Insurance Vs Mutual Funds

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					Mutual funds:
Worldwide TNA of
mutual funds

          EFM 2006/7     2
Worldwide #
mutual funds

          EFM 2006/7     3
Open-end mutual funds
   Active vs passive (index) funds
   Obliged to buy/sell shares at NAV
    – Net Asset Value = Total Net Assets (TNA) per share
   Part of the fund family (run by one management
   Management fee:
    – Asset-based: proportional to TNA
    – Performance-based: must be symmetric around the
                           EFM 2006/7                        4
MF categories
(by Morningstar)
   Broad asset class:
    – Domestic: equity vs bond vs money market vs hybrid
    – International: foreign, world (global), Europe, Pacific, etc.
   (Stated) investment objective
    – Equity: aggressive growth, growth, growth&income, equity-
      income, income
    – Bond: government, municipal, corporate
    – Hybrid: balanced, asset allocation
   (Estimated) investment style: 3x3 matrix
    – Equity: large/mid/small-cap – value/blend/growth
    – Bonds: high/medium/low credit quality –
      short/intermediate/long duration
                                   EFM 2006/7                           5
TNA of US mutual funds

           EFM 2006/7      6
# US mutual funds

          EFM 2006/7     7
Benefits of investing via
   Low transaction costs
    – Easy way to buy a diversified portfolio
   Customer services
    – Liquidity insurance
    – Easy transfer across funds within the family
   Professional management
    – Selecting right stocks at right time?
   The objective of the research:
    – Check the validity of these claims
                              EFM 2006/7               8
Research questions
   Why has it become one of the largest financial
   Why are there more mutual funds than stocks?
   How to measure fund performance adjusted for
   Does fund performance persist?
   How do investors choose between funds?
   Which incentives does it give to fund managers?
   How accurately do categories divide funds?
                         EFM 2006/7                     9
How to measure MF
   Raw return, determined by
    – Risk factors
    – Factor exposures
          Timing ability: changing beta at right time
    – Selection (stock-picking) ability
          Choosing right stocks (for same level of risk)

                              EFM 2006/7                      10
How to measure MF
   Risk-adjusted return:
    – Difference between fund i’s return and benchmark
    – Benchmark: passive portfolio with same risk as fund i
   How to find a right benchmark?
    – Return-based approach: estimate based on past returns
    – Portfolio-based approach: construct a portfolio of
      assets similar to those held by the fund
    – Relative approach: compare to performance of other
                            EFM 2006/7                          11
Factor models
   Regression of excess asset returns on factor
             Ri,t–RF,t = αi + Σkβi,kFk,t + εt,
    –   Market model: RMRF
    –   Fama-French: RMRF, SMB, HML
    –   Carhart: RMRF, SMB, HML, MOM (1y momentum)
    –   Elton-Gruber: RMRF, SMB, HML, excess bond index
   Jensen’s alpha:
    – Shows whether fund i outperforms passive portfolio of
      K factors and RF
                           EFM 2006/7                           12
Mean-variance spanning
   Test whether adding K new assets (MFs) to N old assets
    leads to the shift of the MV frontier:
     – Three cases possible: spanning, intersection, shift
   Regression of new asset returns r (Kx1) on old asset
    returns R (Nx1):
                       rt = α + BRt + εt
     – Generalized Jensen’s alpha
   Test for intersection: there exists η s.t. α-η(lN-BlK)=0
   Test for spanning: α=0 and BlK=lN
     – All additional assets can be written as portfolio of old assets

                                    EFM 2006/7                             13
Other absolute ordinal
   Sharpe ratio: (E(Ri)-RF)/σi
   Treynor ratio: (E(Ri)-RF)/βi
   Appraisal ratio: αi/σ(ε)i
    – Called Treynor-Black ratio when alpha based
      on market model

                        EFM 2006/7                    14
Relative performance
   Use funds in the same category as a benchmark
   Ordinal measures: difference with the mean or
    median return in the fund’s category
   Cardinal measures: category ranking based on
   Drawbacks:
    – There may be substantial differences in risk within the
    – Survivor bias
    – Bad incentives to managers (as in a tournament)
                             EFM 2006/7                           15
How to measure
performance persistence?
   Contingency tables:
    – Sort funds by past and current performance
           E.g., 2x2 (above/below median): winner-winner, WL, LW, LL
    – Check whether actual frequencies are far from those under the null
   Examine zero-investment portfolios formed on the basis
    of past performance
    – Sort funds into deciles by last-year return
    – Test whether top-bottom portfolio has premium unexplained by
      factor models
   Cross-sectional regressions of current performance on past
                                   EFM 2006/7                                16
Need to control for
   Fund attrition
    – Survivor bias
   Cross-correlation in fund returns
    – Fewer degrees of freedom will make s.e. larger
   The measurement error (and mean
    – If measure both current and past performance
      in the same way
                         EFM 2006/7                      17
Brown and Goetzmann
"Mutual fund performance persistence"
 Explore MF performance persistence
  – Absolute vs relative benchmarks
  – Explicitly model survivor bias
  – Disaggregate on the annual basis

