Multi-criteria Decision Making for Evaluating Mutual Funds Investment Strategies

Abstract

Investors often need to evaluate the investment strategies in terms of numerical values based upon various criteria when making investment. This situation can be regarded as a multiple criteria decision-making (MCDM) problem. This approach is oftentimes the basic assumption in applying hierarchical system for evaluating the strategies of selecting the investment style. We employ the criteria measurements to evaluate investment style. To achieve this objective, first, we employ factor analysis to extract independent common factors from those criteria. Second, we construct the evaluation frame using hierarchical system composed of the above common factors with evaluation criteria and then derive the relative weights with respect to the considered criteria. Third, the synthetic utility value corresponding to each investment style is aggregated by the weights with performance values. Finally, we compare with empirical data and find that the model of MCDM predicts the rate of return.

Appendices

Appendix 1

68.1.1 The Description of Evaluative Criteria of Mutual Funds

Criteria	Description
Market timing	The ability of portfolio managers to time market cycles and take advantage of this ability in trading securities
The ratio of fund market share	The ratio of fund invested in securities
The return of market	The fraction of ups or downs of deep bid index in current period divided by the deep bid index in last period
Riskless interest rate	The risk-free interest rate is the interest rate that it is assumed can be obtained by investing in financial instruments with no default risk. In practice most professionals and academics use short-dated government bonds of the currency in question. For Taiwan investments, usually Taiwan bank 1-month deposit rate is used
Flowing of cash	Cash flow refers to the amounts of cash being received and spent by a business during a defined period of time, sometimes tied to a specific project. Measurement of cash flow can be used to evaluate the state or performance of a business or project
Stock selection ability	The ability of fund managers to identify the potential winning securities
P/E ratio	The P/E ratio (price per share/earnings per share) of a mutual fund is used to measure how cheap or expensive its share price is. The lower the P/E, the less you have to pay for the mutual fund, relative to what you can expect to earn from it
Net value/market value	The value of an entity’s assets less the value of its liabilities divided by market value
Cash flowing/market value	It equals cash receipts minus cash payments over a given period of time divided by market value or equivalently, net profit plus amounts charged off for depreciation, depletion, and amortization (business) divided by market value
Net value	Net value is a term used to describe the value of an entity’s assets less the value of its liabilities. The term is commonly used in relation to collective investment schemes
Risk premium	A risk premium is the minimum difference between the expected value of an uncertain bet that a person is willing to take and the certain value that he is indifferent to
Fund size	The volume and scale of mutual funds
The market share of mutual fund	It can be expressed as a company’s sales revenue (from that market) divided by the total sales revenue available in that market. It can also be expressed as a company’s unit sales volume (in a market) divided by the total volume of units sold in that market
The growth rate of mutual fund scale	The fraction of the increase or decrease of the fund scale in current period divided by the fund scale in last period
Dividend yield of mutual fund	The dividend yield on a company mutual fund is the company’s annual dividend payments divided by its market cap or the dividend per share divided by the price per share
Teamwork	The culture of mutual fund company
Number of researcher	The number of researcher of each fund
Education of fund manager	Fund manager’s seniority, quality, and performance
Known of fund manager	Fund manager’s rate of exposed in the medium and number of win a prize
Turnover rate of fund manager	Fund manager leaves his job temporarily

Appendix 2

68.2.1 Summary Statistics for Returns of the Mutual Funds

The notations and definition of the investment style of mutual funds are in panel 2.1.

