Evaluating Portfolio Performance INTRODUCTION Performance evaluation involves measurement and assessment of the outcomes of the investment management decisions Performance evaluation can be divided into three components: Performance Evaluation Performance Measurement Performance Attribution → calculating account's performance based on investment-related changes in an account’s value over specified time periods 2.1 → analyzing both the sources of returns relative to a designated benchmark and the importance of those sources Performance Appraisal → assessing whether the return was generated due to skill or luck → assessing size & consistency of account's relative performance THE IMPORTANCE OF PERFORMANCE EVALUATION The Fund Sponsor’s Perspective Fund sponsors: Fund sponsors refer to owners of large pools of investable assets i.e corporate and public pension funds, endowments and foundations • Fund sponsors need to evaluate the performance of individual managers, investment results within the asset categories and their total investment programs a) It identifies strengths and weaknesses of an investment program and its policies b) It helps to identify both areas & sources of underperformance c) It provides insights regarding the results of active management d) It provides insights regarding need for additional policies/actions and/or changes in currently employed policies e) It helps the fund trustees to evaluate whether IPS policies are being followed consistently and in an appropriate & effective manner Importance of Performance Evaluation: 1) Performance evaluation provides an exhaustive “quality control” check i.e by evaluating both the performance of the fund and its constituent parts relative to objectives and the sources of that performance 2) Performance evaluation is part of the feedback step of the investment management process; therefore, it represents a fundamental component of investment policy of the fund and should be documented in its IPS 3) Performance evaluation acts as a feedback and control mechanism i.e 2.2 The Investment Manager’s Perspective From investment manager perspective, performance evaluation involves reporting investment returns along with the returns of some designated benchmark Besides, more sophisticated analysis can be provided on client’s request Performance evaluation acts as a feedback and control mechanism i.e • It is used to measure the effectiveness of all aspects of the investment processes • It is used to evaluate account’s performance relative to a benchmark THE THREE COMPONENTS OF PERFORMANCE EVALUATION Account: It refers to one or more portfolios of securities, managed by one or more investment management organizations For example, • An account can be a single portfolio invested by a single manager • An account may represent a fund sponsor’s total fund, which may involve several portfolios invested by many different managers across multiple asset categories –––––––––––––––––––––––––––––––––––––– Copyright © FinQuiz.com All rights reserved –––––––––––––––––––––––––––––––––––––– FinQuiz Notes Reading 36 Reading 36 Evaluating Portfolio Performance FinQuiz.com • An account may represent all of a fund sponsor’s assets invested in a particular asset category • An account may represent the combination of all of the portfolios managed by an investment manager according to a specific mandate PERFORMANCE MEASUREMENT Performance evaluation v/s Performance Measurement: • Performance measurement is a component of performance evaluation It represents the first step in the performance evaluation process i.e calculating returns for an account • In Performance evaluation, both the realized return and risk that was assumed to generate that return is taken into account 4.1 Performance Measurement without Intraperiod External Cash Flows Rate of return on an account: It is the percentage change in the account’s market value over some defined period of time (known as the evaluation period or measurement period), after taking into account all external cash flows It refers to return generated by the account only through investment-related sources i.e capital appreciation or depreciation and income External cash flows: External cash flows refer to contributions and withdrawals made to and from an account Internal cash flows: They include dividends and interest payments a) Account’s rate of return during evaluation period ‘t’ when there are no external cash flows: where, MV1 = market value at the end of the period MV0 = market value at the beginning of the period b) Account’s rate of return during evaluation period ‘t’ when a contribution is received at the start of the period: c) Account’s rate of return during evaluation period ‘t’ when a withdrawal is made at the start of the period: d) Account’s rate of return during evaluation period ‘t’ when a contribution is received at the end of the evaluation period: e) Account’s rate of return during evaluation period ‘t’ when a withdrawal is made at the end of the evaluation period: Practice: Example & 2, Volume 6, Reading 36 An important practical recommendation: Whenever possible, it is recommended that a fund sponsor should make contributions to, or withdrawals from, an account at the end of an evaluation period or equivalently, at the beginning of the next evaluation period when the account is valued 4.2 Total Rate of Return The emphasis on income-related return measures (e.g Current yield (income-to-price) and yield-to- maturity) was due to several factors: 1) Portfolio management emphasis on fixed-income assets 2) Due to limited computing power, return based on external cash flows was difficult to compute In contrast, the income-related return measures were simpler and could be performed by hand 3) Due to less competitive investment environment, there was less demand of accurate performance measures Total rate of return measures the change in the investor’s wealth due to both investment income (e.g dividends and interest) and capital gains/losses (both realized and unrealized) Use of Total rate of return as investment performance measure increased due to: i Increase in allocation to equity securities ii Decrease in computing costs iii Increase in larger institutional investors The Bank Administration Institute(BAI)study strongly approves the use of the total rate of return as the only valid measure of investment performance Reading 36 4.3 Evaluating Portfolio Performance FinQuiz.com = 0.10594 or 10.59% The Time-Weighted Rate of Return NOTE: The time-weighted rate of return (TWR) measures the compound rate of growth over a stated evaluation period of one unit of money initially invested in the account • In TWR, the account needs to be valued whenever an external cash flow occurs • TWR measures the actual rate of return earned by the portfolio manager • TWR is preferred to use to evaluate the performance of the portfolio manager when the manager has no control over the deposits and withdrawals made by clients When there are no external cash flows, TWR is computed as follows: In order to calculate time weighted return, first of all, holding period return for each sub-period is computed and then these sub-period returns must be linked together (known as the chain-linking process) to compute