                       EFM 2006/7         18
   Common stock funds in 1976-1988
    – Including dead funds
    – Monthly return data
   Table 1
    – # funds: 372 in 1976, 829 in 1988
    – Total assets rose more than 4 times
    – MaxCap category became relatively less popular

                        EFM 2006/7                       19
Average performance

   Table 2
    – VW mean MF return is below S&P500 return
      by 0.4% p.a., though above index fund
    – Dead funds heavily underperform living funds
    – EW means exceed VW means

                        EFM 2006/7                     20
Fund disappearance
   Disappearance: termination or merging into
    another fund
   Table 3, determinants of prob(death)
    – Lagged relative return: -
    – Lagged relative new money: -
          But insignificant in presence of past performance
    – Relative size: -
    – Expense ratio: +
    – Age: -
                              EFM 2006/7                         21
Performance persistence

   Contingency tables:
    – Sort funds by performance over the last year
      and the current year
    – Winner/loser = above/below median, 2x2
    – Cross-product ratio: (WW*LL)/(WL*LW)=1
      under the null

                        EFM 2006/7                     22
Bootstrapping procedure
   Necessary to control for fund attrition and
    – Use de-meaned sample of fund monthly returns
      in 1987-88
    – For each year, select N funds without
      replacement and randomize over time
    – Assume that poorest performers after the first
      year are eliminated
    – Repeat 100 times
                        EFM 2006/7                       23

   Table 4, odds ratio test for raw returns
    relative to median
    – 7 years: significant positive persistence
    – 2 years: significant negative persistence

                          EFM 2006/7                24
Controlling for differences in
systematic risk
   Use several risk-adjusted performance
    – Jensen’s alpha from the market model
    – One-index / three-index appraisal ratio
    – Style-adjusted return
   Table 6, odds ratio test for risk-adjusted
    returns relative to median
    – Similar results: 5-7 years +, 2 years - persistence
                          EFM 2006/7                          25
Absolute benchmarks

   Figure 1, frequencies of repeat losers
    and winners wrt S&P500
    – Repeat-losers dominate in the second half
      of the sample period
   Table 6, odds ratio test for alpha
    relative to 0
    – 5 years +, 2 years - persistence
                       EFM 2006/7                   26
Investment implications

   Table 7, performance of last-year return
    octile portfolios
    – Past winners perform better than past losers
          Winner-loser portfolio generates significant
    – Idiosyncratic risk is the highest for past winners
          Winner-loser portfolio return is mostly due to bad
           performance of persistent losers
                              EFM 2006/7                          27
   Past performance is the strongest predictor of
    fund attrition
   Clear evidence of relative performance persistence
   Performance persistence is strongly dependent on
    the time period
   Need to find common mgt strategies explaining
    persistence and reversals
    – Additional risk factor(s)
    – Conditional approach

                             EFM 2006/7                    28
Conclusions (cont.)

   Chasing the winners is a risky strategy
   Selling the losers makes sense
    – Why don’t all shareholders of poorly
      performing funds leave?
          Disadvantaged clientele
    – Arbitrageurs can’t short-sell losing MFs!

                             EFM 2006/7             29
Carhart (1997)
"On persistence in mutual fund performance"
 Survivor-bias free sample
 Examine portfolios ranked by lagged 1-year return
    – The four-factor model: RMRF, SMB, HML, and 1-year
    – Explains most of the return unexplained by CAPM…
    – Except for underperformance of the worst funds
   Fama-MacBeth cross-sectional regressions of
    alphas on current fund characteristics:
    – Expense ratio, turnover, and load: negative effect
                             EFM 2006/7                      30
Plan for today
   Up to now:
    – Average performance
          Jensen’s alpha: selection ability
    – Differential performance
          Performance persistence
   Today:
    – Conditional approach to performance evaluation
          Timing ability
          Use dynamic strategies based on public info as a benchmark
                                   EFM 2006/7                             32
Problems with the
unconditional approach
   The market model (with excess returns):
              ri,t = αi + βirM,t + εi,t
    – What if β is correlated with the market return?
    – If cov(β, rM)>0, the estimated α is downward-
   How to measure timing ability?

