ARE BENCHMARK ASSET ALLOCATIONS FOR AUSTRALIAN PRIVATE INVESTORS OPTIMAL?

Transcription

1 ARE BENCHMARK ASSET ALLOCATIONS FOR AUSTRALIAN PRIVATE INVESTORS OPTIMAL? Publshed n the Journal of Wealth Management, 2009, vol. 12, no. 3, pp Lujer Santacruz and Dr Peter J. Phllps Lecturer and Senor Lecturer School of Accountng, Economcs and Fnance Faculty of Busness Unversty of Southern Queensland Toowoomba QLD 4350, Australa Emal addresses: santacru@usq.edu.au and phllpsp@usq.edu.au Keywords: asset allocaton, nvestments, portfolo management, fnancal plannng Short bographes of authors: Lujer Santacruz, the correspondng author, s a Lecturer at the Unversty of Southern Queensland n Australa. He holds a Master of Fnancal Plannng from Grffth Unversty and a Master n Busness Management from the Asan Insttute of Management. Lujer was workng for a fnancal plannng group before he joned the academe. Peter Phllps s a Senor Lecturer at the Unversty of Southern Queensland. Peter obtaned hs PhD n Fnancal Economcs from USQ n Hs current research nterests span topcs n both fnance and economcs.

2 ABSTRACT In ths artcle we examne whether the benchmark asset allocatons recommended by fnancal plannng groups for prvate nvestors are optmal when measured aganst the mean-varance crteron of Modern Portfolo Theory. Usng hstorcal data for the relevant ndces, the mean-varance propertes of the varous asset classes are determned. Portfolos contanng the varous asset classes are formed accordng to the allocatons or weghtngs recommended by fnancal plannng groups. The return-rsk characterstcs of the portfolos formed on the bass of the recommended asset class allocatons are determned and a smple method of so-rsk maxmum return calculaton usng the Excel Solver command s utlsed to determne whether portfolos could be formed that are charactersed by the same levels of rsk but hgher levels of return. These are optmal portfolos that yeld the maxmum return for a gven level of rsk. Applyng ths methodology, the portfolos resultng from the fnancal plannng groups benchmark asset allocatons are found to be sgnfcantly suboptmal. On each occason, a better portfolo (yeldng a hgher expected return for the same rsk) could be found by adjustng the allocatons. INTRODUCTION Fnancal plannng groups generate strategc asset allocatons that are used to gude the allocaton of clent s funds. More than $300 bllon s guded by these strategc asset allocatons. The optmalty of the recommended weghtngs to partcular nvestment classes cash, fxed nterest, nternatonal fxed nterest, shares, nternatonal shares and property s of the utmost mportance to the very large number of nvestors whose savngs are nvested on the bass of these strategc asset allocatons. We use one of the key crterons of modern portfolo theory, meanvarance effcency, to examne the optmalty of fnancal plannng groups strategc asset allocatons. Our results, whch reveal sgnfcant sub-optmalty aganst ths crteron, provde the bass for a careful reconsderaton of the value of generc recommended asset allocatons. The recommended allocatons do provde a bass upon whch portfolos can be formed for nvestors wth dfferent levels of rsk averson. However, fnancal planners and ther clents must be aware that these allocatons may leave some money on the table that may have been captured by a portfolo bearng no addtonal rsk to one formed accordng the fnancal plannng groups strategc asset allocatons. Ths artcle s organsed as follows. In the next secton, the relevant lterature s surveyed and the theoretcal framework that forms the foundaton for our nvestgaton s outlned. In the thrd secton, the research methodology s outlned. We follow an orthodox approach that s based upon Markowtz portfolo theory. Ths nvolves the calculaton of the expected (mean) returns and varance (rsk) of returns for portfolos formed on the bass of fnancal plannng groups strategc asset allocatons. 1

