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Portfolio Performance Evaluation

Portfolio Performance Evaluation. Portfolio Returns . Stocktrak Calculation straight forward $5 million – no cash injection or withdrawal Same for benchmark Not the case for portfolio managers in practice. Calculating Portfolio Return.

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Portfolio Performance Evaluation

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  1. Portfolio Performance Evaluation

  2. Portfolio Returns • Stocktrak • Calculation straight forward • $5 million – no cash injection or withdrawal • Same for benchmark • Not the case for portfolio managers in practice

  3. Calculating Portfolio Return • Percentage change in market value over a period of time, after accounting for external cash flows (contributions and withdrawals) • If no external cash flows: • where MVt is the market value of the portfolio at the end of period t • Example: t = month

  4. Portfolio Return with Cash Flow • With cash flow at beginning of measurement period: • With cash flow at end of measurement period: • Again, MVt is the market value of the portfolio at the end of period t

  5. Time-Weighted Rate of Return (TWR) • Compound growth rate over the evaluation period of one dollar invested • Interim external cash flows result in subperiods that begin with each cash flow, and TWR must link the subperiods together (chain-linking): rTWR= [(1+rt,1) × (1+rt,2) × … × (1+rt,n)] -1 where t is the evaluation period, 1…n are the subperiods • For example, during a year there are 3 subperiods, with returns equal to 1%, 8% and -3%. The time weighted return for the year is: 1.01 X 1.08 X 0.097 – 1 = 0.058 = 5.8%

  6. Money-Weighted Rate of Return (MWR) • Measures compound growth rate in the value of all funds invested over the evaluation period • Equivalent to internal rate of return (IRR) • MWR is the growth rate, Rt, that solves: • MVt = MVt-1(1+Rt)m + CF1(1+Rt)m-L(1) + … + CFn(1+Rt)m-L(n) where: • m = number of time units in the sub-period (e.g., 90 days) • L(i) = number of time units from the beginning of the evaluation period (e.g., a cash flow on the 5th day)

  7. Time-Weighted versus Money-Weighted Return • MWR is more sensitive to timing of external cash flows • Time weighted return is preferable for evaluating a manager who does not have control over the size or timing of cash flows, and is generally required by the Global Investment Performance Standards (GIPS) • MWR may be more appropriate in circumstances where manager can influence cash flow size and timing, such as alternative assets like private equity, infrastructure funds

  8. Benchmarking Performance • Benchmark is typically a stock index, bond index, or a weighted average of different indices • Depends on portfolio mandate • The benchmark is the investor’s passive alternative • Performance against benchmark: rP – rB • Called “active return”, “relative return“, or “value added”, • Benchmark for Stocktrak portfolio

  9. Tracking Error Measures deviations from benchmark • where rPt is the portfolio return, and rBt is the benchmark return • Most common performance measure for index fund / ETF managers • Measures “tracking risk”

  10. Tracking Error • Many actively managed portfolios have a target tracking error. Maintaining this target is a part of portfolio risk management • Having cash in portfolio will increase tracking error • Cash does not always reduce “risk” if you are benchmarked! It increases your tracking risk

  11. Example Target value added, rp-rB Target tracking error What is the relationship between target tracking error and target value added?

  12. Tracking Error and Optimization • Three-dimensional application of the Markowitz Model • State Street Global Markets (currency strategy): • “Maximizes: Expected Return - Risk Aversion x Standard Deviation2 -Tracking Error Aversion x Tracking Error2 ”

  13. Risk-Adjusted Returns • Popular media reports mostly raw returns • If investors care about risk, then may want to consider return per unit of risk • Traditional risk-adjusted measures: • Sharpe ratio • Treynor measure • Appraisal or information ratio • Jensen’s alpha

  14. Sharpe Ratio • A reward-to-variability ratio, using realized returns • Average excess returns per unit of total risk (standard deviation of portfolio returns) • The most popular risk-adjusted measure • Use it to compare different portfolios, or to evaluate portfolio against the benchmark

  15. Treynor Measure • Average excess returns per unit of systematic risk • Need to first estimate the portfolio beta using the Single Index Model • Risk that cannot be diversified away

  16. Jensen’s Alpha • A classic measure of “stock-picking ability” • Benchmark: the CAPM • Estimate using regression analysis • If p > 0 (and statistically significant), then there is “abnormal” portfolio return, over and above what is predicted by the CAPM • (This is based on one factor. Can also use the Fama and French model)

  17. Information Ratio • Also called the Appraisal ratio • Alpha per unit of diversifiable (or non-systematic) risk • Appropriate when considering a move from a passively managed to an actively managed portfolio • Potential benefit: alpha, but will also add diversifiable risk to the portfolio

  18. Information Ratio • Industry Version: • Measures the efficiency with which a portfolio’s tracking risk delivers active return • Difference: Performance is benchmarked to a simple market index, rather than to the CAPM (or the Single Index Model)

  19. Universe Comparison Divide performance of all active managers in the same category (e.g., Canadian equity) into quartiles.

  20. Performance Attribution Analysis • For managers that are benchmarked • Identify sources of relative return: Where did the superior/inferior performance come from? • Can attribute a portfolio’s relative return, rP - rB, to: • Manager’s ability in asset allocation • Ability in sector selection within an asset class • Ability in stock selection within a sector

  21. Performance Attribution Analysis • Let rBi be the return on the ith asset class in the benchmark (e.g. i = equities or bonds) • Let wBi be the weight of the ith asset class in the benchmark, B: • Therefore: • Similarly, for the manager’s portfolio, P:

  22. Performance Attribution Analysis • The manager’s active return, rP - rB, can be written as: where “i” is an asset class (e.g., equity, fixed income...etc.) • With some manipulation, can be re-written as: Active return due to security selection within an asset class Active return due to asset allocation

  23. Numerical Example Policy portfolio Number to be used later Total contribution, rP– rB, is 0.3099% + 1.06% = 1.3699%

  24. Graphical Representation • Provide graph rather than table to clients: Contribution to Relative Return

  25. Performance Attribution Analysis • Security selection comes from: • Sector selection and • Stock selection within each sector • Can further divide performance into these two categories • Sector selection: • Source of relative return: From over-/under-weighting certain sectors relative to the benchmark

  26. Sector Selection If sector return is high, but you under-weighed that sector  contributed negatively Contribution from stock selection within a sector is: 1.47% – 1.0076% = 0.4624%

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