Transcript 11-14 mutual funds
Mutual funds: performance evaluation
Worldwide TNA of mutual funds
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Worldwide # mutual funds
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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 company) Management fee: – Asset-based: proportional to TNA – Performance-based: must be symmetric around the benchmark EFM 2006/7
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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
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TNA of US mutual funds
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# US mutual funds
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Benefits of investing via MF
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
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Research questions
Why has it become one of the largest financial intermediaries?
Why are there more mutual funds than stocks?
How to measure fund performance adjusted for risk?
Does fund performance persist?
How do investors choose between funds?
Which incentives does it give to fund managers?
How accurately do categories divide funds?
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How to measure MF performance?
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
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How to measure MF performance?
Risk-adjusted return: – Difference between fund i’s return and benchmark return – 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 funds EFM 2006/7
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Factor models
Regression of excess asset returns on factor returns R i,t –R F,t = α i + Σ k β i,k F k,t + ε t , – Market model: RMRF – Fama-French: RMRF, SMB, HML – Carhart: RMRF, SMB, HML, MOM (1y momentum) – Elton-Gruber: RMRF, SMB, HML, excess bond index return Jensen’s alpha: – Shows whether fund i outperforms passive portfolio of K factors and R F
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Mean-variance spanning tests
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): r t – Generalized Jensen’s alpha = α + BR t + ε t Test for intersection: there exists η s.t. α-η(l N -Bl K )=0 Test for spanning: α=0 and Bl K =l N – All additional assets can be written as portfolio of old assets EFM 2006/7
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Other absolute ordinal measures
Sharpe ratio: (E(R i )-R F )/σ i Treynor ratio: (E(R i )-R F )/β i Appraisal ratio: α market model i /σ(ε) i – Called Treynor-Black ratio when alpha based on
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Relative performance measures
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 return/α/… Drawbacks: – There may be substantial differences in risk within the category – Survivor bias – Bad incentives to managers (as in a tournament)
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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 performance EFM 2006/7
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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 reversion) – If measure both current and past performance in the same way EFM 2006/7
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Brown and Goetzmann (1995)
"Mutual fund performance persistence" Explore MF performance persistence – Absolute vs relative benchmarks – Explicitly model survivor bias – Disaggregate on the annual basis EFM 2006/7
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Data
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
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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
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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
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Performance persistence
Contingency tables: – Sort funds by performance over the last year and the current year – Winner/loser = above/below median, 2x2 matrix – Cross-product ratio: (WW*LL)/(WL*LW)=1 under the null EFM 2006/7
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Bootstrapping procedure
Necessary to control for fund attrition and cross-correlation: – 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
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Results
Table 4, odds ratio test for raw returns relative to median – 7 years: significant positive persistence – 2 years: significant negative persistence EFM 2006/7
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Controlling for differences in systematic risk
Use several risk-adjusted performance measures: – 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
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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
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Investment implications
Table 7, performance of last-year return octile portfolios – Past winners perform better than past losers Winner-loser portfolio generates significant performance – Idiosyncratic risk is the highest for past winners Winner-loser portfolio return is mostly due to bad performance of persistent losers EFM 2006/7
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Conclusions
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
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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!
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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 momentum… – 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
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Conditional performance evaluation
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
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Problems with the unconditional approach
The market model (with excess returns): r i,t = α i + β i r M,t + ε i,t – What if β is correlated with the market return?
– If cov(β, r M )>0, the estimated α is downward biased!
How to measure timing ability?