the TWR for the entire evaluation period • Note that unless the sub-periods represent a year, the time-weighted rate of return will not be expressed as an annual rate • Each subperiod return within the full evaluation period has a weight = (length of the subperiod / length of the full evaluation period) Advantage of TWR: TWR is not affected by any external cash flows to the account Disadvantage of TWR: • TWR requires determining a value for the account each time any cash flow occurs • Marking to market an account on a daily basis is administratively more cumbersome, expensive and potentially more error-prone Example: ࡲ࢘ ࢋ࢘ࢊ ࢋ ሺ࢚ࢎࢋ ࢌ࢙࢚࢘ ࢙࢞ ࢚ࢎ࢙ሻ࢘ 10,050 െ 10,000 100 ൌ ൌ 1.50% 10,000 ࡲ࢘ ࢋ࢘ࢊ ࢚࢝ ሺ࢚ࢎࢋ ࢋ࢚࢞ ࢙࢞ ࢚ࢎ࢙ሻ࢘ 10,850 െ 10,050 100 ൌ ൌ 8.96% 10,050 The annual return (based on the geometric average) over the entire period is r = [(1.0150) (1.0896)] –1 • Chain-linking process implicitly assumes that the initially invested dollar and earnings on that dollar are reinvested (or compounded) from one subperiod to the next • Generally, pure TWR is not used However despite the limitations of pure TWR, it is preferred by the mutual fund industry Practice: Example & 4, Volume 6, Reading 36 4.4 The Money-Weighted Rate of Return The money-weighted rate of return (MWR) measures the compound growth rate in the value of all funds invested in the account over the entire evaluation period It represents an internal rate of return (IRR) of an investment a) MWR is preferred to use to evaluate the performance of the portfolio manager when the manager has discretion over the deposits and withdrawals made by clients In equation form, the MWR is the growth rate R that solves: MV1= MV0(1+R)m+CF1(1+R)m-L(1)+…+CFn(1+R)m–L(n) where, m = number of time units in the evaluation period (for example, the number of days in the month) CFi = the ith cash flow L(i) = number of time units by which the ith cash flow is separated from the beginning of the evaluation period Advantages of MWR: MWR requires an account to be valued only at the beginning and end of the evaluation period Disadvantages of MWR: • MWR is highly affected by the size and timing of external cash flows to an account • It is not an appropriate to use when the investment manager has little or no control over the external cash flows to an account Practice: Example 5, Volume 6, Reading 36 Reading 36 Evaluating Portfolio Performance 4.5 TWR versus MWR FinQuiz.com Practice: Example 7, Volume 6, Reading 36 TWR MWR 1) TWR represents the growth of a single unit of money invested in the account 2) TWR is unaffected by the size and timing of external cash flows to and from the account 1) MWR represents the average growth rate of all money invested in an account 2) MWR is affected by the size and timing of external cash flows to and from the account • When funds are contributed to an account prior to a period of strong (positive) performance, MWR > TWR • When funds are withdrawn from an account prior to a period of strong (positive) performance, MWR < TWR • When funds are contributed to an account prior to a period of weak (negative) performance, MWR TWR • Under normal situations, both TWR and MWR provide similar results • When large external cash flows occur (i.e > 10% of account) and during that evaluation period, account’s performance is highly volatile, then MWR and TWR will provide significantly different results 4.7 The annualized return measures the compound average annual return earned by the account over the evaluation period It is also referred to as the compound growth rate or geometric mean return rtwr= (1+rt,1)×(1+rt,2)×…×(1+rt,n)1/n–1 Or ࢚࢘࢝࢘ ൌ ݊ඥሺ1 ݎ௧,ଵ ሻ ൈ ሺ1 ݎ௧,ଶ ሻ ൈ … ൈ ሺ1 ݎ௧, ሻ– Or where, n = number of years in the measurement period NOTE: Generally, when measurement periods are < a full year, it is inadvisable to calculate annualized returns Practice: Example 8, Volume 6, Reading 36 4.8 Practice: Example 6, Volume 6, Reading 36 Annualized Return Data Quality Issues The accuracy of performance measurement process depends on the accuracy of inputs used in measuring account’s performance NOTE: BAI and GIPS generally require the use of TWR as a measure of account performance 4.6 The Linked Internal Rate of Return Due to limitations of TWR, BAI recommends to use Linked Internal Rate of Return (LIRR) method In LIRR method, the TWR is approximated by calculating MWR over reasonably frequent time intervals and then those returns are chain-linked over the entire evaluation period • LIRR method is only appropriate to use under normal conditions i.e external cash flows are not large relative to the account (i.e not > 10% of account’s value) and account’s performance is not highly volatile • Under extreme conditions, according to BAI study recommendation, the account should be valued on the date of the intra-month cash flow instead of using LIRR method • Reported rates of return for accounts that comprise of liquid and transparently priced securities and have less external cash flow activity are relatively reliable measures of performance • In contrast, reported rates of return for accounts that comprise of illiquid and infrequently priced assets with heavy external cash flow activity are generally not reliable in nature; it is because of the following reasons: i For thinly traded securities, current market price is not always available and investors have to use estimated prices based on dealer-quoted prices i.e by using matrix pricing approach ii For highly illiquid securities, it is difficult or sometimes impossible to obtain reasonable estimates of market prices; in such cases, investors have to value these securities either at cost or the price of the last trade in those securities Reading 36 Evaluating Portfolio Performance It is essential to use appropriate data collection procedures to have reliable measures of performance i.e FinQuiz.com on a fully accrued basis • It is inadvisable to value accounts on the settlement date and without considering the accrued income • Accounts should be valued on the trade date and Performance evaluation is a relative concept i.e it involves evaluating an account’s performance relative to an appropriate designated benchmark 5.1 Concept of a Benchmark A benchmark reflects the investment style that the fund sponsor expects the manager to follow, and it is used for evaluating the manager’s performance Components of a Portfolio Return: A portfolio return (P) can be divided into following three components 1) Market (M) 2) Style (S) = (manager’s benchmark portfolio market index) = B - M 3) Active management (A) = (manager’s portfolio – benchmark) = P – B P=M+S+A For example, • When portfolio represents a broad market index fund, (B - M) will be It implies that manager has no distinct investment style i.e S = • Also (P - B) = 0; this implies that there is no active management i.e A = • Consequently, P = M Practice: Example 9, Volume 6, Reading 36 5.2 BENCHMARKS Measurable: The benchmark’s return can be readily calculated on a reasonably frequent basis Appropriate: The benchmark is consistent with the manager’s investment style or area of expertise Reflective of current investment opinions: The manager has current investment knowledge (positive, negative, or neutral) of the securities or factor