Data Envelopment Analysis


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Data Envelopment Analysis

  1. 1. Socially Responsible Investing (SRI) <ul><li>Value-Based or “Ethical” mutual funds: </li></ul><ul><ul><li>Create screens to prevent investment in organizations that promote or participate in identified undesirable social, governance, and/or environmental actions or controversial business </li></ul></ul><ul><ul><li>May earn a lower return in the long term </li></ul></ul><ul><ul><li>Have higher diversification costs and thus can have more uncompensated risk </li></ul></ul>
  2. 2. Traditional Portfolio Measures of Performance (Risk Adjusted Return) <ul><li>Sharpe Ratio: </li></ul><ul><ul><li>(Return – Riskfree rate)/ σ </li></ul></ul><ul><li>Treynor Ratio: </li></ul><ul><ul><li>(Return – Riskfree rate)/ β </li></ul></ul><ul><li>Neither can incorporate ethical factors </li></ul>
  3. 3. Value-Seeking Investing <ul><li>Since the late 1990’s, some proponents of SRI started focusing on identifying social and environmental criteria which effect a corporation’s financial performance and resulting share price </li></ul><ul><li>Screens are created to identify corporations that perform positively in these criteria, with the objective of maximizing the return of the portfolio </li></ul>
  4. 4. Measuring Social Responsibility Level <ul><li>Agencies and research institutes exist to: </li></ul><ul><ul><li>Monitor, assess and classify companies and mutual funds on the ground of a set of ethical parameters </li></ul></ul><ul><ul><li>Define enterprise and fund ratings based on ethical criteria </li></ul></ul><ul><ul><li>e.g. Kinder, Lydenberg, Domini & Company </li></ul></ul>
  5. 5. Data Envelopment Analysis (DEA) <ul><li>A linear programming application aimed at evaluating the efficiencies of similar decision-making units (DMUs) based upon the inputs and outputs associated with the DMUs </li></ul><ul><li>A DMU is considered efficient if it gets the most output from its inputs </li></ul><ul><li>Efficiency is defined as the value of its outputs divided by the value of its inputs </li></ul><ul><li>The purpose of DEA is to identify inefficient DMUs when there are multiple outputs and multiple inputs </li></ul>
  6. 6. DEA Applied to Socially Responsible Investing <ul><li>Determines how efficiently a business (or fund) converts inputs to outputs when compared with other businesses (or funds) </li></ul><ul><li>This would allow an investor or fund manager to compare the efficiency of several competing funds or stocks </li></ul><ul><li>Outputs can represent the investor’s objectives: </li></ul><ul><ul><li>To satisfy an ethical need </li></ul></ul><ul><ul><li>To obtain a satisfactory return </li></ul></ul>
  7. 7. Bank Branch Problem Branch OperationCosts Loan Balances Deposit Balances A 100 10 31 B 100 15 25 C 100 20 30 D 100 23 23 E 100 30 20
  8. 8. Efficiency of DMU i <ul><li>Weighted sum of DMU i ’s outputs </li></ul><ul><li>Weighted sum of DMU i ’s inputs </li></ul><ul><li>Where O ij =value of output j for DMU i </li></ul><ul><li>I ij =value of input j for DMU i </li></ul><ul><li> w i =weight of output j </li></ul><ul><li>v j =weight of input j </li></ul><ul><li>n o =number of outputs </li></ul><ul><li>n I =number of inputs </li></ul>
  9. 9. Efficiency of DMU i <ul><li>Data Envelopment Analysis determines the weights to calculate the efficiency for DMU i: </li></ul><ul><li>W j = weight of output j </li></ul><ul><li> V j = weight of input j </li></ul><ul><li>W and V are Decision Variables in Solver! </li></ul><ul><li>Determines weight based on assumption that more of Outputs and less of inputs are desirable </li></ul>
  10. 10. LP formulation for each DMU i <ul><li>Max Σ w j O ij </li></ul><ul><li>By changing w j and v j </li></ul><ul><li>Subject to </li></ul><ul><li> Σ w j O kj <= Σ v j I kj for all k DMUs </li></ul><ul><li> Σ v j I ij = 1 </li></ul><ul><li>DMUs whose objective values are <1 are inefficient: Combinations of other funds using the same weights w j and v j can produce the same or better output with the same or less input. </li></ul>
  11. 11. Example Problem: Evaluating the performance of different bank branches <ul><li>The profitability of retail bank branches is often determined by its loan and deposit balances </li></ul><ul><li>DEA identifies the weights for the loan and deposit balances that are the most complementary to the branch being evaluated </li></ul><ul><li>These ideal weighted balances are then compared to the balances at the other branches for those weights and rated on a scale of 0 to 1 for efficiency </li></ul>
  12. 12. Excel Implementation <ul><li>=Index( range, row number, column number ) </li></ul><ul><li>Returns value in row number and column number of specified range </li></ul><ul><li>Use to automate process of running LP for many funds </li></ul><ul><li>Use VBA to program a loop that inputs relevant row number into the index function, run Solver, and record efficiency score (see page 109-110) </li></ul>
  13. 13. Data Envelopment Analysis for Ethical Mutual Funds <ul><li>Outputs: O 1j = Excess return for fund j </li></ul><ul><li>O 2j = Ethical measure for fund j </li></ul><ul><li>Inputs: I 1j = Risk measure 1 for fund j </li></ul><ul><li> I 2j = Risk measure 2 for fund j…. </li></ul><ul><li> I nj = Risk measure n for fund j </li></ul><ul><li>I (n+1)j = Cost 1 for fund j… </li></ul><ul><li>I (n+m)j = Cost m for fund j… </li></ul>
  14. 14. <ul><li>How would you incorporate the Data Envelopment Model into the Socially Responsible Investment process? </li></ul>