3 Optmal portfolos are then computed that have hgher expected (mean) returns than the fnancal planners portfolos but wthout any addtonal rsk. In the fourth secton, the results of the analyss are presented. Usng the methodology outlned n the prevous secton, the effcency of the fnancal planners portfolos s computed and compared wth the returns generated by the correspondng optmal (mean-varance effcent) portfolos. The portfolos formed on the bass of fnancal plannng groups strategc asset allocatons are found to be mean-varance neffcent. Alternatve portfolos can be formed that are charactersed by hgher returns but no addtonal rsk. The fnal secton concludes the artcle. It s concluded that fnancal plannng groups may consder the hstorcal returns and varance of returns of partcular asset classes as the sole crteron for asset class weght recommendatons. Ths avods any relance upon commonly held subjectve belefs or perceptons about the returns and rsks of alternatve asset classes. LITERATURE REVIEW AND RESEARCH THEORETICAL FRAMEWORK The objectve of ths artcle s to examne the optmalty of fnancal plannng clents strategc asset allocatons. Fnancal plannng clents are a good startng pont n studyng prvate nvestors because fnancal planners exercse consderable control over a substantal porton of the total prvate nvestment pool. The ffty largest fnancal plannng groups have approxmately $316 bllon worth of funds under ther advce [Wlknson 2007] whch s a sgnfcant porton of the total prvate nvestment pool estmated at $1.9 trllon [Headey, Warren & Hardng 2006 and ABS 2005]. The artcle utlses the asset allocatons recommended by fnancal plannng groups to clents as a proxy for fnancal plannng clents strategc asset allocatons. The common practce n personal fnancal plannng s to assess a clent s rsk profle based on factors such as rsk averson, nvestment tme frame and lfe cycle stage and recommend an approprate strategc asset allocaton [Taylor 2007]. Small devatons are allowed when establshng the nvestment account and regular rebalancng s carred out to keep the asset allocatons n lne. It s smlar n other countres where personal fnancal plannng s an establshed practce such as n the US [Kapoor, Dlabay & Hughes 2004] and n the UK [Harrson 2005]. The mportance of ths practce of strategc asset allocaton has been establshed n research lterature [Brnson, Snger & Beebower 1991; Ibbotson & Kaplan 2000]. Gven the crucal role that asset allocaton plays, ths artcle has mplcatons for personal nvestng as well as the practce of personal fnancal plannng. There appears to have been only one prevous nvestgaton nto the optmalty of the prvate nvestors asset allocaton on the bass of fnancal planners recommendatons [Huber & Kaser 2003]. Ths study was undertaken n the US context and found that the advsor-recommended asset allocatons acheve on average 80% to 98% of optmsed portfolo returns. Lke the study cted above, almost all 2

4 the recent nvestgatons of optmalty of asset allocatons utlse the mean-varance formulaton of the Modern Portfolo Theory or MPT [Markowtz 1952] as the theoretcal framework. Ths study utlses MPT as the theoretcal framework for analysng the optmalty of the asset allocaton weghtngs recommended by the fnancal plannng groups. Markowtz specfed two varables relevant to the asset allocaton decson namely expected or ex ante portfolo return and expected or ex ante portfolo rsk (measured by computng the varance of returns). Markowtz showed how the combnaton of assets or asset classes n a portfolo could reduce total portfolo varance and, n so dong, provded the theoretcal ratonale for dversfcaton. If nvestors are solely concerned wth the expected return and rsk of ther portfolos, rsk-averse nvestors wll attempt to maxmse a utlty functon where expected return and standard devaton (rsk) of returns are the only factors that nfluence utlty. Investors are assumed to favour addtonal expected returns and dslke addtonal standard devaton of actual returns from expected returns (rsk). In practce, expected return and rsk are estmated on the bass of hstorcal asset mean returns, varances of returns and assumptons concernng the underlyng probablty dstrbuton of returns. Investors wll choose from among the portfolos avalable n the economc system on the bass of expected return and standard devaton of returns. The generaton of the full set of portfolos from whch nvestors may choose, nvolves the computaton of the expected return and varance for each possble combnaton of rsky assets n the economc system. When the expected return and varance calculatons are done for all possble combnatons of assets n the economc system, the result s a choce set from whch nvestors select a portfolo: Exhbt 1: The set of all portfolos from whch an nvestor may choose Expected return E(R) Rsk σ 2 3

