2018 Study Session # 17, Reading # 33 “EVALUATING PORTFOLIO PERFORMANCE” PE = Performance Evaluation MCP = Manager Continuation Policies CML = Capital Market Line HF = Hedge Funds YC = Yield Curve INTRODUCTION Performance Evaluation Performance Measurement Calculating accounts’ performance based on investment related∆ Performance Attribution Analyzing sources of return& importance of those sources Performance Appraisal Assessing whether the return was generated due to skills or luck Assessing size & consistency of accounts’ relative to performance THE IMPORTANCE OFPERFORMANCE EVALUATION 2.1 The Fund Sponsor's Perspective Fund sponsors ⇒ owners of large pools of investable assets PE is important because: It provides an exhaustive quality control check of the fund & its constituent parts It is a part of feedback of the investment management process It acts as a feedback & control mechanism 2.2 The Investment Manager's Perspective PE involves reporting investment returns along with the return of some benchmark Measures the effectiveness of all aspects of the investment processes THE THREE COMPONENTS OFPERFORMANCE EVALUATION Account ⇒ one or more portfolios of securities managed by one or more investment management organizations Copyright © FinQuiz.com All rights reserved 2018 Study Session # 17, Reading # 33 PERFORMANCE MEASUREMENT 4.1 Performance Measurement without Intra-period External Cash Flows Rate of return on an account ⇒ % ∆ in the account’s MV over some defined period of time after considering all external CF (contributions & withdrawals) If contribution is received at the start of the period: ܸܯ௧ − ሺܸܯ + ܨܥሻ ݎ௧ = ܸܯ + ܨܥ If contribution is received at the end of the evaluation period: ሺܸܯ௧ − ܨܥሻ − ܸܯ ݎ௧ = ܸܯ In case of withdrawals, CF signs will change 4.2 Total Rate of Return Measures the ∆ in the investor’s wealth due to both investment income & capital gains Use of total return measure due to: Allocation to equities Computing costs Institutional investors 4.3 The Time-Weighted Rate of Return Measures the compounded rate of growth over a stated evaluation period of one unit of money initially invested in the account TWR is preferred when manager has no control over the deposits & withdrawals made by clients Account needs to be valued whenever an external CF occurs ݎ௧௪ = ൫1 + ݎ௧,ଵ ൯൫1 + ݎ௧,ଶ ൯ × … × ൫1 + ݎ௧, ൯ − Advantage/Disadvantage of TWR Advantage Disadvantages Not affected by external CF Valuation required each time when an external CF occurs Administratively more cumbersome, expensive & potentially more error prone 4.4 The Money-Weighted Rate of Return Measures the compound growth rate in the value of all funds invested in the account over the entire evaluation period Preferred method when manager has discretion over cash flows MWR is an IRR of an investment Copyright © FinQuiz.com All rights reserved 2018 Study Session # 17, Reading # 33 Advantage/Disadvantage of MWR Advantage Disadvantages A/C is valued at beginning & end of the evaluation period Sensitive to size & timing of external CF Inappropriate when investor has no control over external CF 4.5 TWR versus MWR When funds are contributed to an account prior to a period of strong performance MWR > TWR MWR & TWR provide significantly different results if: Large external CF occurs Account’s performance is highly volatile 4.6 The Linked Internal Rate of Return In LIRR, the TWR is approximated by calculating MWR over reasonably frequent time intervals & then chain links over the entire evaluation period Appropriate to use under normal conditions 4.7 Annualized Return Compounded avg annual return earned by account ଵൗ ݎ௧௪ = ൫1 + ݎ௧,ଵ ൯ × ൫1 + ݎ௧,ଶ ൯ × … × ൫1 + ݎ௧, ൯ − It is not advisable to calculate annualized returns when measurement period < full year 4.8 Data Quality Issues Illiquid & infrequently priced assets with heavy external CF activity generally not reliable in nature For thinly traded securities, usually matrix pricing approach is used A/C should be valued on the trade date rather than settlement date BENCHMARKS 5.1 Concept of a Benchmark Components of portfolio return include: Market (M) Style (S) = manager’s benchmark-market index Active management (A) = manager’s portfoliobenchmark Portfolio return: P=M+S+A Copyright © FinQuiz.com All rights reserved 2018 Study Session # 17, Reading # 33 5.2 Properties of a Valid Benchmark A valid