The Ex Ante Efficiency of Australian Stock
Market Benchmarks

by
Frank Finn †
Timo Koivurinne †




Abstract:
This paper t...
AUSTRALIAN JOURNAL OF MANAGEMENT                                            June 2000


1.   Introduction

T   he ex ante ...
Vol. 25, No. 1                 Finn & Koivurinne: AUSTRALIAN STOCK MARKET BENCHMARKS


unbiased market expectations at tha...
AUSTRALIAN JOURNAL OF MANAGEMENT                                                                  June 2000


            ...
Vol. 25, No. 1               Finn & Koivurinne: AUSTRALIAN STOCK MARKET BENCHMARKS


      The GRS test can be used to tes...
AUSTRALIAN JOURNAL OF MANAGEMENT                                                     June 2000


largely undiversifiable. ...
Vol. 25, No. 1               Finn & Koivurinne: AUSTRALIAN STOCK MARKET BENCHMARKS


Resources Accumulation Index, and the...
AUSTRALIAN JOURNAL OF MANAGEMENT                                                                 June 2000


decision for ...
Vol. 25, No. 1                 Finn & Koivurinne: AUSTRALIAN STOCK MARKET BENCHMARKS


                                   ...
AUSTRALIAN JOURNAL OF MANAGEMENT                                                                                    June 2...
Vol. 25, No. 1                 Finn & Koivurinne: AUSTRALIAN STOCK MARKET BENCHMARKS


                                   ...
AUSTRALIAN JOURNAL OF MANAGEMENT                                          June 2000


                                 Tab...
Vol. 25, No. 1           Finn & Koivurinne: AUSTRALIAN STOCK MARKET BENCHMARKS


the All Industrials and All Resources Acc...
AUSTRALIAN JOURNAL OF MANAGEMENT                                                 June 2000


6.   Conclusions
This paper h...
Vol. 25, No. 1              Finn & Koivurinne: AUSTRALIAN STOCK MARKET BENCHMARKS


      Further studies could extend thi...
AUSTRALIAN JOURNAL OF MANAGEMENT        June 2000




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The Ex Ante Efficiency of Australian Stock Market Benchmarks