5 Some of the portfolos contaned n the choce set are domnated by others. Portfolos that are located on the upper rm of the choce set have a hgher expected return for each level of rsk than portfolos contaned n the nteror of the set. Investors seekng to maxmse utlty as a functon of return and rsk wll be nterested n portfolos that are located as far to the northwest n expected return-rsk space as possble. The upper rm of the choce set s the farthest to the northwest that s possble gven the avalable assets n the economc system. Rsk-averse nvestors seekng to maxmse ther utlty wll therefore be nterested n the set of effcent portfolos that are located farther to the northwest than all other portfolos n the choce set: Exhbt 2: The set of effcent portfolos or the effcent fronter Expected return E(R) Rsk σ 2 Therefore, stated n terms of MPT, the objectve of ths artcle s to determne whether the asset allocatons recommended to nvestors by fnancal plannng groups result n portfolos that are located n the effcent fronter. If the portfolos formed on the bass of these allocatons le wthn the effcent fronter, then t wll be possble to form alternatve portfolos that yeld a hgher expected return wth the same level of rsk. The extent to whch the portfolos formed on the bass of fnancal plannng groups allocatons dverge from optmal portfolos that exhbt the same level of rsk s a measure of the neffcency of the fnancal plannng groups strategc asset allocatons. It s mportant for fnancal planners and ther clents to be aware of the possblty that portfolos that mrror the strategc asset allocatons recommended by fnancal plannng groups may generate returns that are lower than alternatve portfolos wth the same level of rsk. 4

6 DATA AND RESEARCH METHODOLOGY Ths artcle examnes the benchmark asset allocatons of ten of the thrty largest fnancal plannng groups representng approxmately $143 bllon worth of funds under advce [Wlknson 2007]. The fnancal plannng groups, desgnated by letters A to J, have determned the followng nvestor styles and assocated asset allocatons based on ex ante belefs and expectatons about the varous asset classes. Exhbt 3: Benchmark asset allocatons of fnancal plannng groups Fnancal plannng group Investor rsk profle Cash Recommended strategc asset allocaton (%) Property A Conservatve Moderately conservatve Balanced Moderately aggressve Aggressve B Captal secure Conservatve Moderate Balanced Growth Hgh growth C Cautous Conservatve Moderately conservatve Balanced Growth Hgh growth D Defensve Moderately defensve Balanced Growth Hgh growth E, F, G Preservaton Conservatve Moderately conservatve Balanced Assertve Aggressve

7 Fnancal plannng group Investor rsk profle Cash Recommended strategc asset allocaton (%) Property H, I, J Conservatve Moderately conservatve Balanced Growth Hgh growth Monthly total return or accumulaton ndces data were obtaned for each of the asset classes lsted n Exhbt 3, to be used n calculatng hstorcal returns. The ndces are establshed ndustry nvestment performance benchmarks [Gallagher 2002] and are also used by fund managers. The use of ndces to derve the asset class returns for the analyss s justfed by the fact that fnancal planners generally recommend managed funds to clents and are the man dstrbutors of managed funds [AXISS 2004]. The unavalablty of some ndex data for certan perods constraned the analyss to the perod from 31/01/1986 to the tme of wrtng or around a 21-year perod. The monthly returns are derved from the ndex data and are used as the bass for the mean-varance analyss of the portfolos. To provde a way of valdatng the result of the analyss, two sets of analyss are carred out: (1) based on last 21 years data; and (2) based on last 5 years data. The descrptve statstcs for each asset class are presented n the followng tables. Exhbt 4: Descrptve statstcs for last 21 years data Cash Property Mean Std dev Exhbt 5: Descrptve statstcs for last 5-years data Cash Property Mean Std dev

8 It s noted that the mean-varance characterstcs for the varous asset classes are not consstent wth common belef and expectatons. For nstance, Cash and both domnate Internatonal and the same s true for Property and over Internatonal. In addton to asset class returns and varances, the other nputs to the MPT model are the covarances between the asset class returns. These are summarsed n the followng tables. Exhbt 6: Covarance matrx for last 21 years data Cash Property Cash AFI IFI Property AS IS Exhbt 7: Covarance matrx for last 5 years data Cash Property Cash AFI IFI Property AS IS Usng these returns and covarances, we compute the expected (mean) return and varance for each of the portfolos defned by the weghtng schedules presented n Exhbt 3. The varance s a measure of the rsk assocated wth each nvestor style. As expected, the portfolos recommended for more conservatve nvestor styles exhbt a lower varance of returns than those portfolos recommended for less rsk-averse nvestors. Once we have the mean and varance assocated wth the portfolos formed on the bass of the weghtng schedules presented n Exhbt 3, we can compute the set of correspondng optmal portfolos. The optmal portfolos possess the hghest level of mean return attanable by re-weghtng the portfolos whlst mantanng the orgnal level of rsk. The optmal portfolos are computed by solvng the followng quadratc programmng problem for each recommended portfolos n order to assess the effcency or optmalty of these portfolos: 7