                         EFM 2006/7                       33
Market timing tests
   Assume that βt = β0 + γf(RM-RF)
    – Treynor-Mazuy: linear function, f(·)=RM-RF
    – Merton-Henriksson: step function, f(·)=I{RM-RF>0}
    – γ shows whether fund managers can time the market
   Typical results for an average fund
    – Negative alpha: no selection ability
    – Negative gamma: no timing ability

                             EFM 2006/7                     34
Problems with measuring
market timing
   Benchmark assets may have option-like
    – Gamma is positive/negative for some stocks
   Managers may have timing ability at higher
    – Tests using monthly data have low power of identifying
      market timing on a daily basis
   Positive covariance between beta and market
    return could result from using public info
                            EFM 2006/7                           35
Ferson and Schadt (1996)
"Measuring Fund Strategy and
  Performance in Changing Economic
 Evaluate MF performance using conditional
  – Both selection and timing ability
  – Use dynamic strategies based on public info as
    a benchmark
        Consistent with SSFE                        РЭШ
                          EFM 2006/7                   36
   Conditional market model:
              ri,t+1 = αi + βi,trM,t+1 + εi,t+1,
    – where βi,t = β0i + β’1iZt (+ γif(rM,t+1))
    – Zt are instruments
   Estimation by OLS:
     ri,t+1 = αi + (β0i+β’1iZt+γif(rM,t+1)) rM,t+1+εi,t+1
   Extension: a four-factor model
    – Large-cap (S&P-500) and small-cap stock returns,
      government and corporate bond yields
                               EFM 2006/7                     37

   Monthly returns of 67 (mostly equity) funds
    in 1968-1990
   Instruments (lagged, mean-adjusted):
    –   30-day T-bill rate
    –   Dividend yield
    –   Term spread
    –   Default spread
    –   January dummy                             РЭШ
                             EFM 2006/7             38

   Table 2, conditional vs unconditional
    – Market betas are related to conditional
        30-dayT-bill rate, dividend yield, and term
        spread are significant
    – Conditional alphas are higher than the
      unconditional ones
                         EFM 2006/7                      39
Results (cont.)

   Table 3, cross-sectional distribution of t-
    stats for cond. and uncond. alphas
    – Unconditional approach: there are more
      significantly negative alphas
    – Conditional approach: # significantly negative /
      positive alphas is similar
    – Very similar results for one-factor and four-
      factor models
                         EFM 2006/7                        40
Results (cont.)
   Table 4, conditional vs unconditional market
    timing model for naïve strategies
    – Naïve strategies:
           Start with 65% large-cap, 13% small-cap, 20% gvt bonds, 2%
            corporate bonds weights
           Then: buy-and-hold / annual rebalancing / fixed weights
    – Unconditional approach: positive alpha and negative
      gamma for buy-and-hold strategy
           Evidence of model misspecification
    – Conditional approach: insignificant alpha and gamma
                                 EFM 2006/7                                41
Results (cont.)
   Tables 5-6, conditional vs unconditional market
    timing models for actual data
    – Conditional approach: the significance of alpha and
      gamma disappears for all categories but special
      (concentrating on intl investments)
   Table 7, cross-sectional distribution of t-stats for
    cond. and uncond. gammas
    – Fewer (significantly) negative gammas under the
      conditional approach
    – More (significantly) positive gammas under the
      conditional approach, esp. for TM model
                            EFM 2006/7                        42
Interpretation of the
   Dynamic strategies based on instruments
    contribute negatively to fund returns
   Is it the active policy or mechanical effects?
    – The underlying assets may have gammas different from
           Yet, we do not observe similar (α,β,γ) patters for the buy-and-
            hold portfolio
    – New money flows to funds increase their cash holdings
      and lower betas
           Edelen (1999): liquidity-motivated trading lowers both alpha
            and gamma
                                   EFM 2006/7                                   43

   Conditioning on public information:
    – Provides additional insights about fund
    – Allows to estimate classical performance
      measures more precisely
   The average MF performance is no longer
    – Both selection and timing ability
                         EFM 2006/7                44
Bollen and Busse (2001)
"On the timing ability of mutual fund managers"
   Using daily returns in market timing tests
    – Much higher power if managers time the market on a
      daily basis
   Traditional tests:
    – 40% of funds have γ>0, 28% have γ<0
           Cf: 33% +, 5% - based on monthly data
   Compare fund γ’s with those for synthetic
    portfolios (γB):
    – 1/3 of funds have γ>γB, 1/3 have γ<γB                РЭШ
                                 EFM 2006/7                  45
Strategic behavior
Plan for today
   Up to now:
    – Average performance
        Selection vs timing ability
        Unconditional vs conditional

