Portfolio Performance Evaluation

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Portfolio Performance Evaluation

  1. 1. PORTFOLIO PERFORMANCE EVALUATION
  2. 2. MEASURES OF RETURN <ul><li>MEASURES OF RETURN </li></ul><ul><ul><li>complicated by addition or withdrawal of money by the investor </li></ul></ul><ul><ul><li>percentage change is not reliable when the base amount may be changing </li></ul></ul><ul><ul><li>timing of additions or withdrawals is important to measurement </li></ul></ul>
  3. 3. MEASURES OF RETURN <ul><li>TWO MEASURES OF RETURN </li></ul><ul><ul><li>Dollar-Weighted Returns </li></ul></ul><ul><ul><ul><li>uses discounted cash flow approach </li></ul></ul></ul><ul><ul><ul><li>weighted because the period with the greater number of shares has a greater influence on the overall average </li></ul></ul></ul>
  4. 4. MEASURES OF RETURN <ul><li>TWO MEASURES OF RETURN </li></ul><ul><ul><li>Time-Weighted Returns </li></ul></ul><ul><ul><ul><li>used when cash flows occur between beginning and ending of investment horizon </li></ul></ul></ul><ul><ul><ul><li>ignores number of shares held in each period </li></ul></ul></ul>
  5. 5. MEASURES OF RETURN <ul><li>TWO MEASURES OF RETURN </li></ul><ul><ul><li>Comparison of Time-Weighted to Dollar-Weighted Returns </li></ul></ul><ul><ul><ul><li>Time-weighted useful in pension fund management where manager cannot control the deposits or withdrawals to the fund </li></ul></ul></ul>
  6. 6. MAKING RELEVANT COMPARISONS <ul><li>PERFORMANCE </li></ul><ul><ul><li>should be evaluated on the basis of a relative and not an absolute basis </li></ul></ul><ul><ul><ul><li>this is done by use of a benchmark portfolio </li></ul></ul></ul><ul><ul><li>BENCHMARK PORTFOLIO </li></ul></ul><ul><ul><ul><li>should be relevant and feasible </li></ul></ul></ul><ul><ul><ul><li>reflects objectives of the fund </li></ul></ul></ul><ul><ul><ul><li>reflects return as well as risk </li></ul></ul></ul>
  7. 7. THE USE OF MARKET INDICES <ul><li>INDICES </li></ul><ul><ul><li>are used to indicate performance but depend upon </li></ul></ul><ul><ul><ul><li>the securities used to calculate them </li></ul></ul></ul><ul><ul><ul><li>the calculation weighting measures </li></ul></ul></ul>
  8. 8. THE USE OF MARKET INDICES <ul><li>INDICES </li></ul><ul><ul><li>Three Calculation Weighting Methods: </li></ul></ul><ul><ul><ul><li>price weighting </li></ul></ul></ul><ul><ul><ul><ul><li>sum prices and divided by a constant to determine average price </li></ul></ul></ul></ul><ul><ul><ul><ul><li>EXAMPLE: THE DOW JONES INDICES </li></ul></ul></ul></ul>
  9. 9. THE USE OF MARKET INDICES <ul><li>INDICES </li></ul><ul><ul><li>Three Calculation Weighting Methods: </li></ul></ul><ul><ul><ul><li>value weighting (capitalization method) </li></ul></ul></ul><ul><ul><ul><ul><li>price times number of shares outstanding is summed </li></ul></ul></ul></ul><ul><ul><ul><ul><li>divide by beginning value of index </li></ul></ul></ul></ul><ul><ul><ul><ul><li>EXAMPLE: </li></ul></ul></ul></ul><ul><ul><ul><ul><ul><li>S&P500 </li></ul></ul></ul></ul></ul><ul><ul><ul><ul><ul><li>WILSHIRE 5000 </li></ul></ul></ul></ul></ul><ul><ul><ul><ul><ul><li>RUSSELL 1000 </li></ul></ul></ul></ul></ul>
