Global Edition Chapter 25 Bond Performance: Measurement and Evaluation

© 2013 Pearson Education Learning Objectives After reading this chapter, you will understand  the difference between performance measurement and performance evaluation  the various methods for calculating the rate of return over some evaluation period: the arithmetic average rate of return, the time-weighted rate of return, and the dollar-weighted rate of return  the impact of client contributions and withdrawals on the calculated return

© 2013 Pearson Education Learning Objectives (continued) After reading this chapter, you will understand  the method of calculating return that minimizes the effect of client contributions and withdrawals  why it is necessary to establish a benchmark  how normal portfolios are created and the difficulties of creating them  what a fixed-income performance attribution model is and why it is useful in assessing the performance of a portfolio manager

© 2013 Pearson Education Performance Measures  The starting point for evaluating the performance of a manager is measuring return.  Because different methodologies are available and these methodologies can lead to quite disparate results, it is difficult to compare the performances of managers.  Consequently, there is a great deal of confusion concerning the meaning of the data provided by managers to their clients and their prospective clients.  This has led to abuses by some managers in reporting performance results that are better than actual performance.  To mitigate this problem the Committee for Performance Standards of the Association for Investment Management and Research (now the CFA Institute) has established standards for calculating performance results and how to present those results.

© 2013 Pearson Education Performance Measures (continued)  Alternative Return Measures The dollar return realized on a portfolio for any evaluation period (i.e., a year, month, or week) is equal to the sum of i.the difference between the market value of the portfolio at the end of the evaluation period and the market value at the beginning of the evaluation period ii.any distributions made from the portfolio In equation form, the portfolio’s return can be expressed as follows: where R p = return on the portfolio, MV 1 = portfolio market value at the end of the evaluation period; MV 0 = portfolio market value at the beginning of the evaluation period; and, D = cash distributions from the portfolio to the client during the evaluation period.

© 2013 Pearson Education  Alternative Return Measures EXAMPLE. To illustrate the calculation of a return, assume the following information for an external manager for a pension plan sponsor: The portfolio’s market value at the beginning and end of the evaluation period is $25 million and $28 million, respectively, and during the evaluation period $1 million is distributed to the plan sponsor from investment income. What is the portfolio return? Inserting our values of MV 1 = $28,000,000, MV 0 = $25,000,000, and D = $1,000,000, we have: Performance Measures (continued)

© 2013 Pearson Education  Alternative Return Measures There are three assumptions in measuring return as given by the above equation. i.It assumes that a period’s cash inflow into the portfolio from interest is either distributed or reinvested in the portfolio. ii.If there are distributions from the portfolio, they occur at the end of the evaluation period or are held in the form of cash until the end of the evaluation period. iii.No cash is paid into the portfolio by the client. Performance Measures (continued)

© 2013 Pearson Education  Alternative Return Measures From a practical point of view the three assumptions limit the portfolio return application. The longer the evaluation period, the more likely the assumptions will be violated. Thus, a return calculation made over a long period of time, if longer than a few months, would not be very reliable because of the assumption underlying the calculations that all cash payments and inflows are made and received at the end of the period. Not only does the violation of the assumptions make it difficult to compare the returns of two managers over some evaluation period, but it is also not useful for evaluating performance over different periods. Performance Measures (continued)

© 2013 Pearson Education  Alternative Return Measures The way to handle practical issues when computing a portfolio return is to calculate the return for a short unit of time such as a month or a quarter. We call the return so calculated the subperiod return. To get the return for the evaluation period, the subperiod returns are then averaged. There are three methodologies that have been used in practice to calculate the average of the subperiod returns: i.the arithmetic average rate of return ii.the time-weighted rate of return (also called the geometric rate of return) iii.the dollar-weighted rate of return. Performance Measures (continued)

© 2013 Pearson Education  Arithmetic Average Rate of Return The arithmetic average rate of return is an unweighted average of the subperiod returns with the general formula as: where R A = arithmetic average rate of return; R pk = portfolio return for subperiod k for k = 1, …, N; and, N = number of subperiods in the evaluation period. It is improper to interpret the arithmetic average rate of return as a measure of the average return over an evaluation period. The proper interpretation is that it is the average value of the withdrawals (expressed as a fraction of the initial portfolio market value) that can be made at the end of each subperiod while keeping the initial portfolio market value intact. Performance Measures (continued)