exposures constituting the benchmark Specified in advance: The benchmark is specified prior to the start of an evaluation period and known to all interested parties Owned: The investment manager should be aware of and accept accountability for the constituents and performance of the benchmark 5.3 Types of Benchmarks Generally, there are seven primary types of benchmarks 1) Absolute: An absolute return can be a return objective e.g actuarial rate-of-return assumption or a minimum return target that the fund aims to exceed Advantage: It is a simple and straightforward benchmark Disadvantage: Absolute return objectives are not investable; consequently, they not meet the benchmark validity criteria 2) Manager universes: It refers to using the median manager or fund from a broad universe of managers or funds as a performance evaluation benchmark e.g fund that falls at the median when funds are ranked in descending order Properties of a Valid Benchmark Advantage: It is measurable A valid benchmark should have the following seven properties: Unambiguous: The identities and weights of securities or factor exposures constituting the benchmark are clearly defined Investable: The benchmark should represent a passive investment alternative i.e an investor can always opt to forgo active management and simply hold the benchmark Disadvantages: • Except being measurable, it fails all the benchmark validity criteria i.e it is not investable, not appropriate, ambiguous, not specified in advance, not reflective of current investment opinions and not owned by the managers • It suffers from survivorship bias • In order to use these benchmarks, fund sponsors have to rely on the accuracy of the universe Reading 36 Evaluating Portfolio Performance compiled by the compiler (third-party) 3) Broad market indexes: It refers to using broad market indexes as benchmarks e.g S&P 500, Wilshire 5000 etc for U.S common stocks; the Lehman Aggregate and the Citigroup Broad Investment-Grade (U.S BIG) Bond Indexes etc for U.S investment-grade debt Advantages: Market indexes are • • • • • • • Well recognized Easy to understand Widely available Unambiguous Generally investable Measurable Specified in advance Disadvantages: Style reflected in a market index may not be consistent with manager’s investment style e.g using S&P 500 benchmark for evaluating a microcapitalization U.S growth stock manager 4) Style indexes: It refers to using specific portions of an asset category as benchmark e.g largecapitalization growth, large-capitalization value, small-capitalization growth, and small-capitalization value (Mid-capitalization growth and value common stock indexes are also available.) Advantages: Like broad market indexes, investment style indexes are: • Well known • Easy to understand • Widely available Disadvantages: It is not appropriate: • Some style indexes contain weightings in certain securities and economic sectors that are larger than considered prudent • It may be inconsistent with the investment process of the manager being evaluated FinQuiz.com For example, in one-factor model, the return on a security, or a portfolio of securities, is regressed on the return on a broad market index (over a long period e.g 60 months): where, Rp = periodic return on an account RI = periodic return on the market index ap = “zero factor” term It represents the expected value of Rp if the factor value was zero βp = beta = sensitivity of the returns on the account to the returns on the market index εp = residual or nonsystematic element of the relationship Normal portfolio: A normal portfolio is a portfolio, which is exposed to systematic risk factors that are typical for a manager It can be constructed by using the manager’s past portfolios as a guide Advantages: Factor model-based benchmarks facilitate managers and fund sponsors to better understand manager’s investment style Disadvantages: • Factor model-based benchmarks are not always intuitive to the fund sponsor and particularly to the investment managers • Factor model-based benchmarks are not always easy to obtain • Factor model-based benchmarks are potentially expensive to use • Factor model-based benchmarks are ambiguous i.e different benchmarks with the same factor exposures (e.g same beta) can generate different returns • Factor model-based benchmarks may not be investable because the composition of a factorbased benchmark is not specified with respect to the constituent securities and their weights Practice: Example 10, Volume 6, Reading 36 It is ambiguous i.e different definitions of investment style can produce different results 5) Factor model based: Factor models are used to relate one or more systematic sources of return to the returns on an account These specified set of factor exposures can be used as a factor model-based benchmark Factors include market index, company’s size, industry, growth characteristics, financial strength etc 6) Returns based benchmarks: These benchmarks are constructed using (1) the series of a manager’s account returns over a specified period and (2) the series of returns on several investment style indexes over the same period Using these return series, an allocation algorithm solves for the particular set of allocation weights for investment style indexes that most closely track the account’s returns The returnsbased benchmark is represented by these allocation weights where, F1, F2, FK represent the values of factors through K, respectively Advantages: • Returns-based benchmarks are intuitive and easy Reading 36 Evaluating Portfolio Performance to use • They are unambiguous, measurable, investable, and specified in advance • Returns-based benchmarks are useful when only the information regarding account returns is available Disadvantages: • Like the style indexes, returns-based benchmarks may contain securities and economic sectors with greater weights than considered acceptable by managers • They may be inconsistent with the investment process of the manager being evaluated • They require sufficient number of observations to construct a statistically reliable pattern of style exposures • They are not useful to evaluate managers who rotate among style exposures 7) Custom security based benchmark: These benchmarks reflect a manager’s research universe weighted in a particular manner Advantages: • Custom security-based benchmark satisfies all of the benchmark validity criteria • It facilitates managers to monitor and control their investment processes • It facilitates fund sponsors to effectively allocate or budget risk across teams of investment managers Disadvantage: • Custom security-based benchmarks are expensive to construct and maintain • They lack transparency because they are not composed of published indexes 5.4 Building Custom Security-Based Benchmarks A valid custom security-based benchmark is constructed using the following steps: 1) Identify the prominent aspects of the manager’s investment process, selection of assets (including cash) and their weights 2) Select securities for the benchmark that are consistent with the investment process of the manager 3) Use the weighting scheme for the benchmark that is consistent with the investment process of the manager 4) Review the composition of a preliminary