  10. 10. THE USE OF MARKET INDICES <ul><li>INDICES </li></ul><ul><ul><li>Three Calculation Weighting Methods: </li></ul></ul><ul><ul><ul><li>equal weighting </li></ul></ul></ul><ul><ul><ul><ul><li>multiply the level of the index on the previous day by the arithmetic mean of the daily price relatives </li></ul></ul></ul></ul><ul><ul><ul><ul><li>EXAMPLE: </li></ul></ul></ul></ul><ul><ul><ul><ul><ul><li>VALUE LINE COMPOSITE </li></ul></ul></ul></ul></ul>
  11. 11. ARITHMETIC V. GEOMETRIC AVERAGES <ul><li>GEOMETRIC MEAN FRAMEWORK </li></ul><ul><ul><li>GM = (  HPR) 1/N - 1 </li></ul></ul><ul><ul><li>where  = the summation of the product of </li></ul></ul><ul><ul><li> HPR= the holding period returns </li></ul></ul><ul><ul><li> n= the number of periods </li></ul></ul>
  12. 12. ARITHMETIC V. GEOMETRIC AVERAGES <ul><li>GEOMETRIC MEAN FRAMEWORK </li></ul><ul><ul><li>measures past performance well </li></ul></ul><ul><ul><li>represents exactly the constant rate of return needed to earn in each year to match some historical performance </li></ul></ul>
  13. 13. ARITHMETIC V. GEOMETRIC AVERAGES <ul><li>ARITHMETIC MEAN FRAMEWORK </li></ul><ul><ul><li>provides a good indication of the expected rate of return for an investment during a future individual year </li></ul></ul><ul><ul><li>it is biased upward if you attempt to measure an asset’s long-run performance </li></ul></ul>
  14. 14. RISK-ADJUSTED MEASURES OF PERFORMANCE <ul><li>THE REWARD TO VOLATILITY RATIO (TREYNOR MEASURE) </li></ul><ul><ul><li>There are two components of risk </li></ul></ul><ul><ul><ul><li>risk associated with market fluctuations </li></ul></ul></ul><ul><ul><ul><li>risk associated with the stock </li></ul></ul></ul><ul><ul><li>Characteristic Line (ex post security line) </li></ul></ul><ul><ul><ul><li>defines the relationship between historical portfolio returns and the market portfolio </li></ul></ul></ul>
  15. 15. TREYNOR MEASURE <ul><li>TREYNOR MEASURE </li></ul><ul><ul><li>Formula </li></ul></ul><ul><ul><li>where ar p = the average portfolio return </li></ul></ul><ul><ul><li>ar f = the average risk free rate </li></ul></ul><ul><ul><li> p  = the slope of the characteristic </li></ul></ul><ul><ul><li>line during the time period </li></ul></ul>
  16. 16. TREYNOR MEASURE <ul><li>THE CHARACTERISTIC LINE </li></ul>ar p  p SML
  17. 17. TREYNOR MEASURE <ul><li>CHARACTERISTIC LINE </li></ul><ul><ul><li>slope of CL </li></ul></ul><ul><ul><ul><li>measures the relative volatility of portfolio returns in relation to returns for the aggregate market, i.e. the portfolio’s beta </li></ul></ul></ul><ul><ul><ul><li>the higher the slope, the more sensitive is the portfolio to the market </li></ul></ul></ul>
  18. 18. TREYNOR MEASURE <ul><li>THE CHARACTERISTIC LINE </li></ul>ar p  p SML
  19. 19. THE SHARPE RATIO <ul><li>THE REWARD TO VARIABILITY (SHARPE RATIO) </li></ul><ul><ul><li>measure of risk-adjusted performance that uses a benchmark based on the ex-post security market line </li></ul></ul><ul><ul><li>total risk is measured by  p </li></ul></ul>
  20. 20. THE SHARPE RATIO <ul><li>SHARPE RATIO </li></ul><ul><ul><li>formula: </li></ul></ul><ul><ul><li>where SR = the Sharpe ratio </li></ul></ul><ul><ul><li> p = the total risk </li></ul></ul>
  21. 21. THE SHARPE RATIO <ul><li>SHARPE RATIO </li></ul><ul><ul><li>indicates the risk premium per unit of total risk </li></ul></ul><ul><ul><li>uses the Capital Market Line in its analysis </li></ul></ul>