9 Exhbt 8: The quadratc programmng problem max E( R ) = Subject to a target level of varance: And the constrants: 2 p n n =åå = 1 j= 1 P j n å = 1 j w E( R ) s w w r ss = s j 2 ** p n å = 1 w = 1 w ³ 0 Ths s a varaton of the so-return mnmum varance method of dervng the effcent fronter dscussed n most textbooks [Elton et al. 2003; Strong 2006]. The methodology deployed n ths artcle s summarsed step-by-step n the followng table. For each portfolo formed usng the fnancal plannng groups weghtng schedules, the followng steps were undertaken: Exhbt 9: Methodology deployed Step Formula or procedure 1. Compute the expected monthly return and rsk for each of the portfolos formed usng the fnancal plannng groups weghtngs. E( RP) = we( R) n å = 1 s 2 p n n n 2 2 =å ws +åå = 1 = 1 j= 1 ¹ j w w r ss j j j 2. Solve the quadratc programmng problem for each of the portfolos derved n the frst step usng Excel Solver. Solver s a command that utlses what-f analyss to fnd an optmal value for a varable subject to constrants (see Appendx). In ths case, the output varable that wll be optmsed s E(Rp) subject to a certan rsk value and the nput varables that wll be vared are the portfolo weghtngs. 3. Record the expected returns generated by the optmal portfolos determned n the second step. 4. Usng the expected returns and varances of the optmal portfolos, plot the effcent set n expected return-rsk space. 5. Plot the expected returns and varances of the fnancal plannng groups portfolos relatve to the effcent set to show (n)effcency and calculate the percentage shortfall from the optmal return. max E( R ) = P n å = 1 w E( R ) subject to the rsk computed n the frst step 8

10 These steps were carred out for both sets of hstorcal data: (1) the last 21-year perod; and (2) last 5- year perod. A smlar applcaton of the Excel Solver command was utlsed n another asset allocaton optmsaton study [Grover & Lavn 2007] where they used nstead a sngle ndex model. The soluton to the quadratc programmng problem determnes the exstence and defnton of a weghtng schedule that produces a hgher portfolo expected return wth the same level of rsk as the portfolo formed utlsng a fnancal plannng group s weghtng schedule. Such portfolos, f they exst, represent a combnaton of the asset classes lsted n Exhbt 3 that domnates the portfolos formed utlsng the weghtngs suggested by the varous fnancal plannng groups. The portfolos derved from the soluton of the quadratc programmng problem wll be located n the effcent set of portfolos. If such portfolos are shown to exst, the assocated fnancal plannng groups portfolos wll be shown to be located n the nteror of the effcent set n neffcent postons. The results of the nvestgaton are presented n the followng secton. RESULTS Usng the last 21 years data, t was dscovered that the recommended weghtng schedules generated portfolos that le n the nteror of the mean-varance opportunty set and are, therefore, less than optmal when measured on the bass of the mean-varance effcency crteron. The soluton of the quadratc programmng problem for each of the recommended portfolos generated a set of portfolos that le n the effcent fronter. The exstence of these effcent portfolos suggests that fnancal plannng clents strategc asset allocatons could have been mproved by the selecton of alternatve weghtng schedules. These alternatve mean-varance effcent weghtng schedules generate portfolos wth the same level of rsk as the recommended portfolos but produce hgher expected (mean) returns. The results based on the last 21 years data are summarsed n the followng chart and table. 9

11 Exhbt 10: Results based on last 21 years data Recommended portfolos versus effcent fronter (last 21 years data) Expected return Optmal portfolos Recommended portfolos Effcent fronter Rsk Fnancal plannng group Investor rsk profle Rsk Recommended portfolo Expected return Optmal portfolo Shortfall A Conservatve % Moderately conservatve % Balanced % Moderately aggressve % Aggressve % B Captal secure % Conservatve % Moderate % Balanced % Growth % Hgh growth % C Cautous % Conservatve % Moderately conservatve % Balanced % Growth % Hgh growth % 10