  1. 1. The Ex Ante Efficiency of Australian Stock Market Benchmarks by Frank Finn † Timo Koivurinne † Abstract: This paper tests the ex ante efficiency of Australian benchmark portfolios over the period 1980–1996. Indices commonly used as performance evaluation benchmarks were found to be ex ante inefficient when unrestricted short selling was allowed. However, when short selling was restricted, the ex ante efficiency of the benchmarks could not be rejected. Further, the mining/resource and property sectors were not performance-enhancing additions to investment in the industrial sector over the period examined. This has important implications for the performance evaluation of managed investment funds. Keywords: INVESTMENT PERFORMANCE EVALUATION; PORTFOLIO EFFICIENCY; STOCK MARKET BENCHMARKS. † Department of Commerce, The University of Queensland, Brisbane QLD 4072. Email: finn@commerce.uq.edu.au The authors wish to thank Mary Rose Cooney, Stephen Gray and a referee for comments on an earlier version of the paper. Australian Journal of Management, Vol. 25, No. 1, June 2000, © The Australian Graduate School of Management –1–
  2. 2. AUSTRALIAN JOURNAL OF MANAGEMENT June 2000 1. Introduction T he ex ante mean-variance efficiency of market benchmarks such as the Australian All Ordinaries Index is a vital issue for investors, given the correspondence between the ex ante efficiency of indices and the inability of active investors to ‘beat’ the benchmark on a risk-adjusted basis (Grinold 1992). This paper investigates the ex ante efficiency of Australian stock market indices and the implications of any inefficiency for active investors/fund managers whose performance is measured by a comparison with such indices. In particular, we examine whether certain investment sets can be used to exploit any index inefficiency to achieve favourable performance evaluations in the long run. The investment decisions that are examined involve industry weighting strategies, with special attention given to the usefulness of mining/resource sector assets for active investors. This is important in light of the historically anomalous poor performance of the mining sector in Australia on a risk-adjusted basis (Ball and Brown 1980). In addition, the Australian property sector is examined in the same manner. We also examine the effect of short-selling restrictions on the ex ante efficiency of the indices. The study presents evidence that in certain contexts, indices commonly used in Australia such as the All Ordinaries Accumulation Index and the All Industrials Accumulation Index were ex ante inefficient benchmarks over the period 1980 to 1996, and hence may possibly be outperformed by active investment strategies. However, this possibility may be negated if short selling is restricted. Section 2 discusses ex ante efficiency and describes the tests to determine if an index is ex ante efficient. Section 3 outlines the tests conducted to examine the ex ante efficiency of Australian stock market indices. Section 4 outlines the data and methodology, and section 5 the results. The conclusions are in section 6. 2. Ex Ante Efficiency In this study, ex ante efficiency refers to mean-variance efficiency based on market expectations. In an information-efficient market, the equilibrium expectations of the market fully reflect all available information. While expectations at a point in time may be over-estimates or under-estimates, they will be unbiased such that on average, they will be realised and, by definition, market expectations will be the best predictions of future returns and covariances. The ability of active investors is most often gauged by their ability to ‘beat’ a stock market index (or indices) on a risk-adjusted basis. Such an evaluation is done after the fact and hence is an ex post examination of the relative efficiency of an investor’s portfolio and the benchmark index. Why then would a fund manager evaluated on this basis be concerned with whether the benchmark is ex ante efficient? The reason is that for an investor to be able to outperform a benchmark over a long period, the benchmark must necessarily be ex ante inefficient. As Grinold (1992) points out, if this is not the case, no matter how much insight an investor can have of market expectations, or even if he/she can match market expectations, it will be impossible to beat the index on average, let alone consistently. This is because an ex ante efficient index represents, by definition, the best portfolio that can be formed at any given time, based on –2–
  3. 3. Vol. 25, No. 1 Finn & Koivurinne: AUSTRALIAN STOCK MARKET BENCHMARKS unbiased market expectations at that time. In such an environment, a cheaper, passive investment strategy that seeks to match the index rather than beat it will be optimal in the long run. 2.1 Testing Ex Ante Efficiency Testing ex ante efficiency directly is difficult because market expectations are not observable. However, several tests have been developed that allow us to make deductions about ex ante efficiency from ex post data. These tests begin with the following multivariate linear regression model: r it = α ip + βip rpt + eit, for all i = 1 . . .N where: rit = the excess return (excess to the riskless rate) on asset i in period t; rpt = the period t excess return on portfolio p whose efficiency is being tested; eit = the disturbance term for asset i in period t; and N = the number of assets in the test. That is, portfolio p is being tested for efficiency