transparent market which publicly
transmits enough relevant information. The purpose of using a portfolio approach is
to improve the conditions of the investment process by obtaining such properties
(values of their significant variables) of the combination of the securities, which are
not obtainable by any single security. Significant variables popularly considered are
risks and returns. A certain formation of risk and return is only possible within a
given configuration of securities. Improving risk and return conditions through
portfolio is diversification.
6.2 PHASES IN THE PROCESS OF PORTFOLIO MANAGEMENT
The process of portfolio management can be analyzed in several phases
that are arranged within a regulator cycle. Portfolio management is an information
transforming process. As such it may be analyzed in three general phases and can be
discussed further in functional sub-levels:
1. Information input – In this phase, the ingoing informational flow
is encoded in an understandable form. It includes:
Setting goals – A goal is a desired state (configuration) of the
significant variables. After the first controlling cycle, an
additional task is included in objective setting – comparing
the current state with the anticipated one. Standards for
evaluating portfolio performance may be used. Very suitable
for the task is the Sortino ratio or its modification. The ratio is
naturally objective-oriented as it compares the achieved return
to a desired return.
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Receiving, collecting, systemizing information by the process
of receiving and collecting on the behavior and the structure
of the portfolio. This sub-level closes the feedback loop of the
controlled process.
Systemizing information by the process of receiving and
collecting about the market (environment) – This sub-phase
works with information from the known, observed external
factors (market conditions and constraints, obtainable
investment opportunities), and influencing the portfolio
management process.
2. Information processing – This phase is associated with making
the best possible use of the information obtained according to the
needed function of portfolio management. It includes:
Forecasting / estimating the expected values of the significant
variables of the obtainable investment opportunities and the
external factors. Past Portfolio structure derived through
statistical analysis is also necessary.
Solution generation – This is the process of defining and
evaluating feasible states of the portfolio as combinations of
numerous or many securities. An External model to simulate
possible to the portfolio problem is necessary. It is not a
compulsory component but using an example model (‘étalon’)
is normal in investment portfolio management. It is a
computerized simulation model for experimenting and
evaluating the generated solutions. In most cases, the
computer simulation would be programmed along a known
(or new) theory (for instance Markowitz Model).
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Taking decision and selecting a portfolio structure. Only
“optimal” (best possible) solutions out of all feasible are
measured. Using multi-criteria optimization and enforcing the
principle of requisite is needed. A significant variable to be
considered is the investor’s rationality and their preferences
towards risk (and towards other significant variables).
3. Information output – This stage is associated with the
transmission (decoding). The information necessary for the
management affects the portfolio. At this phase, the controlling
actions are emitted toward the portfolio, implying there by an
awareness of the result. After evaluation between the desired
structure and the current structure of the portfolio, the differences
are translated into market orders.
Several real limitations inhibit the decision making and thus make it sub-
optimal:
Discretization, dissectability, availability of an issue of a given
security – The numerical problem becomes a whole number
optimization problem.
Delay of the system reaction, including the time for executing an
order, as well the time for meeting the conditions of the order. The
inertness of the controlled system enforces delays.
Market resistance is the aggregate consequence on the free trade
from brokerages, the inflation rate of the economy, taxes on capital
gains and/or dividends/interests, etc.
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6.3 FUZZY APPROACH TO THE PORTFOLIO PROBLEM
The decision for a portfolio structure relies on ex-ante estimation based
on ex-post data. Hence, the method is carried out under ambiguity generated by the
unknown future outcomes (Marcheva 1995). The huge complexity and abnormality
(Markowitz & Usmen 1996, p. 22) of the financial markets makes the stochastic (let
alone the deterministic) approach less and less applicable, because there is no base
for assuming any given probability distribution of the security return. Other
approaches to deal with the ambiguity of the portfolio are, therefore, being sought
by the investigating community.
A possible tool for the task is the fuzzy approach i.e. using fuzzy
numbers and fuzzy sets to describe indefinite phenomena and/or using fuzzy logic to
process data from uncertain phenomena. A comprehensive fuzzy approach for
portfolio management would be a fuzzy control process entirely made of fuzzy sub-
stages:
Fuzzy information input – fuzzification of data from the portfolio
and the environment. As for the goal setting sub-stage, the goals
originate as semantic variables anyway. So it is just a matter of
making them compatible with the rest of the process in terms of
information.
Fuzzy information processing would mostly use fuzzy logic and
fuzzy mathematics. There are already a lot of proposals of this type
to estimate the significant variables and generate solutions. Some of
them even suggest the ways of fuzzy selection and evaluation of
solutions by fuzzy functions.
Fuzzy information output would be the phase to conduct
defuzzification of the solution and to carry out management actions
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on the portfolio. Once the fuzzy approach for solving problems
under conditions of uncertainty becomes popular among
researchers, it is quite anticipated that there is already a wide range
of projected solutions for different phases and/or tasks of the
process of portfolio management. The propositions are most often
oriented towards the two more technical phases of portfolio
management.
The work involves fuzzy approach for evaluating a portfolio structure
using expertise. A significant observation that has to be made is that the term
‘expertise’ is used in a broad sense. An expert assessment may represent the
computation from a mathematical algorithm, a statement of a person with special
and extended knowledge on the subject or a combination of both. The process of
evaluation of the portfolio begins after a portfolio structure has been already set. The
second phase uses experts’ assessment or evaluations from mathematical algorithms
(called method of expertise hereafter), presented in the method of fuzzy trapezoidal
numbers.