Panel 2.1

Classifications	Investment style	Description
Aa	Asset allocation	A large part of financial planning is finding an asset allocation that is appropriate for a given person in terms of their appetite for and ability to shoulder risk. The designation of funds into various categories of assets
Ag	Aggressive growth	Regardless of the investment style or the size of the companies purchased, funds vary widely in their risk and price behavior which is likely to have a high beta and high volatility
Ei	Equity income	It will invest in common stock but will have a portfolio beta closer to 1.0 than to 2.0. It likely favors stocks with comparatively high dividend yields so as to generate the income its name implied
G	Growth	The pursuit of capital appreciation is the emphasis with growth funds. This class of funds includes those called aggressive growth funds and those concentrating on more stable and predictable growth
Gi	Growth income	It pays steady dividends, and it is still predominately an investment in stocks, although some bonds may be included to increase the income yield of the fund

Monthly mutual funds are from January 1980 to September 1996 for a sample of 65 US mutual funds. The data are from Morningstar Company.

Panel 2.2

Fund name	Investment style	Mean	Standard deviation	Maximum	Minimum
General Securities	Aa	0.477	5.084	15.389	−17.151
Franklin Asset Allocation	Aa	0.407	3.743	10.424	−19.506
Seligman Income A	Aa	0.394	2.414	8.474	−7.324
USAA Income	Aa	0.316	2.024	9.381	−5.362
Valley Forge	Aa	0.293	1.803	9.980	−5.573
Income Fund of America	Aa	0.566	2.552	9.166	−8.836
FBL Growth Common Stock	Aa	0.273	3.599	10.466	−24.088
Mathers	Aa	0.220	3.910	14.405	−14.750
Asset allocation average	Aa	0.391	2.550	8.962	−9.464
American Heritage	Ag	−0.905	6.446	28.976	−33.101
Alliance Quasar A	Ag	0.644	6.547	15.747	−39.250
Keystone Small Co Grth (S-4)	Ag	0.433	7.053	19.250	−38.516
Keystone Omega A	Ag	0.473	6.112	18.873	−33.240
Invesco Dynamics	Ag	0.510	6.009	17.378	−37.496
Security Ultra A	Ag	0.222	6.940	16.297	−43.468
Putnam Voyager A	Ag	0.808	5.781	17.179	−29.425
Stein Roe Capital Opport	Ag	0.578	6.783	17.263	−32.135
Value Line Spec Situations	Ag	0.145	6.240	13.532	−37.496
Value Line Leveraged Gr Inv	Ag	0.601	4.970	14.617	−29.025
WPG Tudor	Ag	0.726	6.010	14.749	−33.658
Winthrop Aggressive Growth A	Ag	0.476	5.596	17.012	−34.921
Delaware Trend A	Ag	0.787	6.536	14.571	−42.397
Founders Special	Ag	0.564	5.900	12.905	−31.861
Aggressive growth average	Ag	0.459	5.814	13.142	−35.335
Smith Barney Equity Income A	Ei	0.601	3.270	7.813	−18.782
Van Kampen Am Cap Eqty-Inc A	Ei	0.510	3.530	12.292	−22.579
Value Line Income	Ei	0.423	3.357	9.311	−18.242
United Income A	Ei	0.714	4.037	11.852	−13.743
Oppenheimer Equity Income A	Ei	0.555	3.422	10.071	−16.524
Fidelity Equity Income	Ei	0.706	3.612	10.608	−19.627
Delaware Decatur Income A	Ei	0.547	3.615	10.269	−20.235
Invesco Industrial Income	Ei	0.601	3.705	9.349	−20.235
Old Dominion Investors	Ei	0.360	3.699	11.498	−21.092
Evergreen Total Return Y	Ei	0.508	3.220	8.074	−13.857
Equity income average	Ei	0.527	3.238	9.094	−18.718
Guardian Park Avenue A	G	0.740	4.391	11.321	−27.965
Founders Growth	G	0.718	4.986	13.055	−25.108
Fortis Growth A	G	0.724	5.983	14.520	−30.771
Franklin Growth I	G	0.570	4.050	12.907	−11.706
Fortis Capital A	G	0.682	4.791	12.818	−21.585
Growth Fund of America	G	0.625	4.722	12.226	−23.962
Hancock Growth A	G	0.484	5.381	15.708	−25.236
Franklin Equity I	G	0.469	5.156	12.818	−32.135
Nationwide growth	G	0.598	4.370	11.444	−27.570
Neuberger&Berman Focus	G	0.434	4.366	12.187	−25.108
MSB	G	0.517	4.665	13.452	−31.178
Neuberger&Berman Partners	G	0.661	3.612	9.311	−19.385
Neuberger&Berman	G	0.606	5.095	11.574	−30.500
Manhattan	G	0.710	4.067	10.125	−19.385
Nicholas	G	0.225	5.234	11.321	−31.451
Oppenheimer A	G	0.727	5.802	19.120	−37.207
New England growth A	G	0.608	4.505	11.121	−26.081
Growth average	G	0.594	4.775	12.649	−26.255
Pioneer II A	Gi	0.517	4.386	10.912	−29.693
Pilgrim America Magna Cap A	Gi	0.611	3.949	10.843	−22.704
Pioneer	Gi	0.410	4.339	12.293	−28.361
Philadelphia	Gi	0.244	4.004	11.074	−23.457
Penn Square Mutual A	Gi	0.504	3.907	11.852	−20.724
Oppenheimer Total Return A	Gi	0.507	4.451	13.861	−22.829
Vanguard/Windsor	Gi	0.726	4.078	10.746	−18.542
Van Kampen Am Cap Gr & Inc A	Gi	0.570	4.781	15.349	−32.135
Van Kampen Am Cap Comstock A	Gi	0.599	4.539	13.167	−34.921
Winthrop Growth & Income A	Gi	0.430	3.987	10.717	−24.088
Washington Mutual Investors	Gi	0.723	3.882	11.409	−20.113
Safeco Equity	Gi	0.587	4.797	14.263	−31.042
Seligman Common Stock A	Gi	0.553	4.224	11.785	−23.331
Salomon Bros Investors O	Gi	0.583	4.194	11.785	−24.980
Security Growth & Income A	Gi	0.233	3.825	10.161	−19.674
Selected American	Gi	0.650	3.969	13.142	−19.385
Putnam Fund for Grth & Inc A	Gi	0.637	3.540	8.456	−22.081
Growth income average	Gi	0.544	3.940	10.380	−24.469