with respect to itself and N other assets or portfolios. If portfolio p is ex ante efficient, then from the mathematics of the efficient set: E(rit) = β ip E(rpt), for all i. From this the following null hypothesis follows: Ho: α ip = 0 for all i = 1 . . . N. Under the assumption that the disturbance terms, eit, are joint normally distributed with mean zero and a stationary covariance matrix conditional on the excess return of portfolio p, Gibbons, Ross and Shanken (1989) develop a test statistic to test the above null hypothesis.1 The GRS test calculates a test statistic equal to: (T − N − 1) (φ* 2 − φ p 2 ) Q= x N 1+ φ p 2 where: φ* = the Sharpe ratio (the ratio of excess return to standard deviation) of the portfolio with the highest Sharpe ratio that can be formed using N assets and portfolio p; φp = the Sharpe ratio of portfolio p; 1. The assumption that the disturbance terms are normally distributed is likely to be violated in stock return data (Richardson & Smith 1993). However, using monthly U.K. data, Fletcher (1994) concluded that the GRS test was fairly robust to violations of the distributional assumption and performed better than other tests of ex ante efficiency which do not make this assumption. –3–
  4. 4. AUSTRALIAN JOURNAL OF MANAGEMENT June 2000 N = the number of assets other than portfolio p that are used to construct the efficient frontier from which φ* is derived; and T = the number of time periods in the sample for which returns are calculated. The Q–statistic has a central F–distribution with N and (T–N–1) degrees of freedom. The p–value of the calculated Q–statistic can be interpreted as the probability of the index that is examined, portfolio p, being ex ante efficient. The hypothesis of efficiency is conventionally rejected if this probability is less than 5%. The GRS test seeks to distinguish between ex ante expectations and ex post realisations. The intuition of the test is as follows. If expectations are known at a given point in time, we can construct the ex ante efficient frontier for all risky assets in mean-standard deviation space. Given the existence of a risk-free asset, rf, the efficient frontier will then become the line through the excess return on rf which is tangent to the efficient set of risky assets. If portfolio p is ex ante efficient, it will be the portfolio at the point of tangency of this line with the mean-standard deviation efficient set of risky assets. After a period of elapsed time we can observe the ex post efficient frontier. Because realisations will in general not equal expectations, portfolio p, even if ex ante efficient, will in general not be the ex post efficient portfolio p*. The relative performances of portfolios p* and p can be tested by their respective Sharpe ratios, φ* and φp. Geometrically, this is equivalent to testing the slope of the line from the excess return on rf through p* versus that of the line from the excess return on rf through p. If the difference in the slopes is sufficiently large we reject the null hypothesis that portfolio p was ex ante efficient. 2.2 Prior Literature Most previous studies that have used the GRS test have focused on the question of whether some index is ex ante efficient per se (Gibbons, Ross & Shanken 1989; Kandel & Stambaugh 1987; Fletcher 1994). However, Grinold (1992) used the GRS test from the point of view of providing insights into the opportunities available for investors to beat an index in the long run. Importantly, Grinold (1992) points out that the conclusions that can be drawn from this test are only interpretable within the context of the optimisation process used to derive the tangency portfolio.2 That is, we can only conclude that an index is inefficient or efficient with respect to those assets used to derive an optimal investment set, and from which the inputs to the Q–statistic are derived. For example, if the investment set consists of assets comprising size deciles then the only conclusions that can be drawn relate to whether an investor could potentially beat the index in the long run by employing an investment strategy which involves under or over-weighting exposure to these size segments. This says nothing about the possibility of beating an index using a different strategy involving different assets so as to ‘bet’ on different factors. 2. The tangency portfolio is at the point of tangency between the mean-standard deviation efficient frontier and a line drawn from the risk-free rate of return. This is the ex post efficient portfolio (p*) whose Sharpe ratio (φ*) is used in the GRS test. –4–
  5. 5. Vol. 25, No. 1 Finn & Koivurinne: AUSTRALIAN STOCK MARKET BENCHMARKS The GRS test can be used to test a rich array of investment possibilities. For example, Grinold (1992) examined the efficiency of five world indices with respect to tilt portfolios that manipulate exposure to factors including size, volatility, momentum and value while holding the other factors in each tilt portfolio constant. The probability of the Australian All Ordinaries Accumulation Index being ex ante efficient with respect to such an investment opportunity set was found to be 0.021%, indicating that the index was inefficient with respect to this investment set. 3. Efficiency Tests Conducted 3.1 All Ordinaries Index To our knowledge, Grinold (1992) is the only published study investigating the ex ante efficiency of an Australian benchmark portfolio. He tested the efficiency of the All Ordinaries Index with respect to an investment