The fuzzy trapezoidal numbers have membership function which
specifically displays a maximum range (instead of a point) of values among the
values of the estimated variable. The fuzzy numbers are then processed in a specific
method for discovering the influences of return on risk among the securities and
within the portfolio. An analysis on delayed influences is done later. The aim of the
approach is to establish a method for evaluating investment portfolios by
determining the mutual influences among different significant variables of the
portfolio (in that case, return and risk) and the unknown impacts between them. The
methodology recommended could also be used as a base for comparison and/or
ranking different portfolios. Finally, the used experts’ assessments may be
aggregated results from other approaches for portfolio management. Thus, the
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approach could be described as a universal tool to combine several methods, while
averaging out their extreme solutions.
6.4 DATABASE DEFINITIONS
A brief description of mutual fund properties is discussed in this section.
Various statistical tools are used to compare the performance of the funds.
Treynor Performance:
Jack Treynor (1965) conceived an index of portfolio performance
measure called as reward to volatility ratio, based on systematic risk defined in
equation (6.1). He assumes that the lender can remove unsystematic risk by holding
a diversified portfolio. Hence his performance measure denoted as TP is the excess
return over the risk free rate per unit of systematic risk, in other words it indicates
risk premium per unit of systematic risk.
p fP
p
r rRisk Pr emiumTSystematic Risk Index
where TP = Treynor’s Ratio, rP = portfolio return, rf = risk free return and P = Beta
coefficient for portfolio. As the market beta is 1, Treynor’s index TP for benchmark
portfolio is (rm-rf) where rm = market return. If TP of the mutual fund scheme is
greater than (rm-rf), then the scheme has outperformed the market. The major
limitation of the Treynor Index is that it can be applied to the schemes with positive
betas during the bull phase of the market. The results will mislead if applied during
bear phase of the market to the schemes with negative betas. The second limitation
is it ignores the reward for unsystematic or unique risk.
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Jensen’s Performance
Risk Standard deviation: Measure of Total Risk Financial analysts and
statisticians prefer to use a quantitative risk surrogate called the variance of returns,
denoted by
p m fR (R R )
where Rf = return on individual mutual fund unit. Rm = mean rate of return
The square root of the variance is called the standard deviation = Var (r).
The standard deviation and the variance are equally acceptable and
equivalent quantitative measures of an asset’s total risk. The variance and standard
deviation are computed from logarithmic monthly returns.
Beta: Measure of Systematic Risk
To obtain the measure of systematic risk (Beta) of the mutual fund
scheme, Market Model is applied. The mathematical form of the model has rp is the
return on the mutual fund scheme, rm is the return on the market, is the intercept,
is the slope or the beta coefficient, ep is the error term.
Higher values of indicate a high sensitivity of fund returns against
market returns; the lower value indicates low sensitivity. Higher values are desired
for the mutual funds during bull phase of the market and lower values are desired
during the bear phase to outperform the market. The error term ep is an
approximation for unique risk. There are unequal sample observations and non-
identical time periods for the selected mutual fund schemes. It is assumed that beta
is stationary during the period. The constants and are computed through
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regression analysis by regressing the monthly market return with the monthly
mutual fund return. The regression also provides the value of r2 (coefficient of
determination) that gives the strength of co-relation between the market and the fund
returns and indicates the extent of diversification.
Sharpe’s Ratio
William F.Sharpe (1966) devised an index of portfolio performance
measure, referred to as reward to variability ratio denoted by SP defined in equation
(6.3). He assumes that a small investor invests fully in the mutual fund and does not
hold any portfolio to eliminate unsystematic risk and hence demands a premium for
the total risk.
p fP
p
r rRisk Pr emiumSTotal Risk
where SP = Sharpe’s Ratio, rP = portfolio return, rf = risk free return, and
P = standard deviation of portfolio returns. The SP for benchmark portfolio is
m f
m
r r
where m = standard deviation of market returns. If SP of the mutual fund scheme is
greater than that of the market portfolio, the fund has outperformed the market.
The superiority of the Sharpe ratio over the Treynor ratio is, it considers
the point whether investors are reasonably rewarded for the total risk in comparison
to the market. A mutual fund scheme with a relatively large unique risk may
outperform the market in Treynor‘s index and may underperform the market in
Sharpe ratio. A mutual fund scheme with large Treynor ratio and low Sharpe ratio
can be concluded to have relatively larger unique risk.
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6.5 DATA ANALYSIS AN INTERPRETATION
6.5.1 IT Sector Funds
6.5.1.1 Introduction
The current status, profile, trailing returns is given in Table 6.1,
Table 6.2, and Table 6.3 respectively. Latest NAV for Franklin Infotech fund, ICICI
Prudential Technology and HDFC Capital Builder fund as of 07/06/2013 is 65.7799,
19.86 and 115.145 respectively. Net Assets for Franklin Infotech fund, ICICI
Prudential Technology and HDFC Capital Builder fund as of 31/03/2013 is 112.39,
109.49 and 467.37 respectively.