Appendix 3

68.3.1 Summary Statistics for Returns of the Mutual Funds

Fund name	Investment style	Mean	Standard deviation	Maximum	Minimum
Asset allocation average	S1	0.391	2.550	8.962	−9.464
Aggressive growth average	S2	0.459	5.814	13.142	−35.335
Equity income average	S3	0.527	3.238	9.094	−18.718
Growth average	S4	0.594	4.775	12.649	−26.255
Growth income average	S5	0.544	3.940	10.380	−24.469

Appendix 4

The MCDM proposed approach consists of eight steps: define the problem, define the evaluation criteria, initial screen, define the preferences on evaluation criteria, define the MCDM method for selection, evaluate the MCDM methods, choose the most suitable method, and conduct sensitivity analysis.

• Step 1: Define the problem. The characteristics of the decision-making problem under consideration are addressed in the problem definition step, such as identifying the number of alternatives, attributes, and constraints. The available information about the decision-making problem is the basis on which the most appropriate MCDM techniques will be evaluated and utilized to solve the problem.

• Step 2: Define the evaluation criteria. The proper determination of the applicable evaluation criteria is important because they have great influence on the outcome of the MCDM method selection process. However, simply using every criterion in the selection process is not the best approach because the more criteria used, the more information is required, which will result in higher computational cost. In this study, the characteristics of the MCDM methods will be identified by the relevant evaluation criteria in the form of a questionnaire. Ten questions are defined to capture the advantages, disadvantages, applicability, computational complexity, etc. of each MCDM method, as shown in the following. The defined evaluation criteria will be used as the attributes of an MCDM formulation and as the input data of decision matrix for method selection:

  • 1. Is the method able to handle MADM, MODM, or MCDM problem?

