Stochastic Dominance and Stochastic Dominance and the Performance of U.K. the Performance of U.K.

Unit TrustsUnit Trusts

Anthony SaundersAnthony Saunders

Charles WardCharles Ward

Richard WoodwardRichard Woodward

U.S. Mutual Fund StudiesU.S. Mutual Fund Studies

Many tests studying the performance Many tests studying the performance of U.S. mutual fundsof U.S. mutual funds

Based on 2 moments of the return Based on 2 moments of the return distributions, the mean and variancedistributions, the mean and variance

Carlson: “The issue of whether Carlson: “The issue of whether mutual funds outperform ‘the mutual funds outperform ‘the market’ depends in large degree on market’ depends in large degree on the selection of both the time period the selection of both the time period and market proxy.”and market proxy.”

UK Mutual Fund StudiesUK Mutual Fund Studies

The same results have been found The same results have been found for U.K. mutual funds, or unit trustsfor U.K. mutual funds, or unit trusts

Trusts have performed poorlyTrusts have performed poorly Unit trusts as a group have Unit trusts as a group have

performed relatively much worse performed relatively much worse than U.S. mutual fundsthan U.S. mutual funds

Briscoe, Samuels, and SmytheBriscoe, Samuels, and Smythe Conducted first mean-variance test of U.K. unit Conducted first mean-variance test of U.K. unit

truststrusts Compared trusts’ risk-return performance to that Compared trusts’ risk-return performance to that

of U.S. mutual funds (as measured by Sharpe) of U.S. mutual funds (as measured by Sharpe) from 1953 to 1963from 1953 to 1963

Found that the average returns for mutual funds Found that the average returns for mutual funds and trusts were similar, but the more risky the and trusts were similar, but the more risky the trust the lower its returns trust the lower its returns

Sharpe had found that the more risky the mutual Sharpe had found that the more risky the mutual fund, the higher its returnsfund, the higher its returns

Concluded that U.K. investors were not risk-Concluded that U.K. investors were not risk-averseaverse• The size of trusts did not fall over that periodThe size of trusts did not fall over that period

FirthFirth

““The Investment Performance of Unit The Investment Performance of Unit Trusts in the Period 1965-1975”Trusts in the Period 1965-1975”

Examined 72 Unit TrustsExamined 72 Unit Trusts Utilized Sharpe’s reward to variability Utilized Sharpe’s reward to variability

ratio and excess return from CAPMratio and excess return from CAPM FindingsFindings

• Poor performancePoor performance• Actual returns were lower than expectedActual returns were lower than expected

FindingsFindings 69 out of 72 (96%) unit trusts had lower 69 out of 72 (96%) unit trusts had lower

reward to variability ratios than the marketreward to variability ratios than the market Sharpe found 23 out of 34 (67%) mutual Sharpe found 23 out of 34 (67%) mutual

funds performed worse than the marketfunds performed worse than the market In terms of CAPM (using alpha)In terms of CAPM (using alpha)

• Only 7 unit trusts had positive alphas (10%)Only 7 unit trusts had positive alphas (10%)• 65 (90%) performed worse than the market65 (90%) performed worse than the market• Whereas Jensen found 62.5% of mutual funds Whereas Jensen found 62.5% of mutual funds

performed worseperformed worse

Findings Con’tFindings Con’t

Average alpha for 72 unit trusts was Average alpha for 72 unit trusts was -.0134 -.0134• They earned 1.34% less than expectedThey earned 1.34% less than expected

Firth’s conclusionFirth’s conclusion• British performance has been slightly British performance has been slightly

worse than American performanceworse than American performance

Ward and SaundersWard and Saunders

““U.K. Unit Trust Performance 1964-1974”U.K. Unit Trust Performance 1964-1974”• 49 Unit trusts examined49 Unit trusts examined• Utilized Sharpe, Treynor, and Jensen Utilized Sharpe, Treynor, and Jensen

performance measuresperformance measures All measures indicated poor performanceAll measures indicated poor performance

• No alpha was positive at 5% levelNo alpha was positive at 5% level

ConclusionConclusion• Unit trusts performed poorly over a long time Unit trusts performed poorly over a long time

period and even worse than American mutual period and even worse than American mutual fundsfunds

Validity of earlier studiesValidity of earlier studies Several authors* argueSeveral authors* argue

• mean-variance performance measures mean-variance performance measures ignore higher moments of the distribution ignore higher moments of the distribution of returnsof returns

• usage of stochastic dominance rules may usage of stochastic dominance rules may be beneficial:be beneficial:

theoretically more appealingtheoretically more appealing produce more precise measure of performanceproduce more precise measure of performance mean-variance may produce erroneous mean-variance may produce erroneous

conclusionsconclusions

*References: Joy and Porter; Porter, Wart, and Ferguson; Meyer

Validity of earlier studies (cont.)Validity of earlier studies (cont.)