Table 6.1 Current Status & Profile of Sector Funds
Sector Funds
Current Stats &
Profile
Franklin
Infotech
ICICI Prudential
Technology Reg HDFC Capital Builder
Latest NAV 65.7799 (07/06/13) 19.86 (07/06/13) 115.145 (07/06/13)
52-Week High 73.8014 (07/03/13) 22.14 (07/03/13) 121.429 (21/01/13)
52-Week Low 56.2358 (26/07/12) 17.12 (26/07/12) 100.999 (18/06/12)
Fund Category Equity: Technology Equity: Technology Equity: Large & Mid Cap
Type Open End Open End Open End
Launch Date Aug-98 Jan-00 Jan-94
Risk Grade Not Rated Not Rated Below Average
Return Grade Not Rated Not Rated Average
Net Assets (Cr) * 112.39 (31/03/13) 109.49 (31/03/13) 467.37 (31/03/13)
Benchmark S&P BSE Infotech S&P BSE Tech CNX 500
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Table 6.2 Trailing Returns of Sector Funds
Sector Funds Returns up to 1 year are absolute and over 1 year are annualised.
Trailing Returns Franklin Infotech ICICI Prudential Technology Reg
HDFC Capital Builder
As on 07 Jun 2013 Fund Category Fund Category Fund Category Year to Date 7.29 5.24 2.58 5.24 -1.4 -3.35
1-Month 3.22 0.73 -0.85 0.73 -1.37 -2.27 3-Month -10.87 -10 -10.3 -10 -0.88 -0.55 1-Year 7.24 9.01 8.58 9.01 13.87 14.98 3-Year 6.19 4.6 10.54 4.6 5.23 4.66 5-Year 7.85 4.49 8.4 4.49 9.84 6.29
Return Since Launch 19.02 -- 5.31 -- 13.45 --
Table 6.3 Best and Worst Performance of Sector Funds
Sector Funds
Best & Worst Performance
Franklin Infotech ICICI Prudential Technology Reg HDFC Capital Builder
Best (Period) Worst (Period) Best (Period) Worst
(Period) Best (Period) Worst (Period)
Month 65.03
(03/12/1999 - 04/01/2000)
-41.14 (21/08/2001 - 21/09/2001)
29.88 (07/11/2001 - 07/12/2001)
-37.53 (09/02/2001 - 13/03/2001)
30.93 (20/03/1998 - 21/04/1998)
-33.87 (12/05/2006 - 13/06/2006)
Quarter 144.09
(22/11/1999 - 22/02/2000)
-50.83 (22/02/2000 - 23/05/2000)
74.86 (09/03/2009 - 10/06/2009)
-47.51 (28/07/2008 - 27/10/2008)
73.18 (09/03/2009 - 10/06/2009)
-39.36 (02/09/2008 - 02/12/2008)
Year 534.27
(04/01/1999 - 04/01/2000)
-73.98 (12/04/2000 - 12/04/2001)
172.63 (09/03/2009 - 11/03/2010)
-70.77 (13/03/2000 - 13/03/2001)
146.48 (24/04/2003 - 23/04/2004)
-56.79 (14/01/2008 - 13/01/2009)
6.5.1.2 Performance analysis
The higher the information ratio, the higher the active return of the
portfolio. The Table 6.4 shows the performance analysis of funds by considering
information ratio. HDFC Capital Builder has higher information ratio (0.08) than
others.
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Table 6.4 Performance Analysis - IT Sector Funds
Description
Franklin Infotech ICICI Prudential Technology Reg HDFC Capital Builder
Year(s)
2012 2011 2010 2009 2008 2007 2012 2011 2010 2009 2008 2007 2012 2011 2010 2009 2008 2007
Market Return % -2.38 -15.62 30.69 124.21 -50.17 -15.64 -2.38 -15.62 30.69 124.21 -50.17 42.01 -2.38 -15.62 30.69 124.21 -50.17 -15.64
Annual Return % -0.94 -15.37 32.63 128.74 -49.65 -15.78 16.63 -18.97 43.35 119.97 -63.97 9.77 28.40 -23.77 27.85 89.67 -55.18 67.57
Correlation 0.09 0.11 0.11 -0.03 0.16 -0.01 -0.04 0.85 0.13 0.52 0.26 -0.01 -0.04 0.62 0.11 0.32 0.57 0.46
Risk 2.67 3.35 2.77 4.61 5.91 3.68 2.44 2.98 2.80 4.12 4.39 3.03 1.87 2.22 1.83 3.83 4.63 3.01
R Square 0.01 0.01 0.01 0.00 0.03 0.01 0.00 0.72 0.02 0.27 0.07 0.00 0.00 0.38 0.01 0.10 0.33 0.21
Information Ratio -0.03 -0.06 0.07 0.16 -0.11 -0.06 0.03 -0.09 0.10 0.18 -0.21 0.01 0.08 -0.14 0.08 0.15 -0.16 0.15
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6.5.1.3 Performance Analysis on Beta Measures
From Table 6.5, all the IT sector funds are having beta less than one
during the last one year, which shows they are less risky compared to their
benchmark index during this period. Out of this three funds, Franklin Infotech
Scheme comes out to be the most aggressive with having beta of 0.08 and ICICI and
HDFC funds is the least aggressive (beta of -0.03).
Table 6.5 Performance Analysis Based On Beta Measures - IT Sector Funds
Name of the Fund Year(s)
2012 2011 2010 2009 2008 2007 2006 2005 2004 2003 2002 2001 2000 Franklin Infotech 0.08 0.10 0.10 -0.03 0.14 -0.01 0.03 0.50 0.92 0.04 0.00 0.06 0.10
ICICI Prudential Technology Reg -0.03 0.69 0.12 0.37 0.18 -0.01 0.24 0.43 0.24 0.12 0.29 -0.04 -0.01
HDFC Capital Builder -0.03 0.39 0.07 0.22 0.41 0.32 0.16 0.26 0.21 0.18 0.02 0.12 0.10
6.5.1.4 Performance Analysis on Sharp Ratio
From Table 6.6, it measures the risk premium of the portfolio relative to
the total amount of risk in the portfolio. This risk premium is the difference between
the portfolios average rate of return and the riskless rate of return. This index assigns
the highest value to assets that have best risk – adjusted average rate of return. The
larger the Sp, better the fund has performed. HDFC Capital Builder scheme has a
higher Sharpe’s ratio (0.08) & expected to perform well among the others Franklin
and ICICI.
