chapter 6 prediction of investor’s investment...

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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


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


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


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


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


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


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)



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)


Table 6.12 shows, Small & Mid Cap Funds, Franklin India Prima-G has

higher information ratio (0.15) than ICICI and HDFC.

197

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

198

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


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





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.

199

Table 6.14 Performance Analysis Based On Sharp Ratio - Small & Mid Cap Funds


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


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


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


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


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

201

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)


Table 6.20 shows, that among the following Tax planning funds;

Franklin is performing well than HDFC tax saver.

202

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





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


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


2012 2011 2010 2009 2008 2007 2006 2005 2004 2003 2002 2001 2000


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


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.

chapter 6 prediction of investor’s investment...

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