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Market timing tests
Assume that β t = β 0 + γf(R M -R F ) – Treynor-Mazuy: linear function, f(·)=R M -R F – Merton-Henriksson: step function, f(·)=I{R M -R F >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
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Problems with measuring market timing
Benchmark assets may have option-like characteristics – Gamma is positive/negative for some stocks Managers may have timing ability at higher horizon – 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
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Ferson and Schadt (1996)
"Measuring Fund Strategy and Performance in Changing Economic Conditions"
Evaluate MF performance using conditional approach – Both selection and timing ability – Use dynamic strategies based on public info as a benchmark Consistent with SSFE
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Methodology
Conditional market model: – where β i,t r i,t+1 = β 0i = α i + β + β’ 1i Z t i,t r M,t+1 + ε i,t+1 , (+ γ i f(r M,t+1 )) – Z t are instruments Estimation by OLS: r i,t+1 = α i + (β 0i +β’ 1i Z t +γ i f(r M,t+1 )) r M,t+1 +ε i,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
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Data
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 EFM 2006/7
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Results
Table 2, conditional vs unconditional CAPM
– Market betas are related to conditional information 30-day T-bill rate, dividend yield, and term spread are significant – Conditional alphas are higher than the unconditional ones EFM 2006/7
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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
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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
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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
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Interpretation of the results
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 zero 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
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Conclusions
Conditioning on public information: – Provides additional insights about fund strategies – Allows to estimate classical performance measures more precisely The average MF performance is no longer inferior – Both selection and timing ability EFM 2006/7
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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 (γ B ): – 1/3 of funds have γ>γ B , 1/3 have γ<γ B EFM 2006/7
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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
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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
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Chevalier and Ellison (1997)
"Risk Taking by Mutual Funds as a Response to Incentives" Estimate the shape of the flow-performance relationship – Separately for young and old funds Estimate resulting risk-taking incentives Examine the actual change in riskiness of funds’ portfolios – On the basis of portfolio holdings in September and December
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Data
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
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The flow-performance relationship
Flow t = ΔTNA t /TNA t-1 – R t – Net relative growth in fund’s assets Semi-parametric regression of annual flows on last-year market-adjusted returns: Flow i,t+1 =Σ k γ k AgeD k f(R i,t -R M,t )+Σ k δ k AgeD k +α 1 (R i,t-1 -R M,t-1 ) +α 2 (R i,t-2 -R M,t-2 )+α 4 IndFlow i,t+1 +α 5 ln(TNA) i,t +ε i,t+1 – f(R i,t -R – AgeD k M,t ) is a non-parametric function estimated separately for young (2-5y) and old funds are dummy variables for various age categories – Fund’s size and growth in total TNA of equity funds are controls
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Results
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
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Estimation of risk-taking incentives
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: h k (r sep , σ, Δσ)=E[γ k (f(R distribution changes from u to v sep +u)-f(R sep +v))] – After increasing nonsystematic risk by Δσ, the last-quarter return – Take Δσ=0.5σ EFM 2006/7
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Results
Figure 3, risk incentives for 2y and 11y funds – 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 performance – Insignificant pattern for old funds EFM 2006/7
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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
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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(R i -R M ) – Unsystematic risk: ΔSD(R i -β i R M ) – Systematic risk: Δ|β i -1| Independent variables: – RiskIncentive: h k – Size: ln(TNA) – RiskIncentive*ln(TNA) – September risk level: to control for mean reversion EFM 2006/7
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Results
Table 4 – The higher risk incentives, the higher actual change in total and unsystematic risk – This effect becomes less important for larger funds – No evidence of mean reversion EFM 2006/7
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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: R i,sep -R M,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
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Results
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
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Conclusions
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 approach EFM 2006/7
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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
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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 hypothesis!
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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
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Methodology
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
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Methodology (cont.)
Decomposing fund’s return: R = CS + CT + AS – Characteristic selectivity: CS=Σ j w j,t-1 [R j,t -R t (b j,t-1 )] w j,t-1 is last-quarter weight of stock j in the fund’s portfolio R t (b j,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=Σ j [w j,t-1 R t (b j,t-1 )-w j,t-5 R t (b j,t-5 )] CT is higher if the fund increases the factor’s exposure when its premium rises – Average style: AS=Σ j w j,t-5 R t (b j,t-5 ) AS measures tendency to hold stocks with certain characteristics EFM 2006/7
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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
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Data
1788 diversified equity US funds in 1975-94 – CRSP: monthly returns, annual turnover, expense ratios, and TNA – CDA: quarterly portfolio holdings (only equity portion) – No survivor bias CRSP files of US stocks EFM 2006/7
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Results
Table 5, decomposition of (equity portion of) MF returns – 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!
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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 risk EFM 2006/7
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