benchmark should have the following properties Unambiguous ⇒ clearly defined identities & weights Investable ⇒ passive investment alternative Measureable ⇒ return can be readily calculate Appropriate ⇒ consistent with manager’s style Reflective of current investment opinions Specified in advance ⇒ known to all interested parties at the start of evaluation period Owned ⇒ manager should be aware & accept accountability 5.3 Types of Benchmarks Absolute Advantage Disadvantage Do not meet benchmark validity criteria (not investable) Simple & straight forward Manager’s Universes Definition Advantage Median manager or fund from a broad universe of mangers or funds as a benchmark Measureable Disadvantage Suffers from survivorship bias Except being measureable, it fails all the benchmark validity criteria Reliance on compilers Broad Market Indexes Advantages Broad market indexes as benchmark e.g S&P 500 Disadvantages Well recognized & easy to understand Widely available & unambiguous Measureable & investable Can be specified in advance Style drift Style Indexes Definition Advantages Using specific portion of asset category as benchmark Well known & easy to understand Widely available Disadvantages Larger than prudent weighting in certain securities May be inconsistent with manager’s investment process Copyright © FinQuiz.com All rights reserved 2018 Study Session # 17, Reading # 33 Factor Model Based Definition Advantage One or more systematic sources of return to the returns on an account Normal portfolio ⇒ portfolio which has exposures to sources of systematic risk factors that is typical for a manager Disadvantage Facilitate manager & fund sponsors to better understand manager’s investment style Difficult to obtain & expensive to use Different benchmarks with the same factor exposures can generate different returns May not be investable Return Based Benchmarks Definition Advantages Disadvantages These benchmarks are constructed using the series of a manager & investment style index’s return Intuitive & easy to use Unambiguous, measureable investable & specified in advance Useful when only the information regarding account return is available May be inconsistent with manager’s investment process Sufficient no of observations required Not appropriate for managers who rotate among style exposures Custom Security-Based Definition Advantage Reflect manager’s research universe weighted in a particular manner Disadvantage Satisfy all of the benchmark validity criteria Effective allocation of risk across all the investment managers Effective monitoring & control of investment processes Expensive to construct & maintain Lack transparency 5.6 Tests of Benchmark Quality Systematic Biases Benchmark should have minimal systematic biases relative to the account (Avg historical β of A/C should be close to 1) Correlation b/w A&S should be zero Difference b/w (P-M) & S should be highly correlated Tracking Error Volatility of account’s return relative to a good benchmark should be < than volatility of the account’s return relative to a market index Copyright © FinQuiz.com All rights reserved 2018 Study Session # 17, Reading # 33 5.6Tests of Benchmark Quality Risk Characteristics Coverage A/C’s exposure to systematic risk should be similar to those of benchmark Systematic bias if A/C’s risk characteristics are always greater or always less than benchmark Benchmark coverage: ݐ ݏ݁݅ݐ݅ݎݑܿ݁ݏ ݂ ܸܯℎܽݐ݊݁ݏ݁ݎ ݁ݎܽ ݐ ൨ ݅݊ ܾݐℎ ݐℎ݁ ܾ݁݊ܿℎ݈݂݉ܽ݅ݐݎ ݀݊ܽ ݇ݎ ܶݐ ݂ ܸܯ ݈ܽݐℎ݁ ݈݂݅ݐݎ Low coverage indicates that the benchmark is poor Turnover Positive Active Positions % of the benchmark’s MV that is purchased/sold for the purpose of periodic rebalancing Passively managed portfolio ⇒low benchmark turnover Large no of +ve active positions ⇒ good custom security based benchmark has to be constructed 5.7 Hedge Funds and Hedge Fund Benchmarks Long only benchmark is inappropriate to evaluate HF performance due to short positions Due to zero net position or –ve net position traditional methods to calculate return does not yield reliable results Hedge Fund Benchmarks Following three are appropriate: Value added return ݎ௩ = ݎ − ݎ Construct separate long & short benchmarks Limitation ⇒ not appropriate if rapidly changing leveraged positions Sharpe ratio Limitations ⇒ assume normal distribution PERFORMANCE ATTRIBUTION Macro attribution ⇒ conducted at the fund sponsor