1 Chapter 19 Performance Evaluation Portfolio Construction, Management, & Protection, 5e, Robert A. Strong Copyright ©2009 by South-Western, a division of Thomson Business & Economics. All rights reserved.

2 Introduction u Performance evaluation is a critical aspect of portfolio management u Proper performance evaluation should involve a recognition of both the return and the riskiness of the investment

3 Importance of Measuring Portfolio Risk u When two investments’ returns are compared, their relative risk must also be considered u People maximize expected utility: A positive function of expected return A negative function of the return variance

4 A Lesson from History: The 1968 Bank Administration Institute Report u The 1968 Bank Administration Institute’s Measuring the Investment Performance of Pension Funds concluded: 1)Performance of a fund should be measured by computing the actual rates of return on a fund’s assets 2)These rates of return should be based on the market value of the fund’s assets

5 A Lesson from History: The 1968 Bank Administration Institute Report (cont’d) 3)Complete evaluation of the manager’s performance must include examining a measure of the degree of risk taken in the fund 4)Circumstances under which fund managers must operate vary so greatly that indiscriminate comparisons among funds might reflect differences in these circumstances rather than in the ability of managers

6 A Lesson from a Few Mutual Funds u The two key points with performance evaluation: The arithmetic mean is not a useful statistic in evaluating growth Dollars are more important than percentages u Consider the historical returns of two mutual funds on the following slide

7 A Lesson from a Few Mutual Funds (cont’d) 23.5% Mutual Shares 19.3% 19.3 –34.6 –16.3 –20.1 – Wall Street Mean Year %184.1%1975 Mutual Shares 44 Wall StreetYear Change in net asset value, January 1 through December 31.

8 A Lesson from a Few Mutual Funds (cont’d)

9 u 44 Wall Street and Mutual Shares both had good returns over the 1975 to 1988 period u Mutual Shares clearly outperforms 44 Wall Street in terms of dollar returns at the end of 1988

10 Why the Arithmetic Mean Is Often Misleading: A Review u The arithmetic mean may give misleading information e.g., a 50 percent decline in one period followed by a 50 percent increase in the next period does not produce an average return of zero

11 Why the Arithmetic Mean Is Often Misleading: A Review (cont’d) u The proper measure of average investment return over time is the geometric mean:

12 Why the Arithmetic Mean Is Often Misleading: A Review (cont’d) u The geometric means in the preceding example are: 44 Wall Street: 7.9 percent Mutual Shares: 22.7 percent u The geometric mean correctly identifies Mutual Shares as the better investment over the 1975 to 1988 period

13 Why the Arithmetic Mean Is Often Misleading: A Review (cont’d) Example A stock returns –40% in the first period, +50% in the second period, and 0% in the third period. [The average rate of return is 3.3%] What is the geometric mean over the three periods?

14 Why the Arithmetic Mean Is Often Misleading: A Review (cont’d) Example Solution: The geometric mean is computed as follows:

15 Why Dollars Are More Important Than Percentages u Assume two funds: Fund A has $40 million in investments and earned 12 percent last period Fund B has $250,000 in investments and earned 44 percent last period

16 Why Dollars Are More Important Than Percentages (cont’d) u The correct way to determine the return of both funds combined is to weigh the funds’ returns by the dollar amounts:

17 Traditional Performance Measures u Sharpe Measure u Treynor Measures u Jensen Measure u Performance Measurement in Practice

18 Sharpe and Treynor Measures u The Sharpe and Treynor measures:

19 Sharpe and Treynor Measures (cont’d) u The Sharpe measure evaluates return relative to total risk Appropriate for a well-diversified portfolio, but not for individual securities u The Treynor measure evaluates the return relative to beta, a measure of systematic risk It ignores any unsystematic risk

20 Sharpe and Treynor Measures (cont’d) Example Over the last four months, XYZ Stock had excess returns of 1.86 percent, –5.09 percent, –1.99 percent, and 1.72 percent. The standard deviation of XYZ stock returns is 3.07 percent. XYZ Stock has a beta of What are the Sharpe and Treynor measures for XYZ Stock?