benchmark selected and make necessary modifications 5) Rebalance the benchmark portfolio regularly as per a predetermined schedule FinQuiz.com NOTE: A proper benchmark must clearly differentiate between the manager’s “normal” or policy investment decisions and the manager’s active investment judgments 5.5 Critique of Manager Universes as Benchmarks The median account in a particular peer group can be used as a return benchmark by the fund sponsors However, it has the following drawbacks: 1) The median account cannot be specified in advance: The median account can be established on an ex-post basis only i.e after the returns earned by all accounts have been calculated and ranked 2) Such a benchmark is not investable because no one knows beforehand who the median manager will be Moreover, the median manager changes from period to period 3) It is not unambiguous because the identity of a median manager remains unknown even after the evaluation period ends 4) As it is ambiguous in nature, it is difficult to verify its appropriateness to determine whether the investment style it represents is consistent with the account being evaluated 5) In order to use manager universes as benchmark, fund sponsors have to rely on the compiler’s representations that accounts have been appropriately screened, the integrity of the input data monitored and a uniform return calculation methodology has been used for all accounts in all periods 6) Manager universes suffer from “survivorship bias” because fund sponsors remove underperforming managers i.e underperforming accounts are removed; median will be biased upwards Without a valid reference point, using the performance of a particular manager or fund is not a suitable performance benchmark that can be used to assess investment skill of a manager 5.6 Tests of Benchmark Quality Benchmarks represent an integral part of risk management at both the investment manager and fund sponsor levels Benchmark choice is critical as it has a direct impact on measuring a manager’s investment skills Uses of good benchmark: • Fairly evaluates the manager and provides a passive alternative • Enhances the effectiveness of performance evaluation process • Highlights the contributions of skillful managers • Enhance the capability to manage investment risk Reading 36 Evaluating Portfolio Performance Effects of using Poor benchmarks: • Using poor benchmarks makes it difficult to understand and assess manager skills • Use of poor benchmarks can lead to incorrectly punishing a good manager and inappropriately rewarding a poor one • Poor benchmarks promote inefficient manager allocations and ineffective risk management • Poor benchmarks increase the chances of unpleasant surprises Tests of Benchmark Quality: Systematic biases: Over time, the benchmark should have minimal systematic biases or risks relative to the account a) Systematic bias can be measured by calculating the historical beta of the account relative to the benchmark i.e on average the historical beta of the account relative to the benchmark should be close to 1.0 b) Systematic bias can be measured by computing the correlation between A and S i.e correlation between A and S should be = It implies that active decisions should be uncorrelated with style c) The difference between the account and the market index i.e E = (P - M) and manager’s style (S) should be highly positively correlated It implies that when manager’s style outperforms (underperforms) relative to the market, we expect both the benchmark and the account to outperform (underperform) the market Tracking error: Tracking error refers to the volatility of A (active return) The volatility (standard deviation) of an account’s returns relative to a good benchmark should be less than the volatility of the account’s returns relative to a market index or other alternative benchmarks When a benchmark has low tracking error, it indicates that the benchmark is capturing important aspects of the manager’s investment style Risk characteristics: Over time, an account’s exposure to systematic sources of risk should be similar to those of the benchmark i.e at times, account risk exposures can be greater or smaller than that of a benchmark However, when the account’s risk characteristics are always greater or always smaller than those of the benchmark, it indicates that a systematic bias exists A good benchmark should reflect (not replicate) the manager’s investment process correspondence exist between the manager’s universe of potential securities and the benchmark • Low coverage indicates that the benchmark is poor Turnover: Benchmark turnover is defined as the percentage of the benchmark’s total market value that is purchased/sold for the purpose of periodic rebalancing of the benchmark • Passively managed portfolio should employ benchmarks with low turnover Positive active positions: Active position = weight of a security in an account weight of the same security in the benchmark • When a manager holds large number of positive active positions, it indicates that a good custom security-based benchmark has been constructed • When a manager holds a high proportion of negative active positions, it indicates that a benchmark poorly represents the manager’s investment style 5.7 Hedge Funds and Hedge Fund Benchmarks Hedge funds generally involve both long and short investment positions Due to short positions in an account, hedge funds involve various performance measurement, administrative and compliance issues; therefore, it is inappropriate to use a typical Long-only benchmark to evaluate their performance Also, hedge funds may have zero net position* (the value of the portfolio’s long positions equal the value of the portfolio’s short positions) or even negative net position Hence, using traditional methods to calculate returns does not yield reliable results *NOTE: ݎ௧ = • High coverage indicates that a strong ܸܯଵ − ܸܯ ܸܯ When MV0 = 0, the account’s rate of return would be either positive infinity or negative infinity Hedge Fund Benchmarks: Following three approaches can be used Estimate Value-added return i.e rv = rp- rB Coverage: Benchmark coverage is defined as: market value of securities that are present in both the benchmark & ݈݂݅ݐݎ Total market value of the portfolio FinQuiz.com where, rv = value-added return on a long-short portfolio rp = portfolio return rB = benchmark return Reading 36 Evaluating Portfolio Performance Construct separate long and short benchmarks using either returns-based or security based benchmark building approaches Note that sum of active weights = a) Return is estimated by adding the performance impacts of all individual (both long &short) positions • A return can be calculated for the period during which the individual security positions were maintained • When an individual security position changes, the previous return period ends and a new return period starts b) Rate of return for a long-short portfolio can also be estimated as follows: Return = Profit and/or loss resulting from the particular hedge fund strategy / amount of assets at risk Return = Profit and/or loss resulting from the particular hedge fund strategy / (absolute value of all the long positions + absolute value of all the short positions) FinQuiz.com • These benchmarks are then combined in appropriate proportions to create a valid benchmark for the manager • Limitation: This approach is not useful for hedge funds (e.g Macro hedge funds) that involve rapidly changing long/short leveraged positions and different asset categories (i.e equities, bonds, commodities etc.) Sharpe ratio: Sharpe ratio of a hedge fund is compared to the Sharpe ratio of universe of other hedge funds with similar investment mandates Limitations: • It suffers from the same drawbacks as that of standard manager universe benchmarks • It assumes normal distribution and uses S.D as a measure of risk; thus, it is not appropriate to use for investment strategies with non-normal distributions PERFORMANCE ATTRIBUTION Performance attribution helps to improve and enhance the portfolio management process Performance attribution involves: • Comparison of an account’s performance with that of a designated benchmark • Decomposing the account’s returns relative to those of the benchmark i.e Identification and quantification of sources of differential returns (different-from-benchmark returns) and • Identification of impact of differential returns on an account’s performance A Macro Attribution: Macro attribution refers to performance attribution that is conducted at the fund sponsor level related to the organization, which is actually conducting the performance attribution 6.1 Impact Equals Weight Times Return The fundamental rule is: Impact = (active) weight × return There are two sources of positive impact on an account’s return relative to a benchmark: 1) Selecting superior (or avoiding inferior) performing assets and 2) Investing in the superior (inferior) performing assets in greater (lesser) proportions relative to that of the benchmark • It involves examining the performance of a total fund B Micro Attribution: Micro attribution refers to performance attribution that is carried out at the investment manager level • It involves examining the performance of individual portfolios relative to designated benchmarks NOTE: The distinction between macro & micro attribution is based on specific decision variables involved; it is not Practice: Example 11 Volume 6, Reading 36 6.2 Macro Attribution Overview For a fund sponsor, the term account is referred to as “Fund” and it is defined as a total fund consisting of investments in various asset categories (e.g domestic stocks, international stocks, domestic fixed income etc.) and these investments are managed by various investment managers Reading 36 6.3 Evaluating Portfolio Performance Macro Attribution Inputs Inputs into Macro Attribution: 1) Policy allocations i.e a fund sponsor sets up a plan that determines the broad allocation of assets to stocks, bonds, and other types of securities within the Fund and to individual managers within the asset categories Policy allocations are a function of the: • Fund sponsor’s risk tolerance • Fund sponsor’s long-term expectations regarding the investment risks and rewards offered by various asset categories and money managers, and • Fund sponsor’s liabilities 2) Benchmark portfolio returns i.e • Fund sponsor selects broad market indexes as the benchmarks for asset categories and • Fund sponsor selects specific benchmarks to represent the managers’ investment styles 3) Fund returns, valuations and external cash flows: Macro attribution can be carried out in two ways: a) Using Rate-of-return metric: In rate-of-return metric, the results of the analysis are presented in terms of the effects of decision-making variables on the differential return • Rate-of-return metric requires computing fund returns at the individual manager level • It is helpful to evaluate fund sponsor’s decisions regarding manager selection b) Using a Value metric: In a value metric, the results of the analysis are presented in terms of the effects of decision-making variables on the differential return in Monetary terms • Value metric requires account valuation and external cash flow data to compute accurate rates of return • It is helpful to evaluate the impact of the fund sponsor’s investment policy decision making on the fund’s performance • Value metric approach is more accessible to both investment professionals and ordinary persons 6.4 Conducting a Macro Attribution Analysis Following are six levels or components of investment policy decision making used to analyze Fund’s performance: 1) 2) 3) 4) 5) 6) Net contributions Risk-free asset Asset categories Benchmarks Investment managers Allocation effects These investment strategies are presented in increasing order of volatility and complexity FinQuiz.com • Each decision-making level in the hierarchy is treated as an investment strategy • The investment results of each decision-making level are compared to the cumulative results of the previous levels This implies that each decisionmaking level represents a valid benchmark i.e an unambiguous, appropriate, and specified-inadvance investment alternative • Fund sponsor determines how much of the total fund’s assets are allocated to each level • The assets are allocated to a more aggressive strategy only if it is expected to generate positive incremental returns This implies that macro attribution analysis is based on computing incremental return of each investment strategy and determining the contribution of each level to the overall return of the fund Net Contributions: • Net contributions include additions to the portfolio • It is assumed that net cash inflows are invested at a zero rate of return i.e assets earn a zero return Thus, Change in the value of fund = Total amount of net contributions Ending value of a fund under the Net Contributions investment strategy = Beginning value + Net contributions Risk-Free Asset: • Risk-free asset investment strategy involves investing all of the Fund’s assets in a risk-free asset (i.e 90-day T-Bills) • It is viewed as a conservative strategy • This strategy assumes that invested assets i.e the Fund’s beginning value and its net external cash inflows (accounting for the dates on which those flows occur) earn risk-free return i.e Change in Fund’s value = Ending value of a fund under the Risk-free asset investment strategy – Beginning value (i.e ending value of the fund under the Net Contributions investment strategy) NOTE: When net contribution does not represent a single, beginning-of-month cash flow, fund’s incremental value (i.e Change in Fund’s value) cannot be obtained simply by multiplying fund’s Beginning value by risk-free rate Asset Category: • Asset Category investment strategy assumes that the Fund’s beginning value and external cash flows are invested passively based on the fund sponsor’s policy allocations to the specified asset category benchmarks • Asset Category investment strategy is a pure index fund approach Reading 36 Evaluating Portfolio Performance a) From a return-metric perspective, the incremental return contribution is computed as follows: FinQuiz.com NOTE: Summed across all managers and asset categories, Aggregate manager benchmark return = wi× wij× rBij where, rAC = incremental return contribution of the Asset Category investment strategy rCi = return on the ith asset category rf = risk-free return wi = policy weight