FUND PERFORMANCE

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FUND PERFORMANCE

• Portfolio Management
• Ali Nejadmalayeri

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Evaluation Process

• The major aspects of evaluation are
• Efficiency of Asset Allocation
• Efficacy of Rebalancing of Asset Classes
• Efficacy of Asset Selection
• The performance measure should account not only
  for return but also risk!

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Snapshot of Performance
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Return

• Return should measure
• Change in NET ASSET VALUE (NAV)
• Cash Distributions, D
• Capital Gain Distributions, C
• So for one period return is

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Return Example

• Imagine a fund with initial fund of 800,000
  which grows to 880,000 in six months. Then, the
  fund receives a cash flow of 220,000 in six
  months which reinvest. The total value at the
  year-end is 1,320,000. Whats the return?
• Change in value for 1st half 10880000/800000
  1
• Change in value for 2nd half 501320000/880000
  1
• Total change in value then is 651320000/800000
  1
• ? Is This the Correct Return?

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Return 1st Method

• Find the sub-period return and then time-weighted
  average them
• 1st half, 10
• 2nd half, 20
• Then find the geometric average
• 1.10 1.20 1.32
• overall return 32

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Return 2nd Method

• Find the beginning and ending Net Asset Value for
  each period, then find the overall change in NAV
• 1st half, assume 800 units then NAV beg
  1000 and NAV end 1100
• 2nd half, assume 1000 units then NAV beg
  1100 and NAV end 1320
• Overall return is 1320/1000 1 32

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Risk Adjusted Return

• Reward-to-Total Risk (Sharp Ratio)
• Appropriate for concentrated portfolios with
  single manager
• Reward-to-Market Risk (Treynor Ratio)
• Appropriate for diffused portfolios with multiple
  managers

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Differential Return

• Corrected for risk, how much extra return is
  generated
• CAPM
• Empirically, we can run this regression

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Differential Return (Contd)

• In general, there could be N factors which affect
  stock return. For instance, besides market risk
  premium, small-large stocks premium, and hi-lo
  book-to-market premium also affect stock returns,
  thus the excess return in is computed from
  following regression

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Performance Comparison

• Beta
• when high means riskier than market
• R2
• When high means better diversified
• Sharp Ratio (Award-to-Volatility)
• When high means more return per total risk
• Traynor Ratio (Award-to-Variability)
• When high means more return per market risk
• Alpha
• When high means excess return over market,
  corrected for risk

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Superior Selection

• Return

Net Selectivity
rp
r(sp)
Diversification Asset Allocation
E(rp)
Market Risk
rf
risk
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Components of Return

• Fama Decomposition
• Return Total Excess Return Risk Free Rate
• Total Excess Return Selectivity Risk
• Selectivity Net Selectivity Diversification

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Market Timing
Fitting a Piece-wise Linear
Fund
Fitting a Curve
The general idea is that if manager time the
positioning well then in a bust the beta of the
fund, slope sensitivity, should be low and in a
boom the beta, slope sensitivity, should be high!
Fitting a Line
Market
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Market Timing

• Nonlinear Relationship
• Beta increases (decreases) as Market booms
  (busts)
• You want cp to be positive indicating market
  timing ability
• Piece-wise Linear
• Beta lower in bust than in boom
• D is 1 when boom, zero when bust. You want cp to
  be positive
• Cash Management
• Cash holding is low (high) in boom (bust)

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Cash Management

• Find normal cash allocation (or, average)
• In boom the ratio should go down, vice versa in
  bust should go up
• Market forecast ability
• What percentage of time the manager correctly
  shifts cash level up and down in anticipation of
  events?

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Setting Up the Goals

• Long-term Goals
• Return Attributes
• Desired Asset Mix and Tolerable Deviations
• Planning Horizon
• Appraising Tactical Asset Mix
• Evaluating the Managers Performance

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Long-term Goals

• Fund Type Value
• Fund Value 400 M - 1 B
• Return Goal 5 real
• Planning Period 3 - 5 years
• Risk to Loss
• 3/8 probability of not earning the return ¼
  probability of loss
• Asset Allocation
• Cash 5 5
• Domestic 85 10
• Europe 10 2

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Appraising Asset Allocation

• 1st, check if average return is in line with
  objectives
• 2nd, if the return is stable, i.e., percentage of
  time not earning the return or making losses is
  in line with objectives
• 3rd, if none of above id true, then simulate what
  asset allocation could have brought the results
  in line with your objectives

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Managers Performance

• Comparison with broad index (or, segment indices
  for specialized funds)
• Comparison for peer fund managers
• Evaluation after adjusting for systematic factors
• Market Beta,
• Style Growth Value
• Industry Classification Sectors
• Stock Selection

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Broad Index and Peers
Return
Stock Fund
25 Median 75
SP 500 Index
Bond Fund
25 Median 75
Lehman Index

• Risk

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Systematic Factors

• Compare to a benchmark, like index, examine how
  overweighted (underweighted) the fund is in a
  number of dimensions
• Style (Growth Value) and Industry
  Classification
• Then, determine what is the percentage
  differential
• Compare all the percentage differentials to find
  what dimension, Market, Style, Industry
  Classification, or Selection, created value

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Information Ratio

• Managers goal is create excess value, but her
  performance fluctuates throughout time, so to
  account for uncertainty we define Information
  Ratio (IR)

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Time-Confidence

• Time horizon that a manager can sustain this type
  of performance in a function of her confidence in
  her own ability