  22. 22. THE SHARPE RATIO ar p  p CML
  23. 23. THE JENSEN MEASURE OF PORTFOLIO PERFORMANCE <ul><li>BASED ON THE CAPM EQUATION </li></ul><ul><ul><li>measures the average return on the portfolio over and above that predicted by the CAPM </li></ul></ul><ul><ul><li>given the portfolio’s beta and the average market return </li></ul></ul>
  24. 24. THE JENSEN MEASURE OF PORTFOLIO PERFORMANCE <ul><li>THE JENSEN MEASURE </li></ul><ul><ul><li>known as the portfolio’s alpha value </li></ul></ul><ul><ul><ul><li>recall the linear regression equation </li></ul></ul></ul><ul><ul><li>y =  +  x + e </li></ul></ul><ul><ul><ul><li>alpha is the intercept </li></ul></ul></ul>
  25. 25. THE JENSEN MEASURE OF PORTFOLIO PERFORMANCE <ul><li>DERIVATION OF ALPHA </li></ul><ul><ul><li>Let the expectations formula in terms of realized rates of return be written </li></ul></ul><ul><ul><li>subtracting RFR from both sides </li></ul></ul>
  26. 26. THE JENSEN MEASURE OF PORTFOLIO PERFORMANCE <ul><li>DERIVATION OF ALPHA </li></ul><ul><ul><li>in this form an intercept value for the regression is not expected if all assets are in equilibrium </li></ul></ul><ul><ul><li>in words, the risk premium earned on the jth portfolio is equal to  j times a market risk premium plus a random error term </li></ul></ul>
  27. 27. THE JENSEN MEASURE OF PORTFOLIO PERFORMANCE <ul><li>DERIVATION OF ALPHA </li></ul><ul><ul><li>to measure superior portfolio performance, you must allow for an intercept  </li></ul></ul><ul><ul><li>a superior manager has a significant and positive alpha because of constant positive random errors </li></ul></ul>
  28. 28. COMPARING MEASURES OF PERFORMANCE <ul><li>TREYNOR V. SHARPE </li></ul><ul><ul><li>SR measures uses  as a measure of risk while Treynor uses  </li></ul></ul><ul><ul><li>SR evaluates the manager on the basis of both rate of return performance as well as diversification </li></ul></ul>
  29. 29. COMPARING MEASURES OF PERFORMANCE <ul><ul><li>for a completely diversified portfolio </li></ul></ul><ul><ul><ul><li>SR and Treynor give identical rankings because total risk is really systematic variance </li></ul></ul></ul><ul><ul><ul><li>any difference in ranking comes directly from a difference in diversification </li></ul></ul></ul>
  30. 30. CRITICISM OF RISK-ADJUSTED PERFORMANCE MEASURES <ul><li>Use of a market surrogate </li></ul><ul><ul><ul><li>Roll: criticized any measure that attempted to model the market portfolio with a surrogate such as the S&P500 </li></ul></ul></ul><ul><ul><ul><ul><li>it is almost impossible to form a portfolio whose returns replicate those over time </li></ul></ul></ul></ul><ul><ul><ul><ul><li>making slight changes in the surrogate may completely change performance rankings </li></ul></ul></ul></ul>
  31. 31. CRITICISM OF RISK-ADJUSTED PERFORMANCE MEASURES <ul><li>measuring the risk free rate </li></ul><ul><ul><ul><li>using T-bills gives too low of a return making it easier for a portfolio to show superior performance </li></ul></ul></ul><ul><ul><ul><li>borrowing a T-bill rate is unrealistically low and produces too high a rate of return making it more difficult to show superior performance </li></ul></ul></ul>

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