assigned to asset category i A = number of asset categories b) From a value-metric perspective, the incremental contribution of the Asset Category investment strategy is computed as follows: Sum [(Each asset category’s policy proportion of the Fund’s beginning value and all net external cash inflows) × (asset category’s benchmark rate of return - risk-free rate)] b) From a value-metric perspective, the incremental contribution of the Benchmarks strategy is calculated as follows: Sum [each manager’s policy proportion of the total fund’s beginning value and net external cash inflows × (manager’s benchmark return – return of the manager’s asset category)] Misfit return or Style bias = Return generated by the aggregate of the managers’ benchmarks - Return generated by the aggregate of the asset category benchmarks Investment Managers: Benchmarks: • The benchmark level investment strategy separates the impact of the managers’ investment styles (represented by the managers’ benchmarks) on the Fund’s value from the effect of the managers’ active management decisions • The benchmark level investment strategy assumes that the Fund’s beginning value and net external cash inflows are passively invested in the aggregate of the managers’ respective benchmarks • The benchmark level investment strategy is a passively managed investment in the benchmarks of the Fund’s managers i.e it is a pure index fund approach • In this strategy, Aggregate manager benchmark return = Weighted* average of the individual managers’ benchmark returns *Where, weights are based on the fund sponsor’s policy allocations to the managers • Investment managers level investment strategy separates the impact of the managers’ active management decisions on the change in the value of a Fund • ‘Investment managers’ level strategy assumes that the fund sponsor has invested in each of the managers according to the managers’ policy allocations In simple words, funds are allocated according to policy as if funds are invested directly in the aggregate of the managers’ actual portfolios • In this strategy, weights assigned to the managers’ returns to estimate aggregate manager return are based on the fund sponsor’s policy allocations to the managers Return to the Investment managers level = Sum (active managers’ returns – their benchmark returns) From the return-metric perspective, contribution of the Investment Managers strategy is computed as follows: a) From a return-metric perspective, where, where, rIS = incremental return contribution of the Benchmarks strategy rBij = return for the jth manager’s benchmark in asset category i rCi = return on the ith asset category wi = policy weight assigned to the ith asset category wij = policy weight assigned to the jth manager in asset category i A = number of asset categories M = number of managers rAij = actual return on the jth manager’s portfolio within asset category i and the other variables are as defined previously Important: The analysis performed at the Investment Managers level facilitates to evaluate the contribution of fund’s managers to the Fund’s performance given that they were funded at their respective policy allocations NOTE: • Allocation of assets to the Fund’s managers is determined by fund sponsors; but they have no control over investment performance of Reading 36 Evaluating Portfolio Performance managers o In order to determine the contribution of the fund sponsor → it is more appropriate to calculate the impact of the differences between the managers’ actual and policy allocations on the Fund’s performance • In contrast, the managers have control over their investment performance, but they not generally determine the allocation of assets placed under their management In order to determine the contribution of the Fund’s managers→ it is more appropriate to assume that they were funded at their respective policy allocations Allocation Effects: • The Allocation Effects incremental contribution is a reconciling factor i.e Allocation Effects incremental contribution = Fund’s ending value - Value calculated at the Investment Managers level • Allocation Effects investment strategy’s contribution results when fund sponsors slightly deviate from their policy allocations • When funds are invested in all of the managers and asset categories exactly according to the established policy allocations, then the Allocation Effects investment strategy’s contribution would be zero Important: The analysis done at the Allocation Effects level can be used to evaluate the impact of deviations of fund sponsor’s decisions from investment manager policy allocations on the Fund’s performance relative to a strategy of consistently maintaining the stated policy allocations FinQuiz.com where, wpi wBi ri rB n = = = = = proportions of the Portfolio proportions of the benchmark return on security i return on the Portfolio’s benchmark number of securities Sources of manager’s value added return i The weights assigned to securities in the Portfolio relative to their weights in the benchmark and ii The returns on the securities relative to the overall return on the benchmark Relative-to-Benchmark Weights and Returns wpi – wBi ri – rB Performance Impact versus Benchmark Positive Positive Positive Negative Positive Negative Positive Negative Negative Negative Negative Positive Source: Exhibit 7, Volume 6, Reading 36 Interpretation: • A manager can add value by overweighting (underweighting) outperforming (underperforming) securities relative to the benchmark • In contrast, the manager can detract value by overweighting (underweighting) underperforming (outperforming) securities relative to the benchmark NOTE: When active managers are hired, fund’s assets are exposed to two additional sources of risks & returns i.e investment style and active management skill 6.5 Limitations of Security-by-security micro attribution: Security-by-security analysis is less useful because as the number of securities increase in a portfolio, the impact of any individual security on portfolio returns becomes insignificant Micro Attribution Overview In micro attribution, the term account refers to a “Portfolio” and it is defined as a specific portfolio invested by a specific investment manager A manager’s value added or active return is computed as follows: Value-added/active return = rv = Portfolio return – Benchmark return = rp - rB Security-by-security analysis: Micro attribution using factor model of returns: This approach involves allocating the value-added return to various sources of systematic returns In factor model, return on a security (or portfolio of securities) is regressed on changes in various factors Factors include: • Sector or industry membership variables • Financial variables i.e balance sheet or income statement items • Macroeconomic variables i.e changes in interest rates, inflation, or economic growth Example: A market model is a type of factor model in which a security’s or portfolio’s return is regressed on the movements of a broad market index Reading 36 Evaluating Portfolio Performance Where, βp = beta of security represents the exposure of a security to a broad market index Practice: Example 12 Volume 6, Reading 36 FinQuiz.com Three components of value-added return: The