set comprised of the index and the four tilt portfolios mentioned above. We attempt to model realistic investment opportunity sets confronting investors, and test the ex ante efficiency of different benchmarks with respect to these investment sets. The investment sets are modelled by different industry sector portfolios and we investigate the probability of an investor being able to beat a given benchmark by ‘betting’ on different industry sector weightings. This models a fundamental choice confronting investors and is akin to the asset allocation problem faced by investors/fund managers. The first test investigates the ex ante efficiency of the Australian All Ordinaries Accumulation Index with respect to itself and different industry sector indices, both with and without restrictions on short selling. Prior studies (Gibbons, Ross & Shanken 1989; Kandel & Stambaugh 1987; Fletcher 1994) use an unconstrained optimisation process which permits unlimited short selling. In Australia, there are certain institutional restrictions on short selling3, and in addition many fund managers impose internal short-selling restrictions making a portfolio comprised of unrestricted short sales an unrealistic investment option in many cases. Thus we compare results obtained from an unconstrained optimisation process with results from a process constrained to minimum sector weightings of zero, that is, no short sales permitted. 3.2 The Mining/Resources Sector Ball and Brown (1980) showed that over the 22-year period from 1958 to 1979, Australian mining stocks under-performed industrial/commercial stocks on a risk- adjusted basis. Over that period, the average return of both groups was approximately the same, but the mining portfolio examined had a standard deviation of returns twice that of the industrial stock portfolio. Ball and Brown (1980) also concluded that this extra risk in mining stocks was not easily diversified away because the correlation coefficient with the industrial/commercial portfolio was +0.72. The GRS test provides a very useful mechanism for testing the likelihood of this being a long-term anomaly and for testing the conclusion that this extra risk is 3. See s. 68 Securities Industry Act 1980 (Cwlth) and ASX Rules 2.11.2–2.11.4. Note: only ‘approved securities’, listed in ASX Rules 6.6 can be short-sold. –5–
  6. 6. AUSTRALIAN JOURNAL OF MANAGEMENT June 2000 largely undiversifiable. Also, in line with the thrust of this paper, the GRS test provides insight into whether the mining/resources sector forms a useful part of an investor’s portfolio. In our framework, this is equivalent to testing whether a diversified industrial portfolio, the All Industrial Accumulation Index, is ex ante efficient with respect to an investment set comprising itself and various mining/resource sector portfolios. These portfolios are the five resource sector accumulation indices compiled by the ASX.4 This is tested with and without short selling using data from January 1980, that is, immediately after the Ball and Brown (1980) period. If mining stocks are indeed less efficient in mean-variance space than industrial/commercial stocks, and if the relative inefficiency of mining stocks cannot be diversified away, then we would expect this to ‘drag down’ the efficiency of the All Ordinaries Accumulation Index. Under this scenario, an industrial index such as the All Industrials Accumulation Index would be a more efficient benchmark than the All Ordinaries Accumulation Index, and a passive investor seeking to match a benchmark would be better off to follow an industrial benchmark. In the context of the GRS test, we can draw conclusions regarding the efficiency of the two indices only if the indices are directly included in the investment set being examined. Thus in this section we also test the ex ante efficiency of the All Ordinaries Accumulation Index with respect to the All Industrials Accumulation Index. 3.3 The Property Sector Apart from the industrial and resources sectors, the other main sector with representation on the Australian Stock Exchange is property, or more specifically property trusts. Ball and Bowers (1986) provide data on the returns and standard deviations of property trusts for the period 1974–1985, with property trusts experiencing slightly higher mean returns and a lower standard deviation of returns than an index of all stocks (ex property trusts) over the period. Property exposure will be present in any industrial portfolio in view of the property assets owned by industrial companies. However, investors can choose to weight their portfolios more towards property by investing in the property sector, represented here by property trusts. This asset allocation choice is examined by testing the ex ante efficiency of a composite Industrials Index (ex property trusts) with respect to an investment set comprising itself and the Property Trusts Accumulation Index. 4. Data and Methodology Industry sector portfolios were modelled over the period January 1980 to October 1996 using industry accumulation indices calculated by the Australian Stock Exchange. As described below, different indices were combined to form different industry portfolios. This made use of the indices beyond October 1996 problematic since the classification of the indices changed after that date. Some indices ceased and others were merged. Monthly closing values were collected for 23 industry sector Accumulation Indices, the All Industrials Accumulation Index, the All 4. That is, diversified resources, gold, oil and gas, other metals, solid fuels. –6–