level (total fund performance) Micro attribution ⇒ carried out at the investment manager level (performance of individual portfolios) Copyright © FinQuiz.com All rights reserved 2018 Study Session # 17, Reading # 33 6.1 Impact Equals Weight Times Return Impact = weight × return Select superior performing assets Overweight superior performing assets relative to benchmark 6.2 Macro Attribution Overview 6.3 Macro Attribution Inputs Policy Allocations Benchmark Portfolio Returns Fund sponsor determines the broad allocation to the fund & individual managers Policy allocations depend on: Fund sponsor’s risk tolerance & liabilities Sponsor’s long term expectations Fund sponsor selects: Broad market indexes as benchmark for asset category Specific benchmark for manager’s style Fund Returns, Valuations, and External CF Rate-of-Return Metric Value Metric Computing fund return at individual manager level to evaluate decision regarding manager selection Requires A/C valuation & external CF data to compute accurate rate of return To evaluate the impact of the fund sponsor’s investment decision-making on the fund’s performance 6.4 Conducting a Macro Attribution Analysis Six components of investment policy decision making with increasing order of volatility & complexity Based on incremental return of each investment strategy & contribution of each level to the overall return of the fund Macro Attribution Components Net Contributions These include additions to the portfolio These CF are invested at zero rate of return ∆ in the value of fund = total amount of net contributions Ending value = beginning value + net contributions Risk-Free Asset Conservative strategy involving all fund’s assets invested at RF ∆In fund’s value = ending value under RF investment strategy-beginning value Copyright © FinQuiz.com All rights reserved 2018 Study Session # 17, Reading # 33 Macro Attribution Components Asset Category Benchmarks Fund’s beginning value & external CF are invested passively based on policy allocations Pure index fund approach Return –metric perspective ݎ = ∑ୀ ݓ × ൫ݎ − ݎ ൯ where ݎ = return contribution of asset category ݎ = return on ith asset category ݓ = weight of asset category i Assume that the fund’s beg value & net external CF are invested in manager’s benchmark Pure index fund approach From a return-metric perspective ୀଵ ୀଵ Value – metric perspective: sum (each manger’s policy proportion of the total fund’s beg value + net external CF)× (manager’s benchmark return – return of the manager’s asset category) Investment Managers Allocation Effects Assumes that the fund sponsor has invested in each of the manager according to the manager’s policy allocation Return to the investment managers level = sum (active managers’ return – their benchmark return) Return metric perspective: ெ ݎ௦ = ݓ × ݓ × ൫ݎ − ݎ ൯ Allocation effects incremental contribution= fund’s ending value-value calculated at the investment manager’s level Allocation effect results when fund sponsors slightly deviate from their policy allocation ெ ݎூெ = ݓ × ݓ × ൫ܣݎ − ܤݎ ൯ ୀଵ ୀଵ 6.5 Micro Attribution Overview Security-by-security analysis: ݎ = ୀଵ ൣ൫ܹ − ܹ ൯ × ሺݎ − ݎ ሻ൧ Manager can add value by overweighting outperforming securities Limitation ⇒ as the no of securities in a portfolio the impact of any individual security becomes insignificant Micro attribution using factor model of returns: Allocating the value added return to various sources of systematic return Market model is a type of factor model 6.6 Sector Weighting/Stock Selection Micro Attribution Holding Based Attributions ݎ = ∑ௌୀଵ ݓ ݎ − ∑ௌୀଵ ݓ ݎ Advantage ⇒ only holdings & their returns are required to perform attribution analysis Limitation ⇒ ignores the impact of transactions Transaction Based Attribution Mostly used in actively managed accounts with high turnover Three components: Pure sector allocation: ௌ ൫ܹ − ܹ ൯ ൫ݎ − ݎ ൯ ୀଵ Within sector selection: ௌ ܹ ൫ݎ − ݎ ൯ ୀଵ assumes same sector weight in portfolio as in benchmark Allocation selection interaction: ௌ ൫ܹ − ܹ ൯ ൫ݎ − ݎ ൯ ୀଵ Copyright © FinQuiz.com All rights reserved 2018 Study Session # 17, Reading # 33 6.7 Fundamental Factor Model Micro Attribution Combines economic sector factors with other fundamental factors Following are steps to perform fundamental factor model: Identify the fundamental factors Determine the portfolio & benchmark sensitivity