12 D Defensve % Moderately defensve % Balanced % Growth % Hgh growth % E, F, G Preservaton % Conservatve % Moderately conservatve % Balanced % Assertve % Aggressve % H, I, J Conservatve % Moderately conservatve % Balanced % Growth % Hgh growth % Average shortfall 8.4% When the same analyss s appled usng the last 5 years data, the results are even more strkng. The recommended portfolos were found to le a consderable dstance from the effcent fronter. The chart below ndcates that a sgnfcantly hgher expected monthly return could be generated by fndng the effcent combnaton assocated wth each of the recommended portfolos and selectng alternatve portfolo weghtng schemes. The mean-varance neffcency of the recommended portfolos based on the last 5 years data results n expected monthly returns that are on average about one-thrd below the expected monthly returns generated by the effcent portfolos. 11

13 Exhbt 11: Results based on last 5 years data Recommended portfolos versus effcent fronter (last 5 years data) Expected return Optmal portfolos Recommended portfolos Effcent fronter Rsk Fnancal plannng group Investor rsk profle Rsk Recommended portfolo Expected return Optmal portfolo Shortfall A Conservatve % Moderately conservatve % Balanced % Moderately aggressve % Aggressve % B Captal secure % Conservatve % Moderate % Balanced % Growth % Hgh growth % C Cautous % Conservatve % Moderately conservatve % Balanced % Growth % Hgh growth % 12

14 D Defensve % Moderately defensve % Balanced % Growth % Hgh growth % E, F, G Preservaton % Conservatve % Moderately conservatve % Balanced % Assertve % Aggressve % H, I, J Conservatve % Moderately conservatve % Balanced % Growth % Hgh growth % Average shortfall 32.2% The presence of taxes would not have a sgnfcant effect on the results. The results reported above are before-tax returns. Once taxes are taken nto account, the returns actually obtaned by nvestors wll be lower for all portfolos and the relatve effcency of the portfolos may be affected to some degree. Ths may potentally reduce the effcency gap between the fnancal planners portfolos and the correspondng optmal portfolos. For example, whereas t mght be optmal (pre-tax) for nvestors to nvest a hgher percentage of ther portfolos n, say, fxed nterest vs-à-vs shares, once the taxaton advantages assocated wth the favourable taxaton treatment of dvdends (n the presence of an mputaton taxaton system) s consdered, the excess returns generated by the optmal portfolo may be dmnshed. However, there are two factors that allow us to conclude that taxaton effects are unlkely to dramatcally alter the conclusons of our analyss. Frst, the re-weghtng nvolved n the formaton of the optmal portfolos rarely nvolves a shft to asset classes where the taxaton treatment s dfferent (or, to be precse) less favourable. In most cases, the re-weghtng nvolved a swtch from nternatonal fxed nterest to fxed nterest for the more conservatve portfolos and a swtch from nternatonal shares to shares and a swtch from shares to property for the less conservatve portfolos. Second, the magntude of the neffcency of the fnancal plannng groups portfolos far exceeds any dsadvantages that may have been accorded to those portfolos or advantages that may have been accorded to the optmal portfolos that would see a reversal of the postons. 13

