Style Analysis and Performance Measure Sharpe, 1992

1
Style Analysis and Performance Measure (Sharpe,
1992)

• A passive fund manager provide an investor with
  an investment style, while an active manager
  provides both style and selection. T
• Focusing on a fund's selection return, defined
  as the difference between the fund's return and
  that of a passive mix with the same style.

2
Style Analysis and Performance Measure

• Ri bi1F1 bi2F2 . binFn ei, (1)
• Fund Return
• Return due to Style (True benchmark)
• Selection Return (ei )
• Passive Active Management

3
Estimation of Selection return Comparison
between Trustees' Commingled U.S. and Fidelity's
Magellan Funds

• Ri bi1F1 bi2F2 . binFn ei, (1)
• The fund's style is estimated, using returns from
  months t-60 through t-1.
• The return on the resultant style is calculated
  for month t (the style benchmark return).
• 3. The difference between the fund's return in
  month t and that of the style benchmark
  determined in steps 1) and 2) is computed. This
  difference is defined as the fund's Selection
  Return for month t.

4

• Average -.06 (6 basis points) per month
• On average, the fund underperformed its style
  benchmark.
• Std Dev 1.69 per month with T(Avg) -0.25

5

• Average -.20 per month Underperformed SP500
  stock index primarily due to its exposure small
  stocks.
• Std Dev 2.13 per month T(Avg) -0.65

6
Discussion

• During the period in question the fund's style
  underperformed that of the SP500 (primarily
  because of its exposure to small stocks).
• Indeed, this accounts for approximately
  two-thirds of the fund's underperformance
  relative to the SP500.

7
Discussion

• An investor choosing Trustees' Commingled U.S.
  Fund could and should have known that its style
  favored value stocks and small stocks.
• The choice to expose some of the portfolio to
  these asset classes should be attributed to the
  investor. Results (good or bad) associated with
  such the choice of a style should be attributed
  to the investor, not to the manager of a fund
  following that style.

8
Fidelity Magellan

• Average return difference 0.18 per month with T
  0.84, against SP500 index.

9

• This shows the fund true outstanding selection
  performance of average 0.57 per month against
  style benchmark.
• Std Dev 1.05 per month T(Avg) 3.76

10
Subtle Issues in Fund manager evaluation

• Some portion of the mutual fund return may be due
  to factors NOT related to his/her ability or
  skills.
• Fund style
• Economy of scale or scope
• Research, size, transaction costs.

11
Some Practical Consideration

• Fund style is assumed to be fairly stable over
  the estimation period.
• Should we use 36 monthly, weekly, or daily
  returns for estimation?