  7. 7. Vol. 25, No. 1 Finn & Koivurinne: AUSTRALIAN STOCK MARKET BENCHMARKS Resources Accumulation Index, and the All Ordinaries Accumulation Index. Data to June 1993 were collected from the STATEX database. Data for the rest of the sample period were collected from the Australian Market Quote service (AMQ). To model the risk-free rate, closing monthly yields quoted by Authorised Dealers on 90-day Bank-Accepted-Bills were used. Data for the periods October 1981 to November 1991 and from July 1993 to October 1996 were available on the AMQ database. Data not available on the AMQ database were collected from the Australian Financial Review.5 For each index, an arithmetic monthly return and standard deviation were calculated, and monthly excess returns were used to calculate Sharpe ratios. For each test, the investment set was defined according to which sectors/assets were assumed available for investment. For tests where the investment set comprises the full complement of industry sectors, it is necessary, due to power considerations in the use of the GRS test, to combine the 23 industry indices into natural groupings based on shared attributes. This is because the power of the GRS test depends critically on T being much greater than N.6 The groupings used are summarised in table 1. Table 1 Group Allocations Group 1 Group 2 Group 3 Group 4 Group 5 Group 6 All Resources Alcohol and Banking Building Property Groups 2, 3, 4 (subsumes all Tobacco Insurance Materials Trusts Industrials (ex of the mining Food and Investment & Chemicals property trusts) indices) Household Financial Developers/ Goods Services Contractors Engineering Transport Media Paper Retail These groupings represent portfolios with equal weighting in each constituent index. Group 1 proxies the resource sector; group 2 combines sectors associated with human consumption; group 3 comprises the financial sector; group 4 is all other industrial sectors except for property trusts; and group 5 is property trusts. For further analysis the groups are merged by combining groups 2, 3 and 4 to form a composite portfolio of industrial/commercial stocks excluding property trusts, hereafter group 6. Hence, the weighting process is simplified to what is a crucial 5. Bank bill rates and index values were verified by comparing overlapping samples from AMQ, STATEX and the Australian Financial Review. Further, overlapping samples for the indices from AMQ and STATEX were also compared. Minor discrepancies were found and STATEX data was preferred in these cases for the sake of continuity. 6. See Kandel and Stambaugh (1987). –7–
  8. 8. AUSTRALIAN JOURNAL OF MANAGEMENT June 2000 decision for many investors, that is, the allocation of funds among the resources sector, the industrial/commercial sector, and the property sector.7 Portfolio or group variances were estimated from the covariance matrix of returns between all the indices. The ‘Solver’ program in Microsoft Excel 1997 was used to vary the weights assigned to each index to find the combination appropriate to each test that had the highest Sharpe ratio during the sample period.8 By definition, this is the sample tangency portfolio. A short-selling constraint, whereby all industry weights must be greater than or equal to zero, was also imposed upon the optimisation process. The Sharpe ratio of the sample tangency portfolio was compared to the Sharpe ratio of the index under examination in each test according to the transformation proposed by Gibbons, Ross and Shanken (1989) and described in section 2.1. 5. Analysis and Results 5.1 Ex Post Results Examination of the ex post Sharpe ratios reveals large differences among the indices. The Sharpe ratios of the indices range from 0.162 to –0.002. These values together with the Sharpe ratios of Groups 1–6 are summarised in table 2. Mining and resource stocks performed especially poorly, consistent with Ball and Brown (1980). This poor performance is particularly evident in the solid fuels sector which under-performed the risk-free rate during the sample period. None of the mining and resource indices performed close to the All Industrials Accumulation Index. Also, it is interesting to note that the Sharpe ratio of the All Ordinaries Accumulation Index was approximately half that of the All Industrials Accumulation Index. The ex post efficient frontier constructed from the 23 industry sector indices and the All Ordinaries, All Industrials and All Resources Accumulation Indices, with no short selling, is shown in figure 1. As discussed in section 2.1, the GRS test distinguishes between ex ante expectations and ex post realisations. Table 2 and figure 1 show the ex post realisations for various portfolios. The ex ante efficiency of different benchmark portfolios is tested in the following sections. 5.2 All Ordinaries Index The results for each GRS test are summarised in table 3. In panel A, the All Ordinaries Accumulation Index is tested for ex ante efficiency, firstly with the five industry grouping (Groups 1–5) in table 1, and secondly with the 3 industry grouping (groups 1, 5, 6) representing the resources, industrials and property sectors. When short selling is unrestricted, the All Ordinaries Accumulation Index is found to be ex ante inefficient with respect to the investment opportunities available in the industry weighting process. The five group optimisation gives 7. The indices for Diversified Industrials, Diversified Resources, Miscellaneous Industrials, Miscellaneous Resources and Entrepreneurial Investors were not included in the groups because these ‘portfolios’ can be expected to be represented by combinations of the other indices. 8. Compare this with Grinold (1992) who assumed that the optimal portfolio had an excess return of 1% per month. –8–