to the fundamental factors at the beginning of evaluation period Specify a valid benchmark for portfolio to determine the performance of each of the factors 6.8 Fixed-Income Attribution Major determinants of F.I account returns include: ∆ in general level of IR ∆ in sector, credit quality, individual security differentials to the Y.C Factors That Contribute to Total Return of F.I Portfolio External I.R Effect Management Effect is estimated using a term structure analysis Manager has no control over external IR environment External IR environment can be separated into expected & unexpected return Estimated by a series of repricing Four components: IR management effect Sector/quality effect Security selection effect Trading actively PERFORMANCE APPRAISAL Performance appraisal ⇒evaluation of investment skill of managers & to make decisions regarding retaining or modifying portion of investment program Level & magnitude of the value-added return should be used to determine manager’s skill 7.1 Risk-Adjusted Performance Appraisal Measures Jensen’s Alpha Measures the excess of the portfolio’s return over that predicted by CAPM ߙ = ݎ − ൣݎ + ߚ ൫ݎ − ݎ ൯൧ Direct measure of performance Treynor Measure ܶ = ோ ିಷ ಲ ఉ Represents the slope of the line b/w RF & the point representing the avg return &β for the security Copyright © FinQuiz.com All rights reserved 2018 Study Session # 17, Reading # 33 7.1 Risk-Adjusted Performance Appraisal Measures M2 Sharpe Ratio ܵ = ோಲ ି Avg incremental return over a market index of a hypothetical portfolio that is created by combining the account with borrowing or lending at Rf so that its SD is identical to the market index ఙಲ Benchmark k is based on ex-post CML Like Treynor ratio, greater slope indicates a better risk return trade off ܯଶ = ݎ + ቂ ோಲ ି ఙ ෝಲ ቃ ߪො Information Ratio ܴܫ = ோಲ ିோಳ ఙ ෝಲಳ +ve (-ve) IR indicates that the manager outperforms (underperforms) the benchmark 7.2 Quality Control Charts Effective & useful way of presenting performance appraisal data Assumptions: Null hypothesis ⇒ manager has no investment skill Value added returns are independent Manager’s investment process is consistent Confidence band ⇒indicates the range within which the manager’s value added returns are expected to fall Confidence range is only for one time period 7.3 Interpreting the Quality Control Chart If value-added returns are distributed more or less randomly around the horizontal line ⇒ deviations from the benchmark are purely random We fail to reject the null hypothesis when investment results of a manager fall within the confidence band THE PRACTICE OF PERFORMANCE EVALUATION Sponsors use qualitative & quantitative factors to evaluate investment managers 8.1 Noisiness of Performance Data Past performance is not a good evaluation tool Long evaluation period must be used to determine truly superior performance Copyright © FinQuiz.com All rights reserved 2018 Study Session # 17, Reading # 33 8.2 Manager Continuation Policy Hiring new managers & firing old managers involves a significant cost in terms of money & time MCP ⇒ to the costs of manager’s turnover & to deal appropriately with future poor performance MCP is used to minimize manager turnover & to consistently apply procedures to overall managers MCP is a two part process Manager monitoring Manager reviews 8.3 Manager Continuation Policy as a Filter MCP can be used as a statistical filter to remove-ve value add managers & retain +ve value added mangers Null hypothesis ⇒ manager has no investment skill Alternative hypothesis ⇒ managers are not zero value added managers Type I error ⇒rejecting the null hypothesis when it is true Type II error ⇒ not rejecting the null when it is incorrect When the width of the confidence band is widened, type I error type II error Copyright © FinQuiz.com All rights reserved & ...2018 Study Session # 17, Reading # 33 PERFORMANCE MEASUREMENT 4.1 Performance Measurement without Intra-period External Cash Flows... representing the avg return &β for the security Copyright © FinQuiz. com All rights reserved 2018 Study Session # 17, Reading # 33 7.1 Risk-Adjusted Performance Appraisal Measures M2 Sharpe Ratio ܵ =... evaluation period must be used to determine truly superior performance Copyright © FinQuiz. com All rights reserved 2018 Study Session # 17, Reading # 33 8.2 Manager Continuation Policy Hiring new managers