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

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

Jan 04, 2023 245 likes •383 views

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

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  • 1. Motivation
  • What is this all about?
  • Performance rankings
  • 2. Risk‐Adjusted Returns
  • Jensen alpha
  • Treynor index
  • Sharpe ratio
  • RAP
  • Sortino ratio
  • Information ratio

Risk & Return (I):

Risk‐Adjusted Returns

Javier Estrada ADFIN – Winter/2014

Javier Estrada IESE Business School Barcelona Spain ADFIN Winter/2014

Motivation

  • Consider any of the popular/periodic rankings of

mutual fund performance

  • What variable would this ranking be based on?

Go

  • What if it were based on longer‐term returns?

Go

  • 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
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Javier Estrada IESE Business School Barcelona Spain ADFIN Winter/2014

Motivation

  • Luck
  • We do not want to pay a manager for being lucky
  • Evaluate performance over ‘long’ periods

Go

  • Risk taking
  • 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

Javier Estrada IESE Business School Barcelona Spain ADFIN Winter/2014

Risk‐Adjusted Returns

  • Jensen alpha
  • αp = Rp – (Rf + MRP⋅βp)
  • Comments
  • Should be used for funds within a diversified portfolio

 Only then βp is a proper measure of risk

  • 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 …

 αp = Rp – RB

  • Very widely used, though not free from problems

Go

 Alpha measures absolute out/underperformance  Not too problematic when used ‘within a style box’

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Javier Estrada IESE Business School Barcelona Spain ADFIN Winter/2014

Risk‐Adjusted Returns

  • Treynor index
  • Tp = (Rp – Rf)/βp
  • Comments
  • Should be used for funds within a diversified portfolio

 Only then βp is a proper measure of risk

  • Aims to solve the limitation of alpha

Go

  • But has two limitations itself

 In what units is Tp 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

Javier Estrada IESE Business School Barcelona Spain ADFIN Winter/2014

Risk‐Adjusted Returns

  • Sharpe ratio
  • Sp = (Rp – Rf)/σp
  • Comments
  • Similar to Tp but with a different measure of risk
  • 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 σp the proper measure of risk?
  • Risk‐adjusted performance (RAP)
  • RAPp = Rf + (Rp – Rf)(σM/σp) = Rf + Sp⋅σM
  • Comments
  • Preserves a ranking made with the Sharpe ratio
  • Expressed in %, hence more intuitive
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Javier Estrada IESE Business School Barcelona Spain ADFIN Winter/2014

Risk‐Adjusted Returns

  • Sortino ratio
  • Np = (Rp – RB)/ΣBp
  • Comments
  • The excess return and downside risk are relative to B
  • Also measured in excess return per unit of risk
  • More recent and gaining ground

Go

  • Information ratio
  • Ip = αp /ωp → αp = Rp–RB and ωp = σ(αp)
  • 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)

Javier Estrada IESE Business School Barcelona Spain ADFIN Winter/2014

Risk‐Adjusted Returns

  • These measures are widely used in practice
  • Alpha and the information ratio are key measures

to evaluate active managers

  • The Sharpe ratio is standard information in most

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

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Javier Estrada IESE Business School Barcelona Spain ADFIN Winter/2014

Appendix

Javier Estrada IESE Business School Barcelona Spain ADFIN Winter/2014

Rankings – Small/Value

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Javier Estrada IESE Business School Barcelona Spain ADFIN Winter/2014

Sad But True

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

Rankings – Small/Value

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Javier Estrada IESE Business School Barcelona Spain ADFIN Winter/2014

Howard Marks “Return alone – and specially 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

  • f risk taken to achieve it.”

Javier Estrada IESE Business School Barcelona Spain ADFIN Winter/2014

Risk‐Adjusted Returns

Back

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Javier Estrada IESE Business School Barcelona Spain ADFIN Winter/2014

Michael Mauboussin

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

Alpha

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Javier Estrada IESE Business School Barcelona Spain ADFIN Winter/2014

Alpha

Javier Estrada IESE Business School Barcelona Spain ADFIN Winter/2014

Alpha

Back

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Javier Estrada IESE Business School Barcelona Spain ADFIN Winter/2014

Alpha – Problems

Back

SML Rf Beta Return A B A B A B RA RB RA,L

Javier Estrada IESE Business School Barcelona Spain ADFIN Winter/2014

Treynor Index

SML Rf Beta Return A B A B A B RA RB RA,L TB TA

Back

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Javier Estrada IESE Business School Barcelona Spain ADFIN Winter/2014

Sortino Ratio

Javier Estrada IESE Business School Barcelona Spain ADFIN Winter/2014

Sortino Ratio

Back

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Javier Estrada IESE Business School Barcelona Spain ADFIN Winter/2014

Information Ratio

Time

P B X

Time

P B Y

RP – RB = 5% RP – RB = 5%

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

Risk‐Adjusted Returns

Back