Table 6.6 Performance Analysis Based On Sharp Ratio - It Sector Funds
Name of the Fund Year(s)
2012 2011 2010 2009 2008 2007 2006 2005 2004 2003 2002 2001 2000
Franklin Infotech -0.03 -0.06 0.07 0.16 -0.11 -0.06 -0.04 0.09 -0.05 0.05 0.01 -0.05 -0.11
ICICI Prudential Technology Reg
0.03 -0.09 0.10 0.18 -0.21 0.01 0.08 0.11 0.02 0.09 0.02 -0.06 -0.09
HDFC Capital Builder
0.08 -0.14 0.08 0.15 -0.16 0.15 0.03 0.12 0.08 0.27 0.02 -0.13 -0.09
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6.5.1.5 Performance Analysis on Treynor Ratio
From Table 6.7, as Treynor Ratio represents mutual fund's excess return
to its standard deviation high Treynor ratio indicates more attractive fund. HDFC
Capital Builder schemes have a higher Treynor s ratio & expected to perform well
among the other schemes.
Table 6.7 Performance Analysis Based On Treynor Ratio - IT Sector Funds
Name of the Fund Year(s)
2012 2011 2010 2009 2008 2007 2006 2005 2004 2003 2002 2001 2000
Franklin Infotech 0.00 -0.06 0.11 0.34 -0.25 -0.02 -0.25 0.15 -0.29 0.15 0.60 -0.13 -0.46
ICICI Prudential Technology Reg
0.07 -0.08 0.15 0.34 -0.40 0.07 0.18 0.17 0.06 0.21 0.08 -0.14 -0.21
HDFC Capital Builder
0.11 -0.11 0.10 0.28 -0.31 0.22 0.09 0.16 0.16 0.32 0.06 -0.10 -0.09
6.5.1.6 Performance Analysis on Jenson Alpha
From Table 6.8, the entire ratio in the compared schemes is negative and
few have positive alpha. Franklin Infotech has the lowest negative Alpha value of -
0.02 implies that the fund return has underperformed the benchmark index by -
0.02% over the last one year. ICICI and HDFC Capital Builder has the positive
Alpha value of 0.04 and 0.08 respectively which implies that the fund return has
over performed the benchmark index by 0.04% and 0.08% respectively over the last
one year. If the value is positive, then the portfolio is earning excess returns.
Table 6.8 Performance Analysis Based On Jenson Alpha - IT Sector Funds
Name of the Fund Year(s)
2012 2011 2010 2009 2008 2007 2006 2005 2004 2003 2002 2001 2000
Franklin Infotech -0.02 -0.09 0.10 0.30 -0.31 -0.08 -0.27 0.18 -0.61 0.13 0.03 -0.16 -0.50
ICICI Prudential
Technology Reg
0.04 -0.16 0.13 0.44 -0.48 0.02 0.19 0.20 0.05 0.20 0.06 -0.17 -0.27
HDFC Capital
Builder
0.08 -0.16 0.08 0.32 -0.44 0.17 0.09 0.16 0.15 0.31 0.05 -0.14 -0.12
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6.5.2 Small & Mid Cap Funds
6.5.2.1 Introduction
The current status, profile, trailing returns of Small & Mid-cap funds are
given in Table 6.9, Table 6.10, and Table 6.11 respectively. Latest NAV for
Franklin India Prima, ICICI Prudential Mid Cap and HDFC Mid Cap Opportunities
fund as of 07/06/2013 is 320.8645, 30.49 and 17.884 respectively. Net Assets
Franklin India Prima, ICICI Prudential Mid Cap and HDFC Mid Cap Opportunities
fund as of 31/03/2013 is 786.10, 223.04 and 2734.14 respectively.
Table 6.9 Current Status & Profile
Small & Mid Cap Funds
Current Stats &
Profile
Franklin India
Prima-G
ICICI Pru
Midcap Reg-G
HDFC Mid-Cap
Opportunities- G
Latest NAV 320.8645 (07/06/13) 30.49 (07/06/13) 17.884 (07/06/13)
52-Week High 336.0005 (07/01/13) 35.04 (07/01/13) 19.047 (15/01/13)
52-Week Low 255.0176 (14/06/12) 28.78 (18/06/12) 15.45 (18/06/12)
Fund Category Equity: Mid &
Small Cap
Equity: Mid &
Small Cap
Equity: Mid & Small Cap
Type Open End Open End Open End
Launch Date Nov-93 Oct-04 Jun-07
Risk Grade Below Average Above Average Below Average
Return Grade Above Average Below Average Above Average
Net Assets (Cr) * 786.10 (31/03/13) 223.04 (31/03/13) 2,734.14 (31/03/13)
Benchmark CNX 500 CNX Midcap CNX Midcap
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Table 6.10 Trailing Returns
Small & Mid Cap Funds Returns up to 1 year are absolute and over 1 year are annualised.