  9. 9. Vol. 25, No. 1 Finn & Koivurinne: AUSTRALIAN STOCK MARKET BENCHMARKS Table 2 Descriptive Statistics of ASX Accumulation Indices / Study Groupings January 1980–October 1996 Average Excess Standard Index/Group Return Deviation Sharpe Ratio (% per month) (%) All Industrials 0.607 5.251 0.116 All Ordinaries 0.310 5.856 0.053 All Resources 0.023 7.641 0.003 Alcohol and Tobacco 0.933 5.777 0.161 Banking 0.767 5.993 0.128 Building Materials 0.439 5.512 0.080 Chemicals 0.750 6.343 0.118 Developers and Contractors 0.770 6.668 0.115 Diversified Industrials 0.812 6.550 0.124 Engineering 0.235 6.155 0.038 Entrepreneurial Investors 0.549 8.353 0.066 Food and Household Goods 0.871 5.356 0.163 Insurance 0.880 6.850 0.128 Investment and Financial Services 0.496 5.257 0.094 Media 1.387 8.933 0.155 Miscellaneous Industrials 0.290 6.901 0.042 Miscellaneous Services 0.222 5.424 0.041 Paper 0.366 5.309 0.069 Property Trusts 0.233 3.631 0.064 Retail 0.500 6.072 0.082 Transport 0.633 7.228 0.088 Diversified Resources 0.422 7.595 0.056 Gold 0.642 13.174 0.049 Oil and Gas 0.061 8.893 0.007 Other Metals 0.046 8.810 0.005 Solid Fuels –0.161 7.106 –0.023 Group 1 0.023 7.641 0.003 Group 2 0.902 5.078 0.178 Group 3 0.714 5.140 0.139 Group 4 0.635 5.493 0.116 Group 5 0.233 3.631 0.064 Group 6 (Industrials ex property) 0.750 4.927 0.152 –9–
  10. 10. AUSTRALIAN JOURNAL OF MANAGEMENT June 2000 Figure 1 Ex Post Efficient Frontier Constructed Using 23 Industry Sector Indices and the All Ordinaries, All Industrials and All Resources Accumulation Indices with No Short Selling January 1980–October 1996 1.6 1.4 Excess Return (% per month) 1.2 1 0.8 All Industrials Acc. Index 0.6 0.4 All Ordinaries Acc. Index 0.2 All Resources Acc. Index 0 0 0 1 1 2 2 3 34 45 56 6 7 7 8 8 9 9 10 Standard Deviation (%) significant results (p = 0.0165) as does the three group optimisation (p = 0.0037). We conclude that the All Ordinaries Accumulation Index was ex ante inefficient over the period 1980 to 1996, and thus a ‘beatable’ benchmark if an unrestricted industry weighting process could be used. When a short-selling restriction is imposed, quite different results emerge. We are unable to reject the ex ante efficiency of the All Ordinaries Accumulation Index in this context, p = 0.352 for the five group optimisation and p = 0.264 for the three group optimisation. Hence we cannot conclude that the All Ordinaries Accumulation Index could be outperformed using an industry weighting strategy without short selling.9 9. The five and three group optimisations resulted in an adequate approximation of the investment set using all 23 individual indices: the maximum Sharpe ratios were 0.1777 and 0.1523, respectively, compared with that using all indices of 0.1888. GRS tests were not conducted using the 23 individual indices because of power considerations. See Kandel and Stambaugh (1987) for further discussion of the tradeoff between the number of time periods, T, and the number of assets in the investment set, N. – 10 –
  11. 11. Vol. 25, No. 1 Finn & Koivurinne: AUSTRALIAN STOCK MARKET BENCHMARKS Table 3 Results of the GRS Tests 1 Investment Set/Benchmark Short Selling Max. Sharpe p–value Ratio Panel A: All Ordinaries Index Groups 1–5, All Ords Index/All Ordinaries Index Yes 0.2759 0.0165* Groups 1, 5, 6, All Ords Index/All Ordinaries Index Yes 0.2716 0.0037** Groups 1–5, All Ords Index/All Ordinaries Index No 0.1777 0.3520 Groups 1, 5, 6, All Ords Index/All Ordinaries Index No 0.1523 0.2642 Panel B: Mining/Resources Sector Resource Indices, All Inds/All Industrials Index Yes 0.3100 0.0173* Resource Indices, All Inds/All Industrials Index No 0.1156 1.0000 All Inds, All Ords/All Ordinaries Index Yes 0.1859 0.0128* All Inds, All Ords/All Ordinaries Index No 0.1156 0.1493 Panel C: Property Sector Property Trusts, Group 6/Group 6 (All Inds ex prop) Yes 0.1620 0.5868 Property Trusts, Group 6/Group 6 (All Inds ex prop) No 0.1523 1.0000 Note: * significant at the 0.05 level; ** significant at the 0.01 level; and 1 the GRS Test tests the ex ante efficiency of the Benchmark Index with respect to the investment set shown before the solidus, /. The difference in results for these two tests is important given that prior studies have implicitly ignored the possibility of short selling constraints. The maximum Sharpe ratio with short selling was greater than 1.5 times that without short selling. Tables 4 and 5 show the optimal ex post weightings for the five and three group optimisations, respectively. The tables indicate that the optimal ex post portfolios with unrestricted weightings would have involved extensive short selling. In excess of five times the portfolio weighting would have been short in the All Ordinaries Accumulation Index itself, an unlikely scenario for mainstream fund managers given institutional and internal fund restrictions on short selling. However, the implications of the results may be quite different for so-called hedge funds, some of which explicitly engage in large scale short selling of individual stocks or of the index. As discussed above, with unrestricted short selling the All Ordinaries Accumulation Index was ex ante inefficient and was thus potentially ‘beatable’ by a hedge fund. – 11 –
