Risk-Adjusted Performance and Informed Decision Making Dr. Arun Muralidhar

2 Arun Muralidhar - Bio  Chairman of Mcube Investment Technologies, LLC and Managing Director at FX Concepts, Inc.  Head of Investment Research and Member of Investment Management Committee, World Bank Investment Department,  Derivatives and Liability Management, World Bank Funding Department,  Managing Director and Head of Currency Research, JPMIM,  BA, Wabash College (1988); PhD, MIT Sloan (1992)

3 Agenda  Background  Why the information ratio is wrong – M 2  Risk budgeting – connecting returns to risk – M 3  Confidence in skill: History matters - SHARAD  Optimal portfolio construction using these measures

4 Relative Risk – Tracking Error  Most commonly used measure  Ann. standard deviation of excess returns  Depends on the standard deviation of the benchmark, strategy and correlation  Few test ex-ante forecast with ex-post outcomes  Papers that recommend that managers stay within tracking error ranges are WRONG

5 Performance Measures  Returns – Absolute and Relative  Annualized versus Cumulative  Ratios – Risk-Adjusted  Sharpe, Information Ratio, Sortino Ratio  Risk-Adjusted Returns  M2, M3, SHARAD  Skill Measures

6 How to Calculate Standard Measures?  Unadjusted measures  Excess return = Portfolio return - Benchmark return  Risk-adjusted ratio measures  Sharpe ratio = Excess over risk free rate/standard deviation of portfolio –higher the ratio, the better the investment opportunity  Information ratio = Excess over benchmark/standard deviation of excess returns –higher the ratio, better the manager

7 Some Advanced Risk-Adjusted Measures  Sortino ratio = Excess/Downside risk measure  Risk-adjusted measures (in return terms)  M 2 = extended Sharpe ratio (in basis points)  M 3 = extended M 2 ratio; corrects for correlation  SHARAD = Normalizes for different length of history  Confidence in Skill – Tells how confident one can be that there is skill (as opposed to noise) in a given track record

8 Riskless asset Return Active portfolio A Standard deviation of unlevered portfolio Benchmark Standard deviation Market risk Active portfolio B Information Ratio is Wrong - M 2 Need to normalize for different Std. deviations B has a negative Information Ratio!

9 Riskless asset Benchmark Return Benchmark Standard deviation Market risk Portfolio B has a Higher M 2 Return Problem: Need to normalize for different correlations i.e., have different tracking error M 2 Return for B M 2 Return for A

10 Correlation-Adjustment: M 3 Measure FundReturn (%) Standard deviation (%)  M2M2 TE(basic) (%) TE(M 2 ) (%) M3M3 (1)(2)(3)(4)(6)(7)(8)(12) F B Correcting for tracking error – different rankings F = Risk-free asset; B = Benchmark (S&P500)

11 Ranking Portfolios: Different Methods RankingUnadjusted Skill using raw returns M2 or Sharpe Skill using M2M3 Skill using M3 Information ratio (1)(2)(3)(4)(5)(6)(7)(8) First Second Third Fourth Fifth Sixth Seventh Eighth Ninth Tenth M 3 is the only one consistent with Skill Information ratio, Sharpe or M 2 say little about Skill Skill = Confidence in Skill Measure M 3

12 Which Measure Should you Use?  Manage portfolio yourself – Sharpe, Information Ratio or M 2  External manager and with a tracking error budget – M 3 (Previous papers ignore possible actions by client)  Worried about skill – M 3  M 2 provides valuable advice on leverage/ deleverage; M 3 provides valuable advice on (a) active versus passive (“beta”) and leverage/deleverage Important to have a risk budget

13 How Do You Compare 2 Strategies with Different Data Histories?  In the past – drop non-overlapping data  Lose valuable information on strategy with longer history  SHARAD Measure – Normalizes for different risk and different data history  SHARAD = {M 3 return}*{Confidence in skill (of M 3 portfolio)}  Confidence in skill acts as a probability measure and explicitly captures the length of data history – more history, greater the confidence in skill

14 Risk Budgeting is only First Step  Cannot force tracking error ranges on managers – client needs to be evaluate how good manager is in dynamically managing risk  Risk-adjusted performance measures are the right way to go, but many are paid on the basis of excess returns  Measures can tell you how good manager is at managing risk  Use creative measures along with risk budgets to achieve optimal portfolio performance