    – Differential performance
          Performance persistence
   Today:
    – Strategic behavior of fund managers
          Choice of risk in the annual tournaments
                             EFM 2006/7                 47
The objective function of
MF manager
   Career concerns
    – High (low) performance leads to promotion (dismissal)
    – High risk increases the probability of dismissal
   Compensation
    – Usually proportional to the fund’s size (and flows)
    – Convex relation between flows and performance gives strong
      incentives to win the MF tournament
   Calendar-year performance is esp important
    – Managers are usually evaluated at the end of the year
    – Investors pay more attention to calendar year performance

                                EFM 2006/7                           48
Chevalier and Ellison
"Risk Taking by Mutual Funds as a Response to
 Estimate the shape of the flow-performance
    – Separately for young and old funds
   Estimate resulting risk-taking incentives
   Examine the actual change in riskiness of funds’
    – On the basis of portfolio holdings in September and
                            EFM 2006/7                        49
   449 growth and growth&income funds in 1982-92
    – Monthly returns
    – Annual TNA
    – Portfolio holdings in September and December
           About 92% of the portfolio matched to CRSP data
   Excluding index, closed, primarily institutional,
    merged in the current year, high expense ratio
    (>4%), smallest (TNA<$10 mln) and youngest
    (age < 2y) funds
                                 EFM 2006/7                     50
The flow-performance
   Flowt = ΔTNAt/TNAt-1 – Rt
    – Net relative growth in fund’s assets
  Semi-parametric regression of annual flows on last-year
   market-adjusted returns:
Flowi,t+1=ΣkγkAgeDkf(Ri,t-RM,t)+ΣkδkAgeDk+α1(Ri,t-1-R M,t-1)
    – f(Ri,t-RM,t) is a non-parametric function estimated separately for
      young (2-5y) and old funds
    – AgeDk are dummy variables for various age categories
    – Fund’s size and growth in total TNA of equity funds are controls

                                 EFM 2006/7                                  51

   Figures 1-2, Table 2: flow-performance
    relationship for young and old funds
    – Generally convex shape
          Linearity is rejected, esp for old funds
    – The sensitivity of flows to performance is
      higher for young funds
    – Flows rise with lagged performance up to 3
      years, current category flows and fall with size
                               EFM 2006/7                  52
Estimation of risk-taking
   Assume:
    – Fees are proportional to the fund’s assets
    – Flows occur at the end of the year
    – No agency problems between MF companies and their managers
   In September of year t+1, the increase in expected end-of-
    year flow due to a change in nonsystematic risk in the last-
    quarter return:
             hk(rsep, σ, Δσ)=E[γk(f(Rsep+u)-f(Rsep+v))]
    – After increasing nonsystematic risk by Δσ, the last-quarter return
      distribution changes from u to v
    – Take Δσ=0.5σ
                                  EFM 2006/7                                 53
   Figure 3, risk incentives for 2y and 11y
    – Young funds with high (low) interim
      performance have an incentive to decrease
      (increase) risk to lock up the winning position
      (catch up with top funds)
          The risk incentives are reversed at the extreme
    – Insignificant pattern for old funds
                              EFM 2006/7                       54
Actual risk-taking in response
to estimated risk incentives
   Cross-sectional regressions of within-year
    change in risk on risk incentive measure
   Focus on the equity portion of funds’
    portfolios (on average, about 90%
    – Risk measures computed based on prior-year
      daily stock data

                        EFM 2006/7                   55
Actual risk-taking in response
to estimated risk incentives
   Dependent variable: change between September
    and December in
    – St deviation of the market-adjusted return: ΔSD(Ri-RM)
    – Unsystematic risk: ΔSD(Ri-βiRM)
    – Systematic risk: Δ|βi-1|
   Independent variables:
    –   RiskIncentive: hk
    –   Size: ln(TNA)
    –   RiskIncentive*ln(TNA)
    –   September risk level: to control for mean reversion
                              EFM 2006/7                         56

   Table 4
    – The higher risk incentives, the higher actual
      change in total and unsystematic risk
    – This effect becomes less important for larger
    – No evidence of mean reversion