21 Sharpe and Treynor Measures (cont’d) Example (cont’d) Solution: First, compute the average excess return for Stock XYZ:

22 Sharpe and Treynor Measures (cont’d) Example (cont’d) Solution (cont’d): Next, compute the Sharpe and Treynor measures:

23 Jensen Measure u The Jensen measure stems directly from the CAPM:

24 Jensen Measure (cont’d) u The constant term should be zero Securities with a beta of zero should have an excess return of zero according to finance theory u According to the Jensen measure, if a portfolio manager is better-than-average, the alpha of the portfolio will be positive

25 Academic Issues Regarding Performance Measures u The use of Treynor and Jensen performance measures relies on measuring the market return and CAPM Difficult to identify and measure the return of the market portfolio u Evidence continues to accumulate that may ultimately displace the CAPM Arbitrage pricing model, multi-factor CAPMs, inflation-adjusted CAPM

26 Industry Issues u “Portfolio managers are hired and fired largely on the basis of realized investment returns with little regard to risk taken in achieving the returns” u Practical performance measures typically involve a comparison of the fund’s performance with that of a benchmark

27 Industry Issues (cont’d) u “Fama’s return decomposition” can be used to assess why an investment performed better or worse than expected: The return the investor chose to take The added return the manager chose to seek The return from the manager’s good selection of securities

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29 Industry Issues (cont’d) u Diversification is the difference between the return corresponding to the beta implied by the total risk of the portfolio and the return corresponding to its actual beta Diversifiable risk decreases as portfolio size increases, so if the portfolio is well diversified the “diversification return” should be near zero

30 Industry Issues (cont’d) u Net selectivity measures the portion of the return from selectivity in excess of that provided by the “diversification” component

31 Volume Weighted Average Price u Portfolio managers want to minimize the impact of their trading on share price A buy order increases demand and price Portfolio managers frequently take the opposite position in the pre-market trading u Volume weighted average price compares the average market price to the average price paid by (or received) by a manager

32 Trading Efficiency Impacts on Performance (cont’d) u Implementation shortfall is the difference between the value of a “on-paper” theoretical portfolio and portfolio purchased u “On-paper” portfolio is based upon price of last reported trade u Actual purchases are likely to lead to higher costs due to Commissions “Bid-Ask” Spread – the prior trade may have been at a bid, while your trade may be at the ask price (reverse if selling) Market trend – are prices moving higher? Liquidity impact – your demand may exceed share available a lower price –Or, shares sold may exceed the number purchased at higher price

33 Dollar-Weighted and Time-Weighted Rates of Return u The dollar-weighted rate of return is analogous to the internal rate of return in corporate finance It is the rate of return that makes the present value of a series of cash flows equal to the cost of the investment:

34 Dollar-Weighted and Time-Weighted Rates of Return (cont’d) u The time-weighted rate of return measures the compound growth rate of an investment It eliminates the effect of cash inflows and outflows by computing a return for each period and linking them (like the geometric mean return):

35 Dollar-Weighted and Time-Weighted Rates of Return (cont’d) u The time-weighted rate of return and the dollar- weighted rate of return will be equal if there are no inflows or outflows from the portfolio

36 Performance Evaluation with Cash Deposits and Withdrawals u The owner of a fund often takes periodic distributions from the portfolio, and may occasionally add to it u The established way to calculate portfolio performance in this situation is via a time- weighted rate of return: Daily valuation method Modified BAI method

37 Daily Valuation Method u The daily valuation method: Calculates the exact time-weighted rate of return Is cumbersome because it requires determining a value for the portfolio each time any cash flow occurs –Might be interest, dividends, or additions to or withdrawals

38 Daily Valuation Method (cont’d) u The daily valuation method solves for R:

39 Daily Valuation Method (cont’d) u MVE i = market value of the portfolio at the end of period i before any cash flows in period i but including accrued income for the period u MVB i = market value of the portfolio at the beginning of period i including any cash flows at the end of the previous subperiod and including accrued income

40 Modified Bank Administration Institute (BAI) Method u The modified BAI method: Approximates the internal rate of return for the investment over the period in question Can be complicated with a large portfolio that might conceivably have a cash flow every day

41 Modified Bank Administration Institute (BAI) Method (cont’d) u It solves for R:

42 An Example u An investor has an account with a mutual fund and “dollar cost averages” by putting $100 per month into the fund u The following slide shows the activity and results over a seven-month period

43 Table19-4 Mutual Fund Account Value DateDescription$ AmountPriceShares Total SharesValue January 1balance forward $7.001, $7, January 3purchase100$ , $7, February 1 purchase100$ , $8, March 1purchase100$ , $8, March 23liquidation5,000$ $4, April 3purchase100$ $4, May 1purchase100$ $4, June 1purchase100$ $5, July 3purchase100$ $5, August 1purchase100$ $5, August 1 account value: $ x $9.84 = $5,500.97

44 An Example (cont’d) u The daily valuation method returns a time- weighted return of 40.6 percent over the seven-month period See next slide