Trailing Returns Franklin India Prima-G
ICICI Pru Midcap Reg-G
HDFC Mid-Cap Opportunities- G
As on 07 Jun 2013 Fund Category Fund Category Fund Category Year to Date -2.92 -7.7 -9.63 -7.7 -4.04 -7.7
1-Month 0.69 -1.42 -3.57 -1.42 -0.26 -1.42 3-Month 2.36 -0.66 -5.22 -0.66 0.77 -0.66 1-Year 24.6 13.46 4.1 13.46 14.87 13.46 3-Year 8.37 4.35 -2.05 4.35 9.82 4.35 5-Year 10.7 7.45 1.07 7.45 13.89 7.45
Return Since Launch 19.44 -- 13.82 -- 10.25 --
Table 6.11 Best and Worst Performance
Small & Mid Cap Funds
Best & Worst Performance
Franklin India Prima-G ICICI Pru Midcap Reg-G HDFC Mid-Cap Opportunities- G
Best (Period) Worst (Period)
Best (Period) Worst (Period)
Best (Period) Worst (Period)
Month 41.70 (06/05/2009 - 05/06/2009)
-34.00 (26/09/2008
- 27/10/2008)
39.46 (06/05/2009 - 05/06/2009)
-40.73 (26/09/2008 - 27/10/2008)
31.48 (06/05/2009 - 05/06/2009)
-30.38 (26/09/2008
- 27/10/2008)
Quarter 90.91 (06/03/2009 - 05/06/2009)
-49.86 (22/02/2000
- 23/05/2000)
87.64 (09/03/2009 - 10/06/2009)
-50.92 (02/09/2008 - 02/12/2008)
71.73 (09/03/2009 - 10/06/2009)
-38.68 (02/09/2008
- 02/12/2008)
Year 217.85 (01/01/1999 - 03/01/2000)
-63.83 (14/01/2008
- 13/01/2009)
165.52 (09/03/2009 - 11/03/2010)
-69.62 (14/01/2008 - 13/01/2009)
142.61 (09/03/2009 - 11/03/2010)
-54.01 (14/01/2008
- 13/01/2009)
6.5.2.2 Performance analysis
Table 6.12 shows, Small & Mid Cap Funds, Franklin India Prima-G has
higher information ratio (0.15) than ICICI and HDFC.
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Table 6.12 Performance Analysis - Small & Mid Cap Funds
Description
Franklin India Prima-G ICICI Pru Midcap Reg-G HDFC Mid-Cap Opportunities- G
Year(s)
2012 2011 2010 2009 2008 2007 2012 2011 2010 2009 2008 2007 2012 2011 2010 2009 2008 2007
Market Return % 31.67 -27.57 13.13 83.34 -57.36 61.14 31.67 -27.57 13.13 83.34 -57.36 61.14 31.67 -27.57 13.13 83.34 -57.36 61.14
Annual Return % 44.70 -22.74 19.11 102.99 -62.72 47.65 40.76 -32.81 17.86 96.51 -68.39 59.42 39.98 -18.69 31.36 91.04 -51.74 29.90
Correlation 0.15 0.20 -0.01 0.04 0.19 -0.07 0.11 0.74 0.18 0.66 0.45 0.79 0.07 0.76 0.20 0.60 0.85 -0.07
Risk 1.74 2.03 2.26 4.64 4.65 2.83 2.06 2.03 2.00 4.23 5.04 3.23 1.91 2.05 2.05 3.77 4.22 1.90
R Square 0.02 0.04 0.00 0.00 0.04 0.00 0.01 0.55 0.03 0.43 0.20 0.62 0.00 0.58 0.04 0.36 0.72 0.00
Information Ratio 0.15 -0.13 0.03 0.14 -0.21 0.08 0.12 -0.20 0.04 0.15 -0.20 0.12 0.13 -0.13 0.09 0.16 -0.16 0.09
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6.5.2.3 Performance analysis on beta measures
From Table 6.13, all the SMALL & MID CAP FUNDS are having beta
less than one during the last one year, which shows they are less risky compared to
their benchmark index during this period. Out of this three funds, Franklin India
Prima-G Scheme comes out to be the most aggressive with having beta of 0.08 and
ICICI Pru Midcap Reg-G (beta of 0.10) and HDFC Mid-Cap Opportunities- G
funds is the least aggressive (beta of 0.06).
Table 6.13 Performance Analysis Based On Beta Measures - Small & Mid Cap Funds
Name of the Fund Year(s)
2012 2011 2010 2009 2008 2007
Franklin India Prima-G 0.11 0.15 -0.01 0.04 0.15 -0.05
ICICI Pru Midcap Reg-G 0.10 0.58 0.16 0.55 0.40 0.69
HDFC Mid-Cap Opportunities- G 0.06 0.58 0.18 0.45 0.61 -0.04
6.5.2.4 Performance analysis on sharp ratio
From Table 6.14, it measures the risk premium of the portfolio relative to
the total amount of risk in the portfolio. This risk premium is the difference between
the portfolios average rate of return and the riskless rate of return. This index assigns
the highest value to assets that have best risk – adjusted average rate of return. The
larger the Sp, better the fund has performed. Franklin India Prima-G scheme has a
higher Sharpe’s ratio (0.15) & expected to perform well among the others and ICICI
Pru Midcap Reg-G and HDFC Mid-Cap Opportunities- G.
