Motivation Consider any of the popular/periodic rankings of Javier - PDF document

Risk & Return (I): Risk ‐ Adjusted Returns Javier Estrada ADFIN – Winter/2014 1. Motivation • What is this all about? • Performance rankings 2. Risk ‐ Adjusted Returns • Jensen alpha • Treynor index • Sharpe ratio • RAP • Sortino ratio • Information ratio Motivation  Consider any of the popular/periodic rankings of Javier Estrada mutual fund performance IESE Business  What variable would this ranking be based on? School Go  What if it were based on longer‐term returns? Barcelona Go Spain  A proper ranking of funds …  needs to account for the impact of … • luck • risk‐taking  in order to correctly isolate … • skill  In other words, a proper ranking should show …  the most skillful managers at the top  the least skillful managers at the bottom ADFIN Winter/2014 1

Motivation  Luck Javier Estrada  We do not want to pay a manager for being lucky IESE Business  Evaluate performance over ‘long’ periods School Go  Risk taking Barcelona Spain  We do not want to pay a manager for obtaining ‘high’ returns simply due to exposure to ‘high’ risk • That opportunity is open to all investors  So we adjust the return delivered by the risk borne • Hence risk ‐ adjusted returns  What about skill?  For this we do want to pay  It can only be isolated in a proper ranking • Based on long ‐term risk ‐ adjusted performance ADFIN Winter/2014 Risk ‐ Adjusted Returns  Jensen alpha Javier Estrada  α p = R p – ( R f + MRP ⋅ β p ) IESE Business  Comments School • Should be used for funds within a diversified portfolio Barcelona  Only then β p is a proper measure of risk Spain • Alpha v . beta  Beta measures voluntary exposure to (market) risk  Alpha measures out/underperformance, given the required return, given the fund’s risk  Over time, beta is getting cheaper and alpha more expensive and difficult to find Go • Importantly, in practice alpha is simply defined as …  α p = R p – R B • Very widely used, though not free from problems Go  Alpha measures absolute out/underperformance  Not too problematic when used ‘within a style box’ ADFIN Winter/2014 2

Risk ‐ Adjusted Returns  Treynor index Javier Estrada  T p = ( R p – R f )/ β p IESE Business  Comments School Barcelona • Should be used for funds within a diversified portfolio Spain  Only then β p is a proper measure of risk • Aims to solve the limitation of alpha Go • But has two limitations itself  In what units is T p measured?  Which would you prefer, a one‐stock fund with β =1, or a fully‐diversified fund with a β =1? • Volatility does matter when funds are evaluated on an individual basis ADFIN Winter/2014 Risk ‐ Adjusted Returns  Sharpe ratio Javier Estrada  S p = ( R p – R f )/ σ p IESE Business  Comments School • Similar to T p but with a different measure of risk Barcelona Spain • Used to evaluate stand‐alone funds • Like alpha, it is very widely used • Unlike alpha, it is not measured in %  Like Treynor, measured in excess return per unit of risk • But is σ p the proper measure of risk?  Risk ‐ adjusted performance (RAP)  RAP p = R f + ( R p – R f )( σ M / σ p ) = R f + S p ⋅ σ M  Comments • Preserves a ranking made with the Sharpe ratio • Expressed in %, hence more intuitive ADFIN Winter/2014 3

Risk ‐ Adjusted Returns  Sortino ratio Javier Estrada  N p = ( R p – R B )/ Σ Bp IESE Business  Comments School • The excess return and downside risk are relative to B Barcelona Spain • Also measured in excess return per unit of risk • More recent and gaining ground Go  Information ratio  I p = α p / ω p → α p = R p – R B and ω p = σ ( α p )  Comments • Measures a manager’s ability to take active risk  Out/underperformance matters  The variability of the out/underperformance matters too • What makes a good active manager? Go  Morningstar stars (Next session) ADFIN Winter/2014 Risk ‐ Adjusted Returns  These measures are widely used in practice Javier Estrada  Alpha and the information ratio are key measures IESE Business to evaluate active managers School  The Sharpe ratio is standard information in most Barcelona Spain mutual fund fact sheets  The Sortino ratio is rapidly becoming more well known and widely used  Morningstar stars (next session) can be rather easily grasped by non‐expert investors Go ADFIN Winter/2014 4

Appendix Javier Estrada IESE Business School Barcelona Spain ADFIN Winter/2014 Rankings – Small/Value Javier Estrada IESE Business School Barcelona Spain ADFIN Winter/2014 5

Sad But True Javier Estrada IESE Business School Barcelona Spain ADFIN Winter/2014 Back Rankings – Small/Value Javier Estrada IESE Business School Barcelona Spain ADFIN Winter/2014 6

Howard Marks Javier Estrada IESE Business School “Return alone – and specially Barcelona Spain return over short periods of time – says very little about the quality of the investment decisions. Return has to be evaluated relative to the amount of risk taken to achieve it.” ADFIN Winter/2014 Risk ‐ Adjusted Returns Javier Estrada IESE Business School Barcelona Spain ADFIN Winter/2014 Back 7

Michael Mauboussin Javier Estrada IESE Business School Barcelona Spain ADFIN Winter/2014 Back Alpha Javier Estrada IESE Business School Barcelona Spain ADFIN Winter/2014 8

Alpha Javier Estrada IESE Business School Barcelona Spain ADFIN Winter/2014 Alpha Javier Estrada IESE Business School Barcelona Spain ADFIN Winter/2014 Back 9

Alpha – Problems Javier Estrada Return IESE R A , L Business School Barcelona Spain B R B SML  B A R A  A R f  A  B Beta ADFIN Winter/2014 Back Treynor Index Javier Estrada Return T A IESE R A , L Business School Barcelona Spain T B B R B SML  B A R A  A R f  A  B Beta ADFIN Winter/2014 Back 10

Sortino Ratio Javier Estrada IESE Business School Barcelona Spain ADFIN Winter/2014 Sortino Ratio Javier Estrada IESE Business School Barcelona Spain ADFIN Winter/2014 Back 11

Information Ratio Javier P Estrada X IESE Business School R P – R B = 5% B Barcelona Spain Time P R P – R B = 5% Y B Time ADFIN Winter/2014 Back Risk ‐ Adjusted Returns Javier Estrada IESE Business School Barcelona Spain ADFIN Winter/2014 Back 12