valueadded return can be decomposed into three components Value-added Return = Pure sector allocation + Allocation/selection interaction + Within-Sector selection 1) Pure sector Allocation: 6.6 Sector Weighting/Stock Selection Micro Attribution A Holdings-based or “buy-and-hold” attribution: In this approach, the manager’s value-added return is computed as follows: Value-added return = Weighted average return on the economic sectors in the Portfolio Weighted average return on the economic sectors in the benchmark wpj wBj rpj rBj S = Portfolio weight of sector j = Benchmark weight of sector j = Portfolio return of sector j = Benchmark return of sector j = number of sectors • In this buy-and-hold approach, each sector’s contribution to the total allocation and selection effects depends upon the beginning portfolio and benchmark weights in that sector and the constituent securities’ returns due to price appreciation and dividend income • The buy-and-hold approach ignores the impact of transactions during the evaluation period Advantage of the buy-and-hold approach: It requires only holdings and their returns to perform attribution analysis Limitations of the buy-and-hold approach: Since the buy-and-hold approach ignores the impact of transactions during the evaluation period, the account’s buy-and-hold return will be different from its timeweighted total return • Thus, a reconciling item named as “trading & other” is used to reflect the net impact of cash flows and security purchases and sales during the evaluation period B Transaction-based attribution analysis: This approach is mostly used in actively managed accounts with high turnover and consequently with a significant “trading & other” factor where, Wpj – WBj = Difference between the weights of the sector in the portfolio and weights of the sector in the benchmark rBj – rB = Difference between the returns for the sector in the benchmark and the return of the overall benchmark (i.e mean return of the benchmark) S = number of sectors • The pure sector allocation return assumes that within each sector, the manager held the same securities as the benchmark and in the same proportions • In pure sector allocation, the impact on relative performance is attributed only to the sectorweighting decisions of the manager 2) Within sector Selection: where, WBj = Weight of the sector in the benchmark rPj – rBj = Difference between the returns of the sector in the Portfolio and the return of the sector in the benchmark S = number of sectors • The Within-Sector Selection return assumes that the weights of each sector in the Portfolio are the same as those of the overall benchmark; however, within the sector the securities may be held by the manager in different-from-benchmark weights • In within sector selection, the impact on relative performance is attributed only to the security selection decisions of the manager 3) Allocation/selection Interaction: It involves the joint impact of the decisions regarding weights of the sectors and individual securities in the portfolio Reading 36 Evaluating Portfolio Performance FinQuiz.com where, NOTE: WPj – WBj = Difference between the weights of the sector in the portfolio and weights of the sector in the benchmark rPj – rBj = Difference between the returns of the sector in the Portfolio and the return of the sector in the benchmark S = number of sectors The manager’s investment skill or value added can be attributed to the following four primary sources: • Generally, when an appropriate benchmark (i.e without any material systematic bias) is selected, the Allocation/Selection Interaction impact will be relatively small • Since the Allocation/Selection Interaction impact is usually due to the security selection decisions, it is combined with the Within-Sector Selection impact Practice: Example 13, 14 & 15, Volume 6, Reading 36 6.7 1) Market timing: It is composed of i Portfolio’s Cash position ii Portfolio’s beta 2) Exposures to fundamental factors 3) Exposures to economic sectors 4) A specific or unexplained return component: This return is attributed to the investment manager Allocation/selection attribution v/s Fundamental Factor Model Micro Attribution Allocation/selection Attribution Fundamental Factor Model Micro Attribution: Strengths • It can be used to decompose performance effects between sectors and securities • It is relatively easy and simple to calculate • It helps to identify factors that can affect portfolio performance other than security selection and sector allocation • It provides a better understanding of the manager’s investment style Weaknesses • It requires identifying an appropriate benchmark • It can generate allocation/ selection interaction; which may create confusion • It requires determining the exposures to factors at the beginning of the evaluation period • It is relatively a complex approach Fundamental Factor Model Micro Attribution Fundamental factor model micro attribution combines economic sector factors with other fundamental factors i.e company’s size, its industry, its growth characteristics, its financial strength etc • It facilitates to analyze the source of portfolio returns based on actual factor exposures relative to manager’s normal factor exposures • This approach is similar to Return-based style analysis However, unlike return-based style analysis, Fundamental factor model micro attribution analysis involves use of other fundamental factors i.e management’s use of leverage, market timing, sector rotation, firm’s size etc Steps of performing Fundamental factor model micro attribution analysis: 1) First of all, identify the fundamental factors 2) Determine the exposures (sensitivity) of the portfolio and the benchmark to the fundamental factors of the model at the beginning of the evaluation period 3) Specify a valid benchmark for the portfolio e.g it can be risk exposures of a style or custom index or a set of normal factor exposures that were typical of the manager’s portfolio over time 4) Determine the performance of each of the factors Practice: Example 16, Volume 6, Reading 36 6.8 Fixed-Income Attribution The sector weighting/stock selection approach to micro attribution can be employed for both fixed income and equity accounts However, in case of fixed-income accounts, it is not useful in analyzing sources of fixedincome account returns because it only facilitates to Reading 36 Evaluating Portfolio Performance separate allocation and selection effects among bond market sector Major determinants of Fixed-income account returns include: • Changes in the general level of interest rates (represented by the government/default-free yield curve) • Changes in sector*, credit quality, individual security differentials, or nominal spreads, to the yield curve o Non-treasury Fixed-income securities underperform relative to Treasury securities when the yield curve rises and the nominal spread widens o Non-treasury Fixed-income securities outperform Treasury when the yield curve falls and the nominal spread remains unchanged or narrows *Changes in sector spread represent an additional source of interest rate exposure e.g sector spread widens when due to higher perceived business risk, investors require higher yields Credit quality spread also