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Table 6.14 Performance Analysis Based On Sharp Ratio - Small & Mid Cap Funds
Name of the Fund Year(s)
2012 2011 2010 2009 2008 2007
Franklin India Prima-G 0.15 -0.13 0.03 0.14 -0.21 0.08
ICICI Pru Midcap Reg-G 0.12 -0.20 0.04 0.15 -0.20 0.12
HDFC Mid-Cap Opportunities- G 0.13 -0.13 0.09 0.16 -0.16 0.09
6.5.2.5 Performance analysis on treynor ratio
From Table 6.15, as Treynor Ratio represents mutual fund's excess return
to its standard deviation high Treynor ratio indicates more attractive fund. All the
three funds have a same Treynor‘s ratio & expected to perform well.
Table 6.15 Performance Analysis Based On Treynor Ratio - Small & Mid Cap Funds
Name of the Fund Year(s)
2012 2011 2010 2009 2008 2007
Franklin India Prima-G 0.14 -0.10 0.09 0.28 -0.35 0.16
ICICI Pru Midcap Reg-G 0.14 -0.16 0.07 0.30 -0.45 0.20
HDFC Mid-Cap Opportunities- G 0.14 -0.08 0.11 0.28 -0.28 0.23
6.5.2.6 Performance analysis on jenson alpha
From Table 6.16, Franklin and ICICI has the positive Alpha value of
0.13 and 0.13 respectively which implies that the fund return has over performed the
benchmark index by 0.13% and 0.13% respectively over the last one year. If the
value is positive, then the portfolio is earning excess returns.
200
Table 6.16 Performance Analysis Based On Jenson Alpha - Small & Mid Cap Funds
Name of the Fund Year(s)
2012 2011 2010 2009 2008 2007 Franklin India Prima-G 0.13 -0.14 0.05 0.27 -0.43 0.12
ICICI Pru Midcap Reg-G 0.13 -0.27 0.05 0.41 -0.61 0.29 HDFC Mid-Cap Opportunities- G 0.12 -0.19 0.09 0.37 -0.51 0.19
6.5.3 Tax Planning Funds
6.5.3.1 Introduction
The current status, profile, trailing returns, of Tax planning funds are
given in Table 6.17, Table 6.18, Table 6.19 respectively. Latest NAV for Franklin
India Tax Shield and HDFC Tax Saver fund as of 07/06/2013 is 320.8645 and 30.49
respectively. Net Assets Franklin India Tax Shield and HDFC Tax Saver fund as of
31/03/2013 is 786.10 and 223.04 respectively.
Table 6.17 Current Status & Profile
Tax Planning Funds
Current Stats & Profile Franklin India Taxshield-G HDFC Tax Saver-G
Latest NAV 320.8645 (07/06/13) 30.49 (07/06/13)
52-Week High 336.0005 (07/01/13) 35.04 (07/01/13)
52-Week Low 255.0176 (14/06/12) 28.78 (18/06/12)
Fund Category Equity: Mid & Small Cap Equity: Mid & Small Cap
Type Open End Open End
Launch Date Nov-93 Oct-04
Risk Grade Below Average Above Average
Return Grade Above Average Below Average
Net Assets (Cr) * 786.10 (31/03/13) 223.04 (31/03/13)
Benchmark CNX 500 CNX Midcap
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Table 6.18 Trailing Returns
Tax Planning Funds
Returns up to 1 year are absolute and over 1 year are annualised.
Trailing Returns Franklin India Taxshield-G HDFC Tax Saver-G
As on 07 Jun 2013 Fund Category Fund Category
Year to Date -2.27 -3.29 -6.02 -3.29
1-Month -0.73 -1.86 -1.68 -1.86
3-Month -0.17 0.11 -2.66 0.11
1-Year 16.22 14.89 9.55 14.89
3-Year 9.13 4.54 3.29 4.54
5-Year 10.15 5.45 9.77 5.45
Return Since Launch 24.99 -- 28.57 --
Table 6.19 Best and Worst Performance
Tax Planning Funds
Best & Worst
Performance
Franklin India Taxshield-G HDFC Tax Saver-G
Best (Period) Worst (Period) Best (Period) Worst (Period)
Month 57.81 (03/12/1999 - 04/01/2000)
-29.18 (24/09/2008 - 24/10/2008)
34.19 (15/12/1999 - 14/01/2000)
-32.30 (26/09/2008 - 27/10/2008)
Quarter 137.13 (22/11/1999 - 22/02/2000)
-34.66 (02/09/2008 - 03/12/2008)
78.93 (09/03/2009 - 10/06/2009)
-39.75 (02/09/2008 - 02/12/2008)
Year 214.23 (10/05/1999 - 09/05/2000)
-51.50 (14/01/2008 - 13/01/2009)
272.59 (24/02/1999 - 24/02/2000)
-55.57 (03/12/2007 - 02/12/2008)
6.5.3.2 Performance analysis
Table 6.20 shows, that among the following Tax planning funds;
Franklin is performing well than HDFC tax saver.