Potential impact of nonstationarity in the Potential impact of nonstationarity in the studied time seriesstudied time series• annual time series were studiesannual time series were studies• relatively high annual volatility of FTI (22.3%) relatively high annual volatility of FTI (22.3%)

vs. DJ (13.5%) vs. DJ (13.5%) • FTI volatility increasing over the study periodFTI volatility increasing over the study period

Porter notes to use monthly time seriesPorter notes to use monthly time series• More data points for more accurate More data points for more accurate

approximationapproximation• Use the most recent data to reduce impact of Use the most recent data to reduce impact of

nonstationaritynonstationarity

The purpose of the studyThe purpose of the study

Assess monthly rather than annual Assess monthly rather than annual performanceperformance

Consider short, but relatively stable Consider short, but relatively stable time periodtime period

Utilize FSD, SSD, and TSDUtilize FSD, SSD, and TSD Confirm or deny the results of earlier Confirm or deny the results of earlier

studies of whether U.K. trusts are studies of whether U.K. trusts are good investment vehicles for good investment vehicles for investorsinvestors

Empirical FindingsEmpirical Findings

Saunders tested monthly returns of 30 Saunders tested monthly returns of 30 major U.K. unit trusts against the major U.K. unit trusts against the Financial Times ‘650’ Index (FTI)Financial Times ‘650’ Index (FTI)

The sample was gathered between The sample was gathered between February 1975 to November 1977February 1975 to November 1977

Previous tests on mutual fund Previous tests on mutual fund performance examined a 10 year performance examined a 10 year periodperiod

ResultsResults

Empirical FindingsEmpirical Findings

The Null Hypothesis is the unit trusts, The Null Hypothesis is the unit trusts, as a group, were not different from as a group, were not different from the Financial Times Indexthe Financial Times Index• Consequently it would be expected that Consequently it would be expected that

the same number of trusts dominate the the same number of trusts dominate the FTI as visa versa FTI as visa versa

Joy and Porter method was used to Joy and Porter method was used to test unit trusts against the FTI, test unit trusts against the FTI, market proxy.market proxy.

Empirical FindingsEmpirical Findings

Second Order Stochastic DominanceSecond Order Stochastic Dominance• 50% of unit trusts outperformed the FTI while 50% of unit trusts outperformed the FTI while

only 20% were dominated by the FTIonly 20% were dominated by the FTI Third Order Stochastic DominanceThird Order Stochastic Dominance

• 66% of unit trusts dominated the FTI while 66% of unit trusts dominated the FTI while only 23% were outperformed by the FTIonly 23% were outperformed by the FTI

Summary and ConclusionSummary and Conclusion Previous studies of unit trust performance Previous studies of unit trust performance

are inconsistent with and inferior to are inconsistent with and inferior to Saunders et al. Saunders et al. • This study indicates that unit trusts have as a This study indicates that unit trusts have as a

whole outperformed the marketwhole outperformed the market• Similar studies using mean-variance efficiency Similar studies using mean-variance efficiency

frontiers did not show the superior performancefrontiers did not show the superior performance Ultimately this study shows that MV models Ultimately this study shows that MV models

put downward bias on the performance put downward bias on the performance measurement of unit trusts relative to the measurement of unit trusts relative to the marketmarket• SD methods are more sensitive and SD methods are more sensitive and

discriminating; moreover SD shows markedly discriminating; moreover SD shows markedly different resultsdifferent results

Summary and ConclusionSummary and Conclusion

27 years later27 years later• As markets become more globalized, As markets become more globalized,

and if listing business continues to move and if listing business continues to move from New York to London and Hong from New York to London and Hong Kong we may see less volatility in those Kong we may see less volatility in those large foreign markets comparatively large foreign markets comparatively speakingspeaking

• This may allow for longer time interval This may allow for longer time interval studiesstudies