1. Stochastic Dominance and the Performance of U.K. Unit Trusts Anthony Saunders Charles Ward Richard Woodward

2. U.S. Mutual Fund Studies Many tests studying the performance of U.S. mutual funds Many tests studying the performance of U.S. mutual funds Based on 2 moments of the return distributions, the mean and variance Based on 2 moments of the return distributions, the mean and variance Carlson: “The issue of whether mutual funds outperform ‘the market’ depends in large degree on the selection of both the time period and market proxy.” Carlson: “The issue of whether mutual funds outperform ‘the market’ depends in large degree on the selection of both the time period and market proxy.”

3. UK Mutual Fund Studies The same results have been found for U.K. mutual funds, or unit trusts The same results have been found for U.K. mutual funds, or unit trusts Trusts have performed poorly Trusts have performed poorly Unit trusts as a group have performed relatively much worse than U.S. mutual funds Unit trusts as a group have performed relatively much worse than U.S. mutual funds

4. Briscoe, Samuels, and Smythe Conducted first mean-variance test of U.K. unit trusts Conducted first mean-variance test of U.K. unit trusts Compared trusts’ risk-return performance to that of U.S. mutual funds (as measured by Sharpe) from 1953 to 1963 Compared trusts’ risk-return performance to that of U.S. mutual funds (as measured by Sharpe) from 1953 to 1963 Found that the average returns for mutual funds and trusts were similar, but the more risky the trust the lower its returns Found that the average returns for mutual funds and trusts were similar, but the more risky the trust the lower its returns Sharpe had found that the more risky the mutual fund, the higher its returns Sharpe had found that the more risky the mutual fund, the higher its returns Concluded that U.K. investors were not risk- averse Concluded that U.K. investors were not risk- averse The size of trusts did not fall over that periodThe size of trusts did not fall over that period

5. Firth Firth “The Investment Performance of Unit Trusts in the Period 1965-1975” “The Investment Performance of Unit Trusts in the Period 1965-1975” Examined 72 Unit Trusts Examined 72 Unit Trusts Utilized Sharpe’s reward to variability ratio and excess return from CAPM Utilized Sharpe’s reward to variability ratio and excess return from CAPM Findings Findings Poor performancePoor performance Actual returns were lower than expectedActual returns were lower than expected

6. Findings 69 out of 72 (96%) unit trusts had lower reward to variability ratios than the market 69 out of 72 (96%) unit trusts had lower reward to variability ratios than the market Sharpe found 23 out of 34 (67%) mutual funds performed worse than the market Sharpe found 23 out of 34 (67%) mutual funds 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 performed worseWhereas Jensen found 62.5% of mutual funds performed worse

7. Findings Con’t Average alpha for 72 unit trusts was -.0134 Average alpha for 72 unit trusts was -.0134 They earned 1.34% less than expectedThey earned 1.34% less than expected Firth’s conclusion Firth’s conclusion British performance has been slightly worse than American performanceBritish performance has been slightly worse than American performance

8. Ward 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 performance measuresUtilized Sharpe, Treynor, and Jensen performance measures All measures indicated poor performance All measures indicated poor performance No alpha was positive at 5% levelNo alpha was positive at 5% level Conclusion Conclusion Unit trusts performed poorly over a long time period and even worse than American mutual fundsUnit trusts performed poorly over a long time period and even worse than American mutual funds

9. Validity of earlier studies Several authors* argue Several authors* argue mean-variance performance measures ignore higher moments of the distribution of returnsmean-variance performance measures ignore higher moments of the distribution of returns usage of stochastic dominance rules may be beneficial:usage of stochastic dominance rules may be beneficial: theoretically more appealing theoretically more appealing produce more precise measure of performance produce more precise measure of performance mean-variance may produce erroneous conclusions mean-variance may produce erroneous conclusions *References: Joy and Porter; Porter, Wart, and Ferguson; Meyer

10. Validity of earlier studies (cont.) Potential impact of nonstationarity in the studied time series Potential impact of nonstationarity in the studied time series annual time series were studiesannual time series were studies relatively high annual volatility of FTI (22.3%) vs. DJ (13.5%)relatively high annual volatility of FTI (22.3%) vs. DJ (13.5%) FTI volatility increasing over the study periodFTI volatility increasing over the study period Porter notes to use monthly time series Porter notes to use monthly time series More data points for more accurate approximationMore data points for more accurate approximation Use the most recent data to reduce impact of nonstationarityUse the most recent data to reduce impact of nonstationarity

11. The purpose of the study Assess monthly rather than annual performance Assess monthly rather than annual performance Consider short, but relatively stable time period Consider short, but relatively stable time period Utilize FSD, SSD, and TSD Utilize FSD, SSD, and TSD Confirm or deny the results of earlier studies of whether U.K. trusts are good investment vehicles for investors Confirm or deny the results of earlier studies of whether U.K. trusts are good investment vehicles for investors

12. Empirical Findings Saunders tested monthly returns of 30 major U.K. unit trusts against the Financial Times ‘650’ Index (FTI) Saunders tested monthly returns of 30 major U.K. unit trusts against the Financial Times ‘650’ Index (FTI) The sample was gathered between February 1975 to November 1977 The sample was gathered between February 1975 to November 1977 Previous tests on mutual fund performance examined a 10 year period Previous tests on mutual fund performance examined a 10 year period

13. Results

14. Empirical Findings The Null Hypothesis is the unit trusts, as a group, were not different from the Financial Times Index The Null Hypothesis is the unit trusts, as a group, were not different from the Financial Times Index Consequently it would be expected that the same number of trusts dominate the FTI as visa versaConsequently it would be expected that the same number of trusts dominate the FTI as visa versa Joy and Porter method was used to test unit trusts against the FTI, market proxy. Joy and Porter method was used to test unit trusts against the FTI, market proxy.

15. Empirical Findings Second Order Stochastic Dominance Second Order Stochastic Dominance 50% of unit trusts outperformed the FTI while only 20% were dominated by the FTI50% of unit trusts outperformed the FTI while only 20% were dominated by the FTI Third Order Stochastic Dominance Third Order Stochastic Dominance 66% of unit trusts dominated the FTI while only 23% were outperformed by the FTI66% of unit trusts dominated the FTI while only 23% were outperformed by the FTI

16. Summary and Conclusion Previous studies of unit trust performance are inconsistent with and inferior to Saunders et al. Previous studies of unit trust performance are inconsistent with and inferior to Saunders et al. This study indicates that unit trusts have as a whole outperformed the marketThis study indicates that unit trusts have as a whole outperformed the market Similar studies using mean-variance efficiency frontiers did not show the superior performanceSimilar studies using mean-variance efficiency frontiers did not show the superior performance Ultimately this study shows that MV models put downward bias on the performance measurement of unit trusts relative to the market Ultimately this study shows that MV models put downward bias on the performance measurement of unit trusts relative to the market SD methods are more sensitive and discriminating; moreover SD shows markedly different resultsSD methods are more sensitive and discriminating; moreover SD shows markedly different results

17. Summary and Conclusion 27 years later 27 years later As markets become more globalized, and if listing business continues to move from New York to London and Hong Kong we may see less volatility in those large foreign markets comparatively speakingAs markets become more globalized, and if listing business continues to move from New York to London and Hong Kong we may see less volatility in those large foreign markets comparatively speaking This may allow for longer time interval studiesThis may allow for longer time interval studies