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Mutual Fund Performance Measurement

 

William F. Sharpe

Graduate School of Business

Stanford University

www-sharpe.stanford.edu

 

 

 

Decisions

One Fund

One Fund plus borrowing or lending

A portfolio of potentially many funds

 

The key question:

Which (if any) fund is relevant in each situation?

 

 

 

 

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
  • Stars or Ratings assigned based on rankings

 

 

Optimal Position in a Fund with Unlimited Short Positions in Assets

Xi = [ expected (ei ) / Var ( ei ) ) ] * ( t / 2 )

Amount of risk taken:

Xi * stdev ( ei )

= [ expected (ei ) / stdev ( ei ) ] * ( t / 2 )

= [ selection Sharpe ratio ] * ( t / 2 )

Relative values independent of investor preferences

 

 

The Optimal Fund for an Asset Class with a Taxonomic Factor Model

Assume that Xj is to be invested in a fund in a given asset class

From the funds in the asset class, select the fund with the largest value of:

expected ( ef ) - ( Xj / t ) * variance ( ef )

A utility-based differential return measure with k a function of:

  • the amount to be invested in the asset class ( Xj )
  • the investor's risk tolerance (t)

The appropriate measure will thus depend on an investor's portfolio and degrees of risk tolerance -- no single measure will be appropriate for everyone

 

 

 

Why There is no Universally Relevant Single Performance Measure

Measures such as Morningstar's risk-adjusted ratings or excess return Sharpe ratios are inappropriate for choosing funds for a multi-fund portfolio since they are based on total risk or excess return risk rather than the contribution of the investment in a fund to overall portfolio risk

Most investors do not or cannot take short positions in asset classes, hence measures such as selection Sharpe ratios which are based on differential return risk may be of limited value

Most investors place enough money in a fund to make alpha an insufficient measure of performance since it does not take risk into account

In most cases, no universal single measure can provide a sufficient statistic for choosing funds for a multi-fund portfolio

 

An Alternative to the Hierarchic Taxonomic Approach with Single Measures of Mutual Fund Performance

Asset Classes as Factors

Funds as Decision Variables

All fund exposures to asset classes taken into account

All components of risk and return considered

Unbiased estimates of future risks, returns and correlations obtained using all relevant information (for example, fund expense ratios)

Efficient combinations of funds obtained using Markowitz' optimization procedures

 

Needed Inputs (1)

For asset classes:

  • future expected returns

  • future risks

  • future correlations

For funds:

  • future asset exposures ( appropriate benchmark portfolios or styles)

  • future fund selection risks

  • future fund selection expected returns

 

 

Needed Inputs (2)

For the investor:

  • Current amount saved

  • Future savings rate

  • Horizon

  • Liabilities

  • Other assets

  • Degree of aggressiveness

 

 

Outputs

For a given set of investor inputs:

  • The associated efficient combination of funds

  • Range of outcomes (in terms relevant for the investor)

For different sets of investor inputs, the associated:

  • Efficient combinations of funds

  • Ranges of outcomes

For the set of inputs ultimately chosen by the investor:

  • The optimal combination of funds

  • The preferred range of outcomes

 

 

The Bottom Line

We all have computers

Why not use them?