© 2013 Pearson Education  Arithmetic Average Rate of Return EXAMPLE. We now illustrate the calculation of the arithmetic average rate of return as an unweighted average of the subperiod returns using the general formula. Assume the portfolio returns were –10%, 20%, and 5% in July, August, and September, respectively. What is the arithmetic average monthly return? Inserting in our given values of R p1 = –10%, R p2 = 20%, and R p3 = 5% for N = 3, we have: Performance Measures (continued)

© 2013 Pearson Education  Time-Weighted Rate of Return The time-weighted rate of return measures the compounded rate of growth of the initial portfolio market value during the evaluation period, assuming that all cash distributions are reinvested in the portfolio. It is also commonly referred to as the geometric rate of return because it is computed by taking the geometric average of the portfolio subperiod returns computed from equation. The general formula is R T = [(1 + R P1 )(1 + R P2 )... (1 + R PN )] 1/ N – 1 where R T is the time-weighted rate of return, RP k is the return for subperiod k, and N is the number of subperiods. Performance Measures (continued)

© 2013 Pearson Education  Time-Weighted Rate of Return EXAMPLE. Let us assume that the portfolio returns were 10%, 20%, and 5% in July, August, and September, as in our previous example. What is the time-weighted rate of return? Inserting in our given values of R p1 = –10%, R p2 = 20%, and R p3 = 5% for N = 3, we have: R T = [(1 + R P1 )(1 + R P2 )... (1 + R PN )] 1/N – 1  R T = [(1 + – 0.10)( )( )] 1/3 – 1  R T = [(0.90)(1.20)(1.05)] 1/3 – 1  R T = or about 4.28% Performance Measures (continued)

© 2013 Pearson Education  Time-Weighted Rate of Return In general, the arithmetic and time-weighted average returns will give different values for the portfolio return over some evaluation period. This is because in computing the arithmetic average rate of return, the amount invested is assumed to be maintained (through additions or withdrawals) at its initial portfolio market value. The time-weighted return, on the other hand, is the return on a portfolio that varies in size because of the assumption that all proceeds are reinvested. Performance Measures (continued)

© 2013 Pearson Education  Time-Weighted Rate of Return In general, the arithmetic average rate of return will exceed the time-weighted average rate of return. The exception is in the special situation where all the subperiod returns are the same, in which case the averages are identical. The magnitude of the difference between the two averages is smaller the less the variation in the subperiod returns over the evaluation period.  For example, suppose that the evaluation period is four months and that the four monthly returns are as follows: RP 1 = 0.04; RP 2 = 0.06 ; RP 3 = 0.02 ; RP 4 = ─  The average arithmetic rate of return is 2.5% and the time- weighted average rate of return is 2.46%, which is a small difference.  In our earlier example in which we calculated an average rate of return of 25% but a time-weighted average rate of return of 0%, the large discrepancy is due to the substantial variation in the two monthly returns. Performance Measures (continued)

© 2013 Pearson Education  Dollar-Weighted Rate of Return The dollar-weighted rate of return is computed by finding the interest rate that will make the present value of the cash flows from all the subperiods in the evaluation period plus the terminal market value of the portfolio equal to the initial market value of the portfolio. Cash flows are defined as follows: A cash withdrawal is treated as a cash inflow. So, in the absence of any cash contribution made by a client for a given time period, a cash withdrawal is a positive cash flow for that time period. A cash contribution is treated as a cash outflow. Consequently, in the absence of any cash withdrawal for a given time period, a cash contribution is treated as a negative cash flow for that period. If there are both cash contributions and cash withdrawals then i.if cash withdrawals exceed cash contributions, then there is a positive cash flow ii.if cash withdrawals are less than cash contributions, then there is a negative cash flow. Performance Measures (continued)

© 2013 Pearson Education  Dollar-Weighted Rate of Return The dollar-weighted rate of return is simply an internal rate- of-return calculation and hence it is also called the internal rate of return. The general formula for the dollar-weighted return is where R D = dollar-weighted rate of return; V 0 = initial market value of the portfolio; V N = terminal market value of the portfolio; and, C k = cash flow for the portfolio (cash inflows minus cash outflows) for subperiod k for k = 1,..., N. Notice that it is not necessary to know the market value of the portfolio for each subperiod to determine the dollar- weighted rate of return. Performance Measures (continued)

© 2013 Pearson Education  Dollar-Weighted Rate of Return The dollar-weighted rate of return and the time-weighted rate of return will produce the same result if no withdrawals or contributions occur over the evaluation period and all investment income is reinvested. The problem with the dollar-weighted rate of return is that it is affected by factors that are beyond the control of the manager. Specifically, any contributions made by the client or withdrawals that the client requires will affect the calculated return. This makes it difficult to compare the performance of two managers. Performance Measures (continued)