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Table 6.20 Performance Analysis -Tax Planning Funds
Description
Franklin India Taxshield-G HDFC Tax Saver-G
Year(s)
2012 2011 2010 2009 2008 2007 2012 2011 2010 2009 2008 2007
Market Return % 31.67 -27.57 13.13 83.34 -57.36 61.14 31.67 -27.57 13.13 83.34 -57.36 61.14
Annual Return % 29.60 -15.68 23.47 75.19 -49.30 56.02 26.67 -22.75 25.73 96.10 -51.88 37.65
Correlation 0.13 0.19 -0.02 0.02 0.16 -0.09 0.05 0.80 0.17 0.65 0.84 0.84
Risk 1.78 2.21 2.00 4.34 5.10 3.39 1.92 2.06 1.91 4.10 4.86 3.25
R Square 0.02 0.04 0.00 0.00 0.02 0.01 0.00 0.64 0.03 0.42 0.70 0.71
Information Ratio 0.08 -0.09 0.05 0.11 -0.13 0.11 0.08 -0.15 0.07 0.15 -0.14 0.07
203
6.5.3.3 Performance analysis on beta measures
From Table 6.21, The Franklin India Taxshield-G fund is having beta
less than one during the last one year, which shows they are less risky compared to
their benchmark index during this period. Out of these two funds, HDFC funds are
the least aggressive (beta of 0.04).
Table 6.21 Performance Analysis Based On Beta Measures - Tax Planning
Name of the Fund
Year(s)
2012 2011 2010 2009 2008 2007 2006 2005 2004 2003 2002 2001 2000
Franklin India Taxshield-G
0.10 0.15 -0.02 0.02 0.13 -0.08 0.17 0.50 0.22 -0.52 0.03 0.30 -0.12
HDFC TaxSaver-G
0.04 0.61 0.14 0.53 0.68 0.75 0.17 0.43 0.14 0.11 0.13 0.62 0.55
6.5.3.4 Performance analysis on sharp ratio
From Table 6.22, it measures the risk premium of the portfolio relative to
the total amount of risk in the portfolio. This risk premium is the difference between
the portfolios average rate of return and the riskless rate of return. This index assigns
the highest value to assets that have best risk – adjusted average rate of return. The
larger the Sp, better the fund has performed. Both funds have same sharp ratio and
expected to perform.
Table 6.22 Performance Analysis Based On Sharp Ratio - Tax Planning
Name of the Fund
Year(s)
2012 2011 2010 2009 2008 2007 2006 2005 2004 2003 2002 2001 2000
Franklin India Taxshield-G 0.08 -0.09 0.05 0.11 -0.13 0.11 0.04 0.12 0.06 0.09 0.02 -0.05 0.08
HDFC TaxSaver-G 0.08 -0.15 0.07 0.15 -0.14 0.07 0.05 0.18 0.09 0.25 0.02 -0.02 -0.06
204
6.5.3.5 Performance analysis on treynor ratio
From Table 6.23, as Treynor Ratio represents mutual fund's excess return
to its standard deviation high Treynor ratio indicates more attractive fund. Franklin
India Taxshield-G scheme have a higher Treynor‘s ratio & expected to perform well
among the other schemes.
Table 6.23 Performance Analysis Based On Treynor Ratio - Tax Planning
Name of the Fund Year(s)
2012 2011 2010 2009 2008 2007 2006 2005 2004 2003 2002 2001 2000
Franklin India Taxshield-G 0.10 -0.06 0.09 0.22 -0.24 0.18 0.10 0.16 0.11 1.02 0.05 -0.04 1.63
HDFC TaxSaver-G 0.09 -0.10 0.09 0.29 -0.27 0.14 0.13 0.23 0.16 0.32 0.06 -0.01 -0.19
6.5.3.6 Performance analysis on jenson alpha
From Table 6.24, Franklin and HDFC has the positive Alpha value of
0.09 and 0.08 respectively which implies that the fund return has over performed the
benchmark index by 0.09% and 0.08% respectively over the last one year. If the
value is positive, then the portfolio is earning excess returns.
Table 6.24 Performance Analysis Based on Jensen’s Alpha - Tax Planning
Name of the Fund
Year(s)
2012 2011 2010 2009 2008 2007 2006 2005 2004 2003 2002 2001 2000
Franklin India Taxshield-G 0.09 -0.11 0.06 0.21 -0.30 0.14 0.09 0.18 0.10 0.86 0.03 -0.10 1.62
HDFC TaxSaver-G
0.08 -0.22 0.07 0.40 -0.53 0.25 0.13 0.24 0.14 0.32 0.04 -0.09 -0.29
205
The relation between mutual fund performance and fund characteristics
is of much interest to financial market practitioners and investors. However, there is
a lack of conclusive knowledge on this issue. This study introduces a method which
examines the relation between fund returns and fund asset size, cash holding, loads,
expense ratios, and turnover. The method can help economists better understand
massive data distribution. It can supplement traditional statistical analysis and assist
in re-designing improved statistical computation, therefore, provides a solid support
for decision making in mutual fund investment. The study also creates awareness
among the investor community in choosing the best mutual fund scheme.
6.6 SYSTEM ARCHITECTURE OF TECHNO-PORTFOLIO ADVISOR
Fuzzy Logic is an analytical tool used in the modeling of those
phenomena that was not in scope of general sciences. In the technology world,
investors have quick access to important details relevant to the decision process.
Techno-Portfolio gives the ability for investors based on the guidelines and formulas
that serve as foundations to the Fuzzy Logic approach. The Techno-portfolio advisor
fuzzy inference System is as shown in Figure 6.2.