                         EFM 2006/7                     57
Actual risk-taking in response
to interim performance
   Dependent variable: change between September
    and December in total risk
   Main independent variable:
    – January-September market-adjusted return: Ri,sep-RM,sep
   Assume that change in risk is a piecewise linear
    function of interim performance
    – 2 fitted kink points
   Estimate separately for young and old funds
                             EFM 2006/7                           58
   Table 5, Figure 4
    – Generally negative relation between actual change in
      total risk and interim performance
    – Most slopes and kink points are not significant
   Alternative approach to measure total risk:
    – Using monthly returns: σ(Oct-Dec)-σ(Jan-Sep)
           Very noisy, esp for last quarter (only 3 points!)
   Table 6, Figure 5
    – Generally positive (!) relation between actual change in
      total risk and interim performance
                                    EFM 2006/7                     59
   The flow-performance relationship is convex
   This generates strategic risk-taking incentives
    during the year
   Mutual funds seem to respond to these incentives
   The change in fund’s risk (measured via portfolio)
    is negatively related to its interim performance
    – Though contradictory evidence based on return-based
                           EFM 2006/7                         60
Brown, Harlow, and
Starks (1996)
"Of tournaments and temptations: An analysis of
  managerial incentives in the MF industry"
 Contingency table approach:
    – Sort funds by mid-year return and within-year change in
      total risk
          Risk-adjustment ratio based on monthly returns: σ(7:12)/σ(1:6)
    – 2x2 matrix: return/RAR above/below median
    – Each cell should have 25% of funds under the null
   Find 27% frequency of high-return low-RAR
    funds in 1980-1991
    – Support the tournament hypothesis
                                 EFM 2006/7                                   61
Busse (2001)
"Another look at mutual fund tournaments"
 Same contingency table approach using daily and
  monthly data
    – Disaggregate: annual tournaments
   Control for cross-correlation and auto-correlation
    in fund returns
    – Compute p-values from bootstrap
   No significant evidence for the tournament
                           EFM 2006/7                      62
Wermers (2000)

"MF performance: An empirical
    decomposition into stock-picking talent,
    style, transactions costs, and expenses "
   Decompose fund’s return into several components
    to analyze the value of active fund management
   Portfolio-based approach:
    – Using portfolio holdings data

                            EFM 2006/7                  63
   Finding the benchmark: one of 125 portfolios
    – In June of each year t, rank stocks by size (current ME)
      and form 5 quintile portfolios
    – Subdivide each of 5 size portfolios into 5 portfolios
      based on BE/ME as of December of t-1
    – Subdivide each of 25 size-BM portfolios into 5
      portfolios based on past 12m return
    – From July of t to June of t+1, compute monthly VW
      returns of 125 portfolios
                             EFM 2006/7                            64
Methodology (cont.)
   Decomposing fund’s return: R = CS + CT + AS
    – Characteristic selectivity: CS=Σjwj,t-1[Rj,t-Rt(bj,t-1)]
           wj,t-1 is last-quarter weight of stock j in the fund’s portfolio
           Rt(bj,t-1) is current return on the benchmark ptf matched to
            stock j in quarter t-1
           CS measures the fund’s return adjusted for 3 characteristics
    – Characteristic timing: CT=Σj[wj,t-1Rt(bj,t-1)-wj,t-5Rt(bj,t-5)]
           CT is higher if the fund increases the factor’s exposure when
            its premium rises
    – Average style: AS=Σjwj,t-5Rt(bj,t-5)
           AS measures tendency to hold stocks with certain
                                    EFM 2006/7                                   65
Methodology (cont.)

   Comparing with return-based approach:
    – Potentially higher power: no need to estimate
      factor loadings
    – But: may be biased due to window-dressing
    – But: only equity portion of fund’s portfolio

                         EFM 2006/7                     66

   1788 diversified equity US funds in 1975-94
    – CRSP: monthly returns, annual turnover,
      expense ratios, and TNA
    – CDA: quarterly portfolio holdings (only equity
    – No survivor bias
   CRSP files of US stocks
                         EFM 2006/7                      67
   Table 5, decomposition of (equity portion of) MF
    –   Gross return: 15.8% p.a. > 14.3% VW-CRSP index
    –   CS = 0.75%, significant
    –   CT = 0.02%, insignificant
    –   AS = 14.8%
    –   Expense ratio = 0.79%, up from 65 to 93 b.p.
    –   Transactions costs = 0.8%, down from 140 to 48 b.p.
    –   Non-equity portion of the fund’s portfolio: 0.4%
    –   Net return: 13.8% < 14.3% VW-CRSP index!
                             EFM 2006/7                         68
Mutual funds: summary
   Many funds hardly follow their stated objectives
   On average, MFs do not earn positive
    performance adjusted for risk and expenses
   Bad performance persists
   Money flows are concentrated among funds with
    best performance
   Poorly performing funds are not punished with
    large outflows
   Funds try to win annual tournaments by adjusting
                         EFM 2006/7                      69

Description: Insurance Vs Mutual Funds document sample