45 Table19-5 Daily Valuation Worksheet DateSub PeriodMVBCash Flow Ending Value MVE MVE/MVB January 1$7, January 31$7, $7,660.08$7, February 1 2$7, $8,755.89$8, March 13$8, $8,778.40$8, March 234$8, ,000$4,103.11$9, April 35$4, $4,309.09$4, May 16$4, $4,750.10$4, June 17$4, $5,240.67$5, July 38$5, $5,071.64$4, August 19$5, $5,500.97$5, Product of MVE/MVB values = 1.406;  R = 40.6%

46 An Example (cont’d) u The BAI method requires use of a computer u The BAI method returns a time-weighted return of 42.1 percent over the seven-month period (see next slide)

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48 An Approximate Method u Proposed by the American Association of Individual Investors:

49 Intuition

50 An Approximate Method (cont’d) u Using the approximate method in Table 17- 6:

51 Performance Evaluation When Options Are Used u Inclusion of options in a portfolio usually results in a non-normal return distribution u Beta and standard deviation lose their theoretical value if the return distribution is nonsymmetrical u Consider two alternative methods when options are included in a portfolio: Incremental risk-adjusted return (IRAR) Residual option spread (ROS)

52 Incremental Risk-Adjusted Return from Options u The incremental risk-adjusted return (IRAR) is a single performance measure indicating the contribution of an options program to overall portfolio performance A positive IRAR indicates above-average performance A negative IRAR indicates the portfolio would have performed better without options

53 Incremental Risk-Adjusted Return from Options (cont’d) u Use the unoptioned portfolio as a benchmark: Draw a line from the risk-free rate to its realized risk/return combination Points above this benchmark line result from superior performance –The higher than expected return is the IRAR

54 Incremental Risk-Adjusted Return from Options (cont’d)

55 Incremental Risk-Adjusted Return from Options (cont’d) u The IRAR calculation:

56 An IRAR Example u A portfolio manager routinely writes index call options to take advantage of anticipated market movements u Assume: The portfolio has an initial value of $200,000 The stock portfolio has a beta of 1.0 The premiums received from option writing are invested into more shares of stock

57 Table19-9 Modified BAI Method Worksheet (Using Interest Rate of 42.1%) Week Unoptioned Portfolio Long Stock Plus Option Premiums Less Short Options a Equals Optioned Portfolio 0$200,000$214,112$14,112$200, ,000203,4068,868194, ,700209,50810,746198, ,528217,88814,064203, ,528213,53011,220202, ,474207,1247,758199, ,213215,40910,614204, ,249221,87113,164208,707 a Option values are theoretical Black-Scholes values based on an initial OEX value of 300, a striking price of 300, a risk-free interest rate of 8 percent, an initial life of 90 days, and a volatility of 35 percent. Six OEX calls are written.

58 An IRAR Example (cont’d) u The IRAR calculation (next slide) shows that: The optioned portfolio appreciated more than the unoptioned portfolio The options program was successful at adding 11.3 percent per year to the overall performance of the fund

59 Table19-10 IRAR Worksheet Unoptioned PortfolioRelative ReturnOptioned Portfolio Relative Return $200, $200,000 $190, $194, $195, $198, $203, $203, $199, $202, $193, $199, $201, $204, $207, $208, Mean = 1.007Mean = Standard Deviation = Standard Deviation = Risk-free rate = 8%/year = 0.15%/week SHu = ( ) ÷ = SHo = ( ) ÷ = IRAR = ( – ) x = per week, or about 12% per year

60 IRAR Caveats u IRAR can be used inappropriately if there is a floor on the return of the optioned portfolio e.g., a portfolio manager might use puts to protect against a large fall in stock price u The standard deviation of the optioned portfolio is probably a poor measure of risk in these cases

61 Residual Option Spread u The residual option spread (ROS) is an alternative performance measure for portfolios containing options u A positive ROS indicates the use of options resulted in more terminal wealth than only holding the stock u A positive ROS does not necessarily mean that the incremental return is appropriate given the risk

62 Residual Option Spread (cont’d) u The residual option spread (ROS) calculation:

63 Residual Option Spread (cont’d) u The worksheet to calculate the ROS for the previous example is shown on the next slide u The ROS translates into a dollar differential of $1,452

64 Residual Options Spread Worksheet u Unoptioned Portfolio (0.95)(1.03)(1.04)(0.98)(0.97)(1.04)(1.03) = u Optioned Portfolio (0.9727)(1.0217)(1.0255)(0.9926)(0.9854)(1.0272)(1.0191) = u ROS = – = u Given an initial investment of $200,000, the ROS translates into a dollar differential of $200,000 x = $1,452.

65 Final Comments u IRAR and ROS both focus on whether an optioned portfolio outperforms an unoptioned portfolio Can overlook subjective considerations such as portfolio insurance