  12. 12. AUSTRALIAN JOURNAL OF MANAGEMENT June 2000 Table 4 Five Group Optimisation—Optimal Ex Post Weightings Using Five Industry Sector Groupings January 1980–October 1996 Investment Set Weights With Weights Without Component Short Sales Short Sales Group 1 1.470 – Group 2 1.960 0.973 Group 3 1.188 – Group 4 1.798 – Group 5 –0.171 0.027 All Ordinaries –5.244 – Max. Sharpe Ratio 0.2759 0.1777 Table 5 Three Group Optimisation—Optimal Ex Post Weightings Using Three Industry Sector Groupings January 1980–October 1996 Investment Set Weights with Weights Without Component Short Sales Short Sales Group 1 1.402 – Group 5 –0.182 – Group 6 4.859 1 All Ordinaries –5.080 – Max. Sharpe Ratio 0.2716 0.1523 5.3 The Mining/Resources Sector Table 2 shows the poor ex post risk-adjusted performance of the All Resources Index and each of the individual resource indices relative to the All Industrials Index. This poor ex post performance is also clearly evident in figure 1. Combining our results with those of Ball and Brown (1980), the mining/resource sector has demonstrated inferior performance in mean-variance space for almost 40 years, 1958–1996. The results of the GRS tests in panel B of table 3 provide further insight. When a short selling restriction is imposed on an investment set comprising the All Industrials Accumulation Index and the mining/resource sector indices, the tangency portfolio is the All Industrials Accumulation Index itself, p = 1.000. The All Industrials Accumulation Index was ex ante efficient with respect to this investment set, indicating that an investor could not improve performance by investing in the mining indices. The absence of any mining indices in the tangency portfolio supports the conclusion of Ball and Brown (1980) that the extra risk in mining stocks is not easily diversified away. The correlation coefficient between – 12 –
  13. 13. Vol. 25, No. 1 Finn & Koivurinne: AUSTRALIAN STOCK MARKET BENCHMARKS the All Industrials and All Resources Accumulation Indices for our period was 0.73, remarkably consistent with that found by Ball and Brown (1980) for the correlation between diversified industrial and mining portfolios for their sample period, that is 0.72. When short selling is allowed, again quite different results are obtained. The results indicate that the All Industrials Accumulation Index was ex ante inefficient with respect to an investment set containing itself and various mining sector indices, p = 0.0173. However, this is solely due to short selling the mining sector. An investor who could short sell without restrictions could enhance the performance of an industrial sector portfolio by short selling the mining sector. This is intuitively evident from the ex post risk-adjusted performance of the mining sector. The conclusions regarding the mining/resources sector are reinforced by the results of the tests of the ex ante efficiency of the All Ordinaries Accumulation Index with respect to the All Industrials Accumulation Index, shown in the bottom two lines of panel B of table 3. When short selling is unrestricted, the All Ordinaries Accumulation Index was ex ante inefficient, p = 0.0128. When short selling is restricted, the tangency portfolio is again the All Industrials Accumulation Index itself. Thus, when short selling is restricted, a passive investor seeking to match a benchmark would be better off to follow the industrial benchmark rather than the all ordinaries benchmark which includes the mining/resources sector. The result also has implications for an active fund manager whose performance is assessed relative to a benchmark of the All Ordinaries Accumulation Index. Such a fund manager would have been able to beat the benchmark simply by tilting the investment portfolio away from the resources sector and towards the industrial sector. 5.4 The Property Sector Consistent with Ball and Bowers (1986), the property sector showed a lower standard deviation of returns than did the industrial sector, refer to table 2. In fact, the Property Trust Accumulation Index had the lowest standard deviation of any of the individual indices for our sample period. However, this lower risk was accompanied by lower excess returns relative to the other industrial indices. To test whether the property sector was a performance enhancing addition to the industrial sector, we tested the ex ante efficiency of our composite Industrials Index (ex property trusts), group 6 in table 1, with respect to itself and the Property Trust Index, group 5. The results are summarised in panel C of table 3. When short selling was restricted the tangency portfolio was group 6 itself, and the GRS test indicates p = 1.00. That is, the composite Industrials Index (ex property trusts) was ex ante efficient with respect to this investment set. When short selling was allowed, the tangency portfolio was short in property. However, the maximum Sharpe ratio of this portfolio was not sufficient to allow rejection of the ex ante efficiency of the industrial (ex property) portfolio, p = 0.587. That is, we cannot conclude that the addition of the property sector enhanced the performance of an industrial (ex property) investment set. – 13 –