© 2013 Pearson Education  Annualizing Return The evaluation period may be less than or greater than one year. Typically, return measures are reported as an average annual return. This requires the annualization of the subperiod returns. The subperiod returns are typically calculated for a period of less than one year. The subperiod returns are then annualized using the following formula: annual return = (1 + average period return) number of periods in year – 1 Performance Measures (continued)

© 2013 Pearson Education Performance Attribution Analysis  Bond attribution models seek to identify the active management decisions that i.contributed to the performance of a portfolio ii.give a quantitative assessment of the contribution of these decisions  The performance of a portfolio can be decomposed in terms of four active strategies in managing a fixed- income portfolio: i.interest-rate expectation strategies ii.yield curve expectations strategies iii.yield spread strategies iv.individual security selection strategies

© 2013 Pearson Education Performance Attribution Analysis (continued)  Benchmark Portfolios To evaluate the performance of a manager, a client must specify a benchmark against which the manager will be measured. There are two types of benchmarks that have been used in evaluating fixed-income portfolio managers: i.market indexes published by dealer firms and vendors ii.normal portfolios

© 2013 Pearson Education  Benchmark Portfolios A normal portfolio is a customized benchmark that includes “a set of securities that contains all of the securities from which a manager normally chooses, weighted as the manager would weight them in a portfolio.” Thus a normal portfolio is a specialized index. It is argued that normal portfolios are more appropriate benchmarks than market indexes because they control for investment management style, thereby representing a passive portfolio against which a manager can be evaluated. Performance Attribution Analysis (continued)

© 2013 Pearson Education  Benchmark Portfolios The construction of a normal portfolio for a manager requires i.defining the universe of fixed-income securities to be included in the normal portfolio ii.determining how these securities should be weighted (i.e., equally weighted or capitalization weighted) Plan sponsors work with pension consultants to develop normal portfolios for a manager. The consultants use vendor systems that have been developed for performing the needed statistical analysis and the necessary optimization program to create a portfolio displaying similar factor positions to replicate the “normal” position of a manager. A plan sponsor must recognize that there is a cost to developing and updating the normal portfolio. Performance Attribution Analysis (continued)

© 2013 Pearson Education  Benchmark Portfolios A more appropriate benchmark for institutional investors such as defined benefit pension plans is one that reflects its liability structure. It has been argued that the major reason for the failure of both public and private defined benefit plans is the wrong benchmarks have been used. Instead of using a bond index as is commonly used, the appropriate benchmark should be one that is customized liability index based on a specific pension plan’s actuarially determined liability structure. Performance Attribution Analysis (continued)

© 2013 Pearson Education  Performance Attribution Analysis Models Clients of asset management firms need to have more information than merely if a portfolio manager outperformed a benchmark and by how much. They need to know the reasons why a portfolio manager realized the performance relative to the benchmark. It is possible that the manager can outperform a benchmark due to a mismatch in duration and invested in specific securities that did poorly. There is no way that the client can determine that by simply looking at the portfolio’s return relative to the benchmark’s return. Performance Attribution Analysis (continued)

© 2013 Pearson Education  Performance Attribution Analysis Models There are single metrics that have been commonly used to measure performance. Although useful, single metric do not provide sufficient more information about performance to address questions that need answers. The model that can be used is performance attribution analysis, a quantitative technique for identifying the sources of portfolio risk and performance so that the contributions of members of the portfolio management team can be measured and the major portfolio decisions can be quantified. Performance Attribution Analysis (continued)

© 2013 Pearson Education  Performance Attribution Analysis Models There are several performance attribution models that are available from third-party entities. In selecting a third-party model, there are requirements that a good attribution model should possess in order to evaluate the decision-making ability of the members of the portfolio management team: additivity, completeness, and fairness. Additivity means that contribution to performance of two or more decision makers of the portfolio management team should be equal to the sum of the contributions of those decision makers. Completeness means that when the contribution to portfolio performance of all decision makers is added up, the result should be equal to the contribution to portfolio performance relative to the benchmark. Fairness means that the portfolio management team members should view the performance attribution model selected as being fair with respect to representing their contribution. Performance Attribution Analysis (continued)