Figure 6.2 Fuzzy Inference System-Techno-Portfolio Advisor
206
The rules to be used for investment decision-making can take into
account the following variables: age, return rate, goal. For illustration variable “age”
hold the set of ranges: “more than 60 (in years)”, “40 to 60 (in years) and “less than
40 (in years)”, the variable “return rate” holds the following ranges: “ 4 to 6 (in
percentage)”, “6 to 8 (in percentage)”, “8 to 10 (in percentage)”, “10 to 15 (in
percentage”, 15 to 20 (in percentage)”. The following set of states: “Child Future /
Wealth / Health / Retirement” has been mapped to the variable “goal”. Fuzzy
Inference Rules of Techno-Portfolio Advisor inherit the above terms such as:
Rule 1 : If age is between 18-40 and goal is Child Future and return rate is
between 4-10 then portfolio style (Ultra Conservative) is More
Equity and Less Debt
Rule 2 : If age is between 18-40 and goal is Wealth and return rate is between
4-10 then portfolio style (Conservative) is More Equity and Less
Debt
Rule 3 : If age is between 18-40 and goal is Health and return rate is between
4-10 then portfolio style (Moderate) is More Equity and Less Debt
Rule 4 : If age is between 40-60 and goal is Child Future and return rate is
between 10-15 then portfolio style(Aggressive) is Equal Equity and
Equal Debt
Rule 5 : If age is between more than 60 and goal is Retirement and return rate
is between 4-10 then portfolio style(Highly Aggressive) is Less
Equity and More Debt
Rule 6 : If ratioChecker(treynor) is Positive then fundstatus = 1
207
Rule 7 : If ratioChecker(sharp) is Positive then fundstatus = 1
Rule 8 : If ratioChecker(Beta) is Positive then fundstatus = 1
Rule 9 : If ratioChecker(Jensonalpha) is Positive then fundstatus = 1
Functional block diagram of Techno-Portfolio Advisor is shown in
Figure 6.3.
6.7 IMPLEMENTATION AND FUNCTIONALITY
6.7.1 Data Preparation
Step 1 : Data Cleansing
6.7.2 Data Fixing Process
This function consists of loading the data from excel files that was
captured from AMFI and other related sites into a master record containing all the
companies portfolio details and deleting any transaction that contain missing data or
incomplete data.
Step 2 : Computation
A group of activities consisting of the functions such as active stock
selection, computation of Jensen Alpha, Beta, Treynor and Sharp ratios are
calculated.
208
Figure 6.3 Functional block diagram of Techno-Portfolio Advisor
6.7.3 Integrated Development Environment (IDE) Interface
The IDE of Techno-Portfolio Advisor allows the investor to enter the
preferences that are necessary to investment options and where by what-if analysis
or sensitivity analysis becomes possible. The IDE interface is shown in Figure 6.4.
209
Figure 6.4 IDE interface- Techno-Portfolio Advisor
The Techno-Portfolio Advisor was implemented in Java. For data
management, MYSQL was used. The portfolio selection is done using MATLAB. It
has been tested on Windows Platform with Intel Core 2 CPU and 80GB memory.
The system receives the investor preferences as parameters for computing the
optimal investment options using MATLAB from the trained database as shown in
the following figure(s): Figure 6.5, Figure 6.6, Figure 6.7, Figure 6.8, Figure 6.9 and
Figure 6.10.
Figure 6.5 Fuzzy mamdani inference engine
210
Figure 6.6 Gaussian function for membership variable return rate
Figure 6.7 Gaussian function for membership variable portfolio style
211
Figure 6.8 Fuzzy inference rule editor
Figure 6.9 Inference rule viewer
212
Figure 6.10 Surface viewer
The System outputs the investment options and is stored in a unique
record. If investor enters invalid input then the system re-invoked with different new
investor parameters values and the system process would be executed again.
6.8 ANALYSIS AND RESULTS
Five Test cases were create and executed with various investor
parameters as shown in Figure. 6.11, Figure. 6.12 and Figure 6.13. The sample input
screen is as in Figure 6.11. The output for the above investor preferences is shown in
Figure 6.12 by the Techno-Portfolio advisor. Basing on the age, return rate, inflation
rate and investment amount, the portfolio style is chosen by the inference engine as
Aggressive.
213
Figure 6.11 IDE interface-Techno-Portfolio Advisor-input
Figure 6.12 Test case 1: Techno-Portfolio Advisor-output
214
Figure 6.13 Test case 2: Techno-Portfolio Advisor-output
Hence the asset allocation is 50% debut and 50% equity. Further based
on the quantitative data such as Treynor, sharp, beta and Jensen ratios, the optimal
funds for the investor are chosen by the system.
The investor has to pay 15481 monthly for 5 years or pay 177904
annually. The optimal funds are HDFC Capital Builder, Franklin India Prima-G and
Franklin India Taxshield-G funds as in Figure 6.12.
6.9 CONCLUSION
The relation between mutual fund performance and fund characteristics
is of much interest to financial market practitioners and investors. However, there is
a lack of conclusive knowledge on this issue. This study introduces a method which
examines the relation between fund returns and fund asset size, loads, expense ratios
and turnover. The study focuses developing Techno-Portfolio Advisor which
provides investment options and optimal funds for achieving their objectives.
215
Performance analysis of various mutual funds is calculated using Treynor
ratio, Jenson’s alpha, Sharpe and beta ratios. The Techno Portfolio advisor predict
the investment decision of investors across mutual fund companies using Fuzzy
Logic considering the parameters such as investor age, return rate and goal. The
system is developed based on the fuzzy inference rule. The System fulfills the
investor’s objectives and preferences in terms rate of return, risk and asset allocation
and diversification in order to reach an optimum solution. Therefore, Techno-
Portfolio Advisor provides a solid support for decision making in mutual fund
investment. The study also creates awareness among the investor community in
choosing the best mutual fund scheme.