changes with the changes in the required yields for fixed-income securities of a given rating Note that the impact of changes in interest rate and spread on the investment performance of a given portfolio depends upon the nature of the market changes and the interest-sensitive characteristics of the portfolio This implies that different fixed-income instruments and portfolios will respond differently to yieldcurve movements Factors that contribute to total return of a fixed-income portfolio include: 1) External interest rate effect: The return attributed to the external interest rate environment is estimated using a term structure analysis of a universe of Treasury securities • The overall external interest rate effect represents the performance of a passive, default-free bond portfolio • The manager does not have any control over the external interest rate environment The manager can only adjust the portfolio’s interest-sensitive characteristics for the expected changes in yieldcurve and spread External interest rate effect can be further separated into: a) Expected Return: It refers to a return generated from the implied forward rates (the expected return) b) Unexpected Return: It refers to the difference between the actual realized return and the market implied return from the forward rates FinQuiz.com 2) Management effect: The management effect is estimated by a series of re-pricings It provides information regarding the effects of management process on the portfolio returns The management effect can be decomposed into four components: a) Interest rate management effect: It indicates the ability of the manager to predict interest rate changes The interest rate management effect can be further divided into returns due to duration, convexity, and yield-curve shape changes How to calculate interest rate management contribution (return): Reprice each security in the portfolio by treating it as a default-free security The interest rate management contribution =Aggregate return of these repriced securities – Return of the entire Treasury universe b) Sector/quality effect: It is used to measure the ability of the manager to over-weight outperforming sectors and under-weight underperforming sectors How to calculate sector/quality return: Reprice each security in the portfolio using the average yield premium in its respective category and calculate the gross return using those prices Sector/quality return = Gross return - external interest rate effect - interest rate management effect c) Security selection effect: It is used to measure the ability of the manager to select outperforming assets (securities) within the selected sectors Security selection effect for each security = Total return of a security –all the other components Portfolio security selection effect = market-value weighted average of all the individual security selection effects d) Trading activity: It represents the effect of sales and purchases of bonds over a given period It can be used to evaluate the ability of managers to trade efficiently Trading activity return = Total portfolio return – all the other components NOTE: Fixed income portfolio attribution analysis is complex and data/computation intensive Reading 36 Evaluating Portfolio Performance FinQuiz.com Source: Exhibit 13, Volume 6, Reading 36 Refer to example on Volume 6, Reading 36, PERFORMANCE APPRAISAL The objective of performance appraisal is to evaluate investment skill of managers and to make decisions regarding retaining or modifying portions of investment program • Investment skill refers to the ability to outperform an appropriate benchmark consistently over time • A skillful manager is expected to produce a larger value-added return more frequently than his or her less talented peers It is important to note that manager’s skill should not be determined solely on the level of value-added return; rather, it should be determined by the magnitude of the value-added return relative to the variability of value-added return 7.1 • It is important to note that Jensen’s alpha is a direct (absolute) measure of performance i.e it measures performance of a portfolio without comparing it to other portfolios *Expected Return refers to return required to compensate for systematic according to SML Treynor Measure (reward-to-volatility or excess return to nondiversifiable risk) Treynor’s measure is used to measure portfolio’s average excess return per unit of systematic risk Risk-Adjusted Performance Appraisal Measures Performance appraisal measures are used to compare returns generated by an account manager with the account’s corresponding risk (i.e the account’s market/systematic risk, as measured by its beta and the account’s total risk, as measured by its standard deviation) Types of Risk-adjusted Performance Appraisal Measures: Ex post Alpha or Jensen’s alpha The ex post alpha or Jensen’s alpha measures the excess of the portfolio’s return over that predicted by the CAPM during the evaluation period i.e Alpha = Actual return on the portfolio during evaluation period – Expected return on the portfolio given its systematic risk (measured by its beta)* • Treynor’s measure represents the slope of the line between the Risk-free rate and the point representing the average return and beta for the security o Greater slope indicates a better risk-return tradeoff Note that any portfolio with a positive ex-post alpha must plot above the ex-post SML o Thus, higher Treynor’s measure indicates better performance • Like the ex post alpha, the Treynor measure relates an account’s excess returns to its systematic risk and the benchmark is based on ex-post SML Sharpe Ratio (reward-to-variability) Sharpe ratio measures the portfolio’s average excess return per unit of total risk (measured by standard deviation of returns) i.e α=rP – [rf + βP(rM – rf)] • Its benchmark is based on ex-post Security Market Line (SML) • A portfolio that consistently generates positive excess return (adjusted for risk) will have a positive alpha and it would plot above the SML • A portfolio that consistently generates negative excess return (adjusted for risk) will have a negative alpha and it would plot below the SML • A portfolio that generates zero alpha would plot on the SML • In case of Sharpe ratio, benchmark is based on expost capital market line (CML) • Like Treynor ratio, greater slope indicates a better risk-return tradeoff Reading 36 Evaluating Portfolio Performance FinQuiz.com M2 skill M2 represents the mean incremental return over a market index of a hypothetical portfolio which is created by combining the account with borrowing or lending (leveraging or de-leveraging, respectively*) at the riskfree rate so that its standard deviation is identical to that of the market index results regarding the existence of manager skill When a portfolio is completely diversified All measures will agree on ranking of portfolios because with complete diversification, total variance = systematic variance When portfolios are not completely diversified The Treynor and Jensen measures can rank relatively undiversified portfolios much higher than the Sharpe measure& M2 • M2 can be used to compare the portfolio return to that predicted by the CML o When M2 measure for the portfolio > ( (