Morningstar's Risk-Adjusted Ratings: Their Use and Misuse     William F. Sharpe www-sharpe.stanford.edu

 

 

 

Mutual Fund Performance Measures Use statistics from: historic frequency distribution many periods Example: combination of mean and standard deviation for past 36 months To predict statistics for: future probability distribution one period Example: combination of mean and standard deviation for next month

 

 

Statistics: M Ex Ante: Expected Return Expected geometric return etc. Ex Post: Arithmetic average return Geometric average return Compounded total return over period etc.

 

 

 

 

Statistics: S Ex Ante: Standard Deviation of Return Variance of Return Expected loss etc. Ex Post: Standard deviation of return Variance of Return Average loss etc.

 

 

 

Performance Measures Return M Utility-based M - k * S Scale-independent M / S

 

 

 

Variables Total Return Fund Return Excess Return Fund Return - Return on a risk-free instrument Differential Return Fund Return - Return on an appropriate benchmark portfolio

 

 

Absolute and Relative Measures Absolute Use statistics as computed for all funds Relative Each fund assigned to a peer group Performance of funds ranked within each peer group Comparisons based on: Differences Ratios Rankings Stars 5 stars: top 10% 4 stars: next 22.5% etc.

Frequently-used Measures Relative   Total Return Excess Return Differential Return Return Lipper     Utility-based   Morningstar (form)   Scale-independent   Morningstar (subst.) Micropal Absolute   Total Return Excess Return Differential Return Return     selection mean (alpha) Utility-based       Scale-independent   Sharpe ratio selection Sharpe ratio

 

 

 

Scale-independent Measures Variable = Return on A minus return on B Strategy requires zero investment long position in A short position in B Change in value can be doubled by doubling sizes of positions For scale k: Mk = k* M1 SDk = k* SD1 Mk / SDk = M1 / SD1 Therefore, ratio is scale-independent

 

 

 

Scale-independent Measures with Positive Expected Returns

 

Scale-independent Measures with Negative Average Returns

 

 

Morningstar Peer Groups Peer Groups Asset classes Categories Asset Classes Domestic equity International equity Taxable bond Municipal bond Domestic equity categories Diversified (9) Specialty (9) Hybrid Convertible

 

Morningstar Diversified Equity Categories Based on portfolio composition price/earnings, price/book market capitalization Averaged over past three years Style Boxes Large Value Large Blend Large Growth Medium Value Medium Blend Medium Growth Small Value Small Blend Small Growth

 

 

 

Morningstar Ratings Stars: Rank within asset class (e.g. equity) 3-year, 5 year, 10 year and weighted average of 3,5, and 10 year Net of load charges Category Ratings: Rank within asset category (e.g. Large Growth equity) 3-year Load charges not taken into account Percentages: 1 (worst) 2 3 4 5 (best) 10% 22.5% 35% 22.5% 10%

 

 

 

Morningstar Statistics, 3-year Ratings M Compounded return on fund - compounded return on Treasury bills Loss if fund return > Treasury bill return, loss = 0 if fund return < Treasury bill return, loss = - (fund return - bill return) S Average Monthly Loss sum ( monthly loss) takes all 36 months into account

 

 

Morningstar Risk-adjusted Rating RARf = Mf / M_ - Sf / S_ M_ if mean ( Mf ) >= compound return on Treasury bills, mean ( Mf ) if mean ( Mf ) < compound return on Treasury bills, compound return on Treasury bills S_ mean ( AMLf )

 

 

 

Morningstar Risk-adjusted Ratings as Utility-based Measures RARf = Mf / M_ - Sf / S_ = ( 1/M_ ) * [ Mf - ( M_ / S_ ) * Sf ] Rankings unaffected by initial constant ( 1/M_ ) Rankings depend on: Mf - k * Sf where: k = M_ / S_

A bi-linear VnM Utility Function with threshold = 4% and utility ratio = 2.5

Optimal Leverage when Utility = Return - k*Risk

Optimal Leverage when Utility = Return - k*Risk2

 

 

 

RAR as a Function of Expected Excess Return and Standard Deviation

 

 

 

 

Iso-RAR Curves

 

 

 

Iso-Excess Return Sharpe Ratio Lines and Approximate Iso-RAR Curves

 

 

The Iso-SR and Iso-RAR Lines for a Single Fund

 

 

 

 

 

Regions in Which the SR and RAR Criteria Conflict

 

 

 

Rankings Based on Morningstar's Category RARs and Excess Return Sharpe Ratios 1,286 Diversified Equity Funds, 1994-1996

 

 

 

Three-year Star Ratings and Mean-variance combinations, 1,286 Diversified Equity Funds, 1994-1996

Performance of Two Funds in Bad Times

 

 

 

Morningstar RAR Measures versus Excess Return Sharpe Ratios Morningstar RAR Measures poor statistical properties similar to excess return Sharpe ratios in periods of good performance similar to utility-based rankings in periods of medium to poor performance utility-based rankings unlikely to reflect investor preferences Not appropriate for selecting funds within peer groups for a multi-fund portfolio Excess Return Sharpe ratios Good statistical properties (equals t-statistic divided by square root of number of periods) Reflect rankings for investors choosing one fund plus borrowing or lending Not appropriate for selecting funds within peer groups for a multi-fund portfolio

 

Selection Sharpe ratios ( information ratios ) Selection return Return on fund minus return on an appropriate benchmark or combination of benchmarks Selection Sharpe ratio Mean selection return divided by standard deviation of selection return Characteristics Scale-independent Suitable if asset exposures can be separated from selection returns and any desired scale can be chosen Generally give different rankings than Excess return Sharpe ratios

Market-neutral Funds Appropriate benchmark Treasury bills Excess return Sharpe ratio Mean/SD of: [ fund return - Treasury bill return ] Selection Sharpe ratio Mean/SD of: [ fund return - benchmarkl return ] Mean/SD of: [ fund return - Treasury bill return ] The category for which the Excess return Sharpe ratio is most suitable

A Better Way to Build a Multi-Fund Portfolio For each fund, estimate future values of: Exposures to major asset classes Expected return over benchmark with similar exposures (added return) Standard deviation of return over benchmark (added risk) Combine with: Asset expected returns Asset risks and correlations Investor risk tolerance, constraints, tax situation, etc. To find: Best possible combination of funds for the investor in question