15 CONCLUSION fnancal plannng clents followng the fnancal plannng groups recommended asset allocaton strateges would have found ex post that ther shortfall n expected returns has been substantal, based on both the last 21 years and last 5 years data. These shortfalls are even more sgnfcant when one consders that the recommended asset allocatons are supposed to be strategc and are mantaned for a long nvestment horzon. To hghlght the magntude of the shortfalls we have dentfed that a $100,000 optmal portfolo earnng 10% pa wll compound to $1.74 mllon n 30 years but wll only be $1.40 mllon f the return s 9.2% pa or 8% less as was the result for the analyss based on last 21 years data. It would be a lot less wth the 32% sub-optmalty result for the analyss based on last 5 years data. If the level of mean-varance neffcency revealed by ths analyss of the hstorcal returns seres s ndcatve of the future performance of the fnancal plannng groups portfolos vs-à-vs those portfolos formed on the bass of Markowtz portfolo methods and hstorcal returns data, fnancal plannng clents mght fnd ther termnal wealth to be substantally lower than that whch could have been generated (wthout bearng any addtonal rsk n the form of hgher return varance). It s lkely that the benchmark asset allocatons of fnancal plannng groups are based on the commonly held belefs or perceptons regardng the nherent return-rsk characterstcs of the varous asset classes. These belefs are not necessarly supported by hstorcal data. For nstance, t s not generally held to be the case that both Property and wll domnate Internatonal. However, ths s what was revealed by the hstorcal data for the last 21 years and even more so by the last 5 years of data. Ths rases the queston whether analysts formulatng asset allocaton polces should focus solely actual hstorcal performance rather than commonly held belefs about the return-rsk characterstcs of partcular asset classes. The fact that sub-optmalty appears to be unform across the fnancal plannng groups seems to ndcate a consensus among analysts as far as these belefs are concerned. The ex-post approach based on actual hstorcal performance s sometmes noted as a crtcsm of the Markowtz model but compared to ex-ante analyss could t be the more practcal approach? The nvestgaton of strategc asset allocaton holds many tantalsng prospects for future research. One of the more nterestng avenues for future research concerns the possblty of nvestgatng the formulaton of the fnancal plannng groups strategc asset allocatons from the pont of vew of behavoural fnance. Fnancal plannng groups do not appear to base ther recommendatons solely upon the mean-varance crteron and nstead rely upon analyss and judgement that takes nto consderaton a larger number of varables. To the extent that ths wder analyss must nclude a subjectve assessment of varous aspects of the nvestment envronment and context, behavoural 14

16 fnance provdes a framework wth whch to analyse the decson-makng process that s undertaken by fnancal plannng groups. The focus of future research would be on the presence of varous bases n the decson-makng processes of the fnancal plannng groups durng the formulaton of strategc asset allocatons. These bases under-reacton, over-reacton, myopc loss averson, over-confdence and the utlsaton of heurstcs or rules of thumb 1 have been dentfed n the nvestment behavour of both professonal and non-professonal nvestors n a varety of contexts. Gven the mportance of strategc asset allocaton recommendatons, t would certanly be worthwhle explorng the constructons of these recommendatons from the vewpont of behavoural fnance. 1 See, for an overvew, Thaler (1999). 15

17 REFERENCES ABS 2005, Year Book Australa, Bureau of Statstcs, Canberra. AXISS 2004, Dstrbuton of Managed Funds n Australa, AXISS Australa, Sydney. Brnson, GP, Snger, BD & Beebower, GL 1991, 'Determnants of portfolo performance II: an update', Fnancal Analysts Journal, vol. 47, no. 3, pp Elton, EJ, Gruber, MJ, Brown, SJ & Goetzmann, WN 2003, Modern Portfolo Theory and Investment Analyss, 6th edn, J. Wley & Sons, New York. Gallagher, D 2002, 'Investment Manager Characterstcs, Strategy and Fund Performance', Doctor of Phlosophy thess, The Unversty of Sydney. Harrson, D 2005, Personal Fnancal Plannng: Theory and Practce, Fnancal Tmes Prentce Hall, Harlow. Headey, B, Warren, D & Hardng, G 2006, Famles, Income and Jobs: a Statstcal Report of the HILDA Survey, Melbourne Insttute of Appled Economc and Socal Research, Melbourne. Huber, C & Kaser, H 2003, 'Asset allocaton recommendatons of fnancal advsors: are they rsk/return optmal?' Journal of Wealth Management, vol. 6, no. 2, pp Ibbotson, RG & Kaplan, PD 2000, 'Does asset allocaton polcy explan 40, 90, or 100 percent of performance?' Fnancal Analysts Journal, vol. 56, no. 1, p. 26. Kapoor, JR, Dlabay, LR & Hughes, RJ 2004, Personal Fnance, 7th edn, The McGraw-Hll/Irwn seres n fnance, nsurance, and real estate, McGraw-Hll, Boston. Markowtz, H 1952, 'Portfolo selecton', Journal of Fnance, vol. 7, no. 1, pp Strong, RA 2006, Portfolo Constructon, Management, and Protecton, 4th edn, Thomson South- Western, Australa. Taylor, S 2007, Fnancal Plannng n Australa, LexsNexs Butterworths, Sydney. Thaler, R.H. 1999, The End of Behavoural Fnance, Fnancal Analysts Journal, November/December, pp Wlknson, J 2007, 'Carvng up the ever-ncreasng FUA pe', Money Management, vol. 21, no. 23, pp