  14. 14. AUSTRALIAN JOURNAL OF MANAGEMENT June 2000 6. Conclusions This paper has tested the ex ante efficiency of a number of Australian stock market indices with respect to a number of different investment sets. This corresponds to testing whether a particular index can be ‘beaten’ by an active investor in the long run. It is important to note that the analysis in the paper is presented within the mean-variance paradigm. The results may not be valid within an alternative risk- return model which incorporates, for example, higher moments of the distribution of returns. It should also be noted that if a particular benchmark index is found to be ex ante inefficient, the implication is that it is possible for an active investor to beat the benchmark in the long run. However, this possibility may be remote from a practical standpoint, especially when the ex ante inefficiency of the benchmark implies large weightings in short positions. Over the period January 1980 to October 1996 the All Ordinaries Accumulation Index was found to be ex ante inefficient with respect to industry weighting strategies when short selling was unrestricted. However, a similar conclusion could not be drawn when short selling was restricted. In fact, in all of our tests when short selling was restricted, the ex ante efficiency of the relevant benchmark could not be rejected. The mining/resources sector significantly under-performed the industrial sector over our sample period. When this result is combined with the earlier results of Ball and Brown (1980), the Australian resources sector has significantly under- performed the industrial sector in mean-variance space for almost 40 years. Further, the GRS test indicates that in the absence of large-scale short selling, the All Industrials Accumulation Index was ex ante efficient with respect to itself and the mining/resources indices. The conclusion is that in an ex ante sense an investor could not enhance the performance of the All Industrials Index by including investment in the mining/resources sector. Similarly, the property sector, as represented by the Property Trust Accumulation Index, added nothing in an ex ante sense to the industrial sector, regardless of whether or not short selling was restricted. These results have important implications for both active and passive investors. For investors assessing the performance of an active fund manager, the industrial index (ex property trusts) was a more efficient benchmark than a broader market benchmark which included the resources or property sectors. Similarly, the industrial index (ex property trusts) was the better portfolio for a passive investor to seek to emulate. These results must seriously question the widespread fund performance standard of benchmarking the market portfolio as the All Ordinaries Accumulation Index. The results of the paper also have implications for the use of the Capital Asset Pricing Model in investment performance evaluation, since the CAPM assumes that the market portfolio is efficient. For example, Dybvig and Ross (1985) have shown that if betas are calculated using an inefficient market proxy, assets that under- perform the benchmark in mean-variance space can exhibit apparent abnormal performance in mean-beta space. The result that a benchmark (with unrestricted short selling) is ex ante inefficient is a double-edged sword for active investors. It gives them hope of out-performing the benchmark, yet deprives them of an appropriate evaluation method for assessing whether or not this has been done. – 14 –
  15. 15. Vol. 25, No. 1 Finn & Koivurinne: AUSTRALIAN STOCK MARKET BENCHMARKS Further studies could extend this paper to investment contexts other than the industry weighting strategies tested here. Given that the GRS test gives a measure of unconditional efficiency, similar hypotheses could be tested for conditional efficiency where asset betas and residual variances are allowed to vary over time.10 (Date of receipt of final transcript: February, 2000. Accepted by Stephen Gray, Area Editor) References Ball, R. & Bowers, J. 1986, ‘Shares, bonds, treasury notes, property trusts and inflation: Historical returns and risks, 1974–1985’, Australian Journal of Management, vol. 11, no. 2, pp. 117–37. Ball, R. & Brown, P. 1980, ‘Risk and return from equity investments in the Australian mining industry: January 1958–February 1979’, Australian Journal of Management, vol. 5, nos. 1 & 2, pp. 45–66. Dybvig, P. & Ross, S. 1985, ‘The analytics of performance measurement using a security market line’, Journal of Finance, vol. 40, no. 2, pp. 401–16. Ferson, W., Kandel, S. & Stambaugh, R. 1987, ‘Tests of asset pricing with time-varying expected risk premiums and market betas’, Journal of Finance, vol. 42, pp. 201–20. Fletcher, J. 1994, ‘The mean-variance efficiency of benchmark portfolios: U.K. evidence’, Journal of Banking and Finance, vol. 18, pp. 637–85. Gibbons, M., Ross, S. & Shanken, J. 1989, ‘A test for the efficiency of a given portfolio’, Econometrica, vol. 57, no. 5, pp. 1121–52. Grinold, R.C. 1992, ‘Are benchmark portfolio’s efficient?’ The Journal of Portfolio Management, vol. 19, no. 1, pp. 34–40. Kandel, S. & Stambaugh, R. 1987, ‘On correlations and inferences about mean-variance efficiency’, Journal of Financial Economics, vol. 18, pp. 61–90. Richardson, M. & Smith, T. 1993, ‘A test for multivariate normality in stock returns’, Journal of Business, vol. 66, no. 2, pp. 295–321. Shanken, J. 1990, ‘Intertemporal asset pricing: An empirical investigation’ Journal of Econometrics, vol. 45, pp. 99–120. 10. For example, see Ferson, Kandel and Stambaugh (1987) and Shanken (1990). – 15 –
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