© 2013 Pearson Education  Types of Performance Attribution Models Performance attribution models can be classified into three types: 1)sector-based attribution models, 2)factor-based attribution models, and 3)hybrid sector-based/factor-based attribution models. The simplest model is the sector-based attribution, also referred to as the Brinson model. In this model, the portfolio return relative to the benchmark is represented by two decisions: 1)the allocation of funds among the different sectors and 2)the selection of the specific securities within each sector. → The first decision is referred to as the asset allocation decision and the second the security selection decision. Performance Attribution Analysis (continued)

© 2013 Pearson Education  Types of Performance Attribution Models Factor-based attribution models actually allow a decomposition of the yield curve risk into level risk and changes in the shape of the yield curve. For example, suppose that the attribution due to yield curve risk is determined to be as follows: Risk FactorPortfolio DPortfolio EPortfolio F Yield curve risk1401–60 Level risk Shape risk5−59−63 Notice that once yield curve risk is decomposed as shown above, it turns out that the manager of Portfolio E did indeed make interest rate bets. It turns out that the two bets almost offset each other so that net there was only a one basis point return attributable to the interest rate bet. Portfolio D’s bet on changes in the shape of the yield curve. The interest rate bet manager basically made a major duration bet but virtually no by the manager of Portfolio F was on changes in the shape of the yield curve but otherwise was basically duration neutral. Performance Attribution Analysis (continued)

© 2013 Pearson Education  Types of Performance Attribution Models As the name suggests, a hybrid sector- based/factor-based attribution model combines the previous two attribution models. This model allows for much more detail regarding not only the bets on the primary systematic risk factors driving returns but the impact of decisions with respect to sector and security selection. The level of detail in such models depends on what might be sought by the client or the portfolio manager. Performance Attribution Analysis (continued)

© 2013 Pearson Education Key Points ● Performance measurement involves calculation of the return realized by a portfolio manager over some evaluation period. ● Performance evaluation is concerned with determining whether the portfolio manager added value by outperforming the established benchmark and how the portfolio manager achieved the calculated return. ● The rate of return expresses the dollar return in terms of the amount of the initial investment (i.e., the initial market value of the portfolio). ● Three methodologies have been used in practice to calculate the average of the sub-period returns: (1) the arithmetic average rate of return, (2) the time-weighted (or geometric) rate of return, and (3) the dollar-weighted return.

© 2013 Pearson Education Key Points (continued) ● The arithmetic average rate of return is the average value of the withdrawals (expressed as a fraction of the initial portfolio market value) that can be made at the end of each period while keeping the initial portfolio market value intact. ● The time-weighted rate of return measures the compounded rate of growth of the initial portfolio over the evaluation period, assuming that all cash distributions are reinvested in the portfolio. The time-weighted return is the return on a portfolio that varies in size because of the assumption that all proceeds are reinvested. In general, the arithmetic average rate of return will exceed the time-weighted average rate of return. The magnitude of the difference between the two averages is smaller the less the variation in the sub-period returns over the evaluation period.

© 2013 Pearson Education Key Points (continued) ● The dollar-weighted rate of return is computed by finding the interest rate that will make the present value of the cash flows from all the sub-periods in the evaluation period plus the terminal market value of the portfolio equal to the initial market value of the portfolio. The dollar-weighted rate of return is an internal rate-of-return calculation and will produce the same result as the time-weighted rate of return if (1) no withdrawals or contributions occur over the evaluation period, and (2) all coupon interest payments are reinvested. ● The problem with using the dollar-weighted rate of return to evaluate the performance of money managers is that it is affected by factors that are beyond the control of the money manager. Specifically, any contributions made by the client or withdrawals that the client requires will affect the calculated return, making it difficult to compare the performance of two portfolio managers.

© 2013 Pearson Education ● The role of performance evaluation is to determine if a portfolio manager added value beyond what could have been achieved by a passive strategy in a benchmark portfolio. The analysis requires the establishment of a benchmark. ● One such benchmark is a normal portfolio. This is a customized benchmark that includes a set of securities that contains the universe of securities that a manager normally selects from and weighted as the manager would weight them in a portfolio. Advocates claim that normal portfolios are more appropriate benchmarks than market indexes because they control for investment management style, thereby representing a passive portfolio against which a manager can be evaluated. Key Points (continued)

© 2013 Pearson Education ● For defined benefit pension plans, a more appropriate benchmark would be a customized liability index determined by the fund’s actuarially projected future liabilities. ● Performance attribution models can be used explain why the active return of a portfolio was realized. The three types of performance attribution models available are sector-based attribution models, factor-based attribution models, and hybrid sector-based/factor-based attribution models. Key Points (continued)