  • 2. Does the method evaluate the feasibility of the alternatives?

  • 3. Is the method able to capture uncertainties existing in the problem?

  • 4. What input data are required by the method?

  • 5. What preference information does the method use?

  • 6. What metric does the method use to rank the alternatives?

  • 7. Can the method deal changing alternatives or requirements?

  • 8. Does the method handle qualitative or quantitative data?

  • 9. Does the method deal with discrete or continuous data?

  • 10. Can the method handle the problem with hierarchy structure of attributes?

• Step 3: Initial screen in the initial screen step. The dominated and infeasible MCDM methods are eliminated by dominance and conjunctive. An alternative is dominated if there is another alternative which excels it in one or more attributes and equals it in the remainder. The dominated MCDM methods are eliminated by the dominance method, which does not require any assumption or any transformation of attributes. The sieve of dominance takes the following procedures. Compare the first two alternatives, and if one is dominated by the other, discard the dominated one; then compare the un-discarded alternative with the third alternative and discard any dominated alternative; and then introduce the fourth alternative and repeat this process until the last alternative has been compared. A set of non-dominated alternatives may possess unacceptable or infeasible attribute values. The conjunctive method is employed to remove the unacceptable alternatives, in which the decision maker sets up the cutoff value he/she will accept for each of the attributes. Any alternative which has an attribute value worse than the cutoff values will be eliminated.

• Step 4: Define the preferences on evaluation criteria. Usually, after the initial screen step is completed, multiple MCDM methods are expected to remain; otherwise we can directly choose the only one left to solve the decision-making problem. With the ten evaluation criteria defined in step 2, the decision maker’s preference information on the evaluation criteria is defined. This will reflect which criterion is more important to the decision maker when he/she makes decisions on method selection.

• Step 5: Define the MCDM method for selection. Existing commonly used MCDM methods are identified and stored in the method base as candidate methods for selection. The simple additive weighting (SAW) method is chosen to select the most suitable MCDM methods considering its simplicity and general acceptability. Basically, the SAW method provides a weighted summation of the attributes of each method, and the one with the highest score is considered as the most appropriate method. Though SAW is used in this study, it is worth noting that other MCDM methods can be employed to handle the same MCDM methods selection problem.

• Step 6: Evaluate the MCDM methods. Mathematical formulation of appropriateness index (AI) is used to rank the MCDM methods. The method with the highest AI will be recommended as the most appropriate method to solve the problem under consideration.

• Step 7: Choose the most suitable method. For optimization of specification of grinding wheel, the MCDM method which has the highest AI will be selected as the most appropriate method to solve the given decision-making problem. If the DM is satisfied with the final results, he/she can implement the solution and move forward. Otherwise, he/she can go back to step 2 and modify the input data or preference information and repeat the selection process until a satisfied outcome is obtained. Be displayed to provide guidance to DM is provided guidance about how to get the final solution by using the selected method. In addition, the detailed mathematical calculation steps are also built in the MATLAB-based DSS, which highly facilitates the decision-making process. Thus, the DM can input their data according to the instruction and get the final results by clicking one corresponding button.

• Step 8: Conduct analysis. In this section, selection of an optimized specification of grinding wheel problem is conducted to improve the capabilities of the grinding operation products by proposed MCDM decision support system. It is observed that different decision makers often have different preference information on the evaluation criteria and different answers to the ten questions; thus, analysis should be performed on the MCDM method selection algorithm in order to analyze its robustness with respect to parameter variations, such as the variation of decision maker’s preference information and the input data. If the decision maker is satisfied with the final results, he/she can implement the solution and move forward. Otherwise, he/she can go back to step 2 and modify the input data or preference information and repeat the selection process until a satisfied outcome is obtained. In this implementation, emphasis is put on explaining the holistic process of the intelligent MCDM decision support system. Thus, the step-by-step problem-solving process is explained and discussed for this decision-making problem.