Factor exposure indexes Value factor

Transcription

1 Research Factor exposure ndexes Value factor ftserussell.com August 204

2 . Summary The value effect s one of the most studed market anomales [2-5]. The value effect or value premum refers to the tendency of stocks wth lower valuaton ratos to earn above average returns over the long run. For example, the cross-sectonal varaton of stock returns across countres can be partly explaned by a global value factor [6]. Such a value effect has been observed across many dfferent markets, regons and sample perods []. In ths paper, we use a combnaton of several common valuaton measures to capture the value premum. We assess forecast measures of Earnngs Yeld, Book to Prce, Cash Flow Yeld, Sales to Prce and Dvdend Yeld. All valuaton measures are calculated on a 2-month forward bass usng IBES estmates. We fnd a value premum that s economcally sgnfcant usng both absolute and relatve measures of value. However, the ablty to capture any value premum vares across valuaton measures. In terms of absolute measures of value, Earnngs Yeld s the most sgnfcant, followed by Cash Flow Yeld, Sales to Prce, Book to Prce and fnally Dvdend Yeld. Country relatve measures of value are generally comparable to absolute measures of value n ther ablty to dentfy a value premum: the exceptons are Earnngs Yeld whch s poorer and Sales to Prce, whch s superor to ts absolute measure. Furthermore, when value s measured by Earnngs Yeld, Cash Flow Yeld and Sales to Prce, value effects are relatvely persstent over tme. The strength and persstency of ndvdual value effects and levels of correlaton amongst ndvdual valuaton measures suggest that a combnaton of Earnngs Yeld, Cash Flow Yeld and Sales to Prce s approprate. We llustrate the smulated hstorcal performance characterstcs of varous composte value factors wthn the context of a set of llustratve ndexes. Gven the hgh correlaton between Cash Flow Yeld and Book to Prce and the smlarty of ndex level characterstcs between ndexes formed on two and three-factor compostes, we prefer a three-factor composte value measure. Snce our analyss s very much based n sample, ths s a cautous choce whch ensures greater factor dversty. Ths choce has the further advantage that our composte factor has a greater orentaton towards factors that are less susceptble to manpulaton (Cash Flow Yeld and Sales to Prce) than to those that are (Earnngs Yeld). Index characterstcs, ncludng capacty, levels of dversfcaton and the degree of exposure to the factor of nterest are robust to the frequency and tmng of the ndex rebalance. Rebalance frequency has a substantal mpact on turnover. An annual rebalance mnmses turnover; we make the pragmatc decson to rebalance annually n September order to synchronse ndex rebalances wth revews of the underlyng ndex unverse and other factor (Qualty) ndexes. We construct a broad value ndex that ncludes all underlyng ndex consttuents. We subsequently form a narrow value ndex contanng fewer stocks and dsplayng greater exposure to value and assess the robustness of performance outcomes. Ths ncreased exposure to value results n mprovements n performance compared to a broad value ndex. The paper s structured as follows: Secton 2 assesses alternatve measures of valuaton from the perspectve of sgnal strength, persstency and correlaton. FTSE Russell Factor exposure ndexes value factor

3 Secton 3 examnes practcal factor ndexes based on ndvdual valuaton measures. A broad composte value ndex s examned n Secton 4 n the context of an approprate rebalance frequency. Secton 5 examnes the mplcatons of formng a narrow composte value ndex. Secton 6 concludes. 2. Regresson analyss In order to assess the pure factor performance characterstcs of each value factor, we perform the regresson analyss detaled n Appendx A. Ths analyss results n the return to each deal factor mmckng portfolo and therefore avods any dependence on the method of ndex constructon chosen. We examne consttuents of the FTSE Developed unverse, performng monthly cross-sectonal regressons for the perod March 2000 to December 203. Table shows the average deal monthly factor returns and t-stats for each ndvdual factor wth and wthout the ncluson of ndustry and country membershp as addtonal factors. An equally weghted regresson scheme and monthly local prce returns are used to form each cross-sectonal regresson. Earnngs Yeld s the strongest and most sgnfcant factor n absolute terms, followed by Cash Flow Yeld, Sales to Prce, Book to Prce and fnally Dvdend Yeld. All ndustry relatve measures result n lower absolute levels of sgnfcance and mean returns. All country relatve measure results are comparable to the absolute factor outcomes wth the exceptons of Earnngs Yeld whch s poorer and Sales to Prce whch s superor to ts absolute measure. Ths suggests that absolute value measures may be used for Earnngs Yeld, Book to Prce, Cash Flow Yeld and Dvdend Yeld, whlst a country relatve measure s approprate for Sales to Prce. Throughout the rest of ths document we adopt these measures. Chart dsplays the two year rollng average t-stats through tme for each valuaton factor. The graphc llustrates the sgnfcance of Earnngs Yeld, Cash Flow Yeld and Sales to Prce s relatvely persstent through tme. Although Book to Prce s relatvely stable, post early 2007 t-stats are manly negatve. Dvdend yeld s relatvely unstable and nsgnfcant throughout most of the perod. FTSE Russell Factor exposure ndexes value factor 2

4 Table. Factor Returns and t-stats Factor Absolute Relatve to Industry Relatve to Country Return t-stat Return t-stat Return t-stat Earnngs Yeld 0.24% % % 0.89 Book to Prce 0.6% % % 0.66 Cash Flow Yeld 0.22% % % 0.86 Sales to Prce 0.9% % % 0.93 Dvdend Yeld 0.% % % 0.37 Source FTSE: FTSE Developed, mean, monthly factor return and cross-sectonal t-statstc; March 2000 to December 203. Past performance s no guarantee of future results. Returns shown may reflect hypothetcal hstorcal performance. Please see the dsclamer page for mportant legal dsclosures. Chart. Persstence of Sgnfcance 6 02/ / / / / / / / / / / / / / / / /200 08/200 02/20 24 Month Rollng Average T- Stat 08/20 02/202 08/202 02/203 08/ Earnngs Yeld Book to Prce Cash Flow Yeld Sales to Prce Dvdend Yeld Source FTSE: FTSE Developed, rollng two year average t-statstc; March 2000 to December 203. Past performance s no guarantee of future results. Returns shown may reflect hypothetcal hstorcal performance. Please see the dsclamer page for mportant legal dsclosures. FTSE Russell Factor exposure ndexes value factor 3

5 Chart 2 shows the cumulatve deal factor return for each value factor. The performance of value n general has been flat post September However all factors apart from Dvdend Yeld capture the value rally post the September 2008 global fnancal crss. Chart 2.Cumulatve Factor Returns Cumulatve Return / / /200 09/200 03/ / / / / / / / / / / / / / / / /200 09/200 03/20 09/20 03/202 09/202 03/203 09/203 Earnngs Yeld Book to Prce Cash Flow Yeld Sales to Prce Dvdend Yeld Source FTSE: FTSE Developed; March 2000 to December 203. Past performance s no guarantee of future results. Returns shown may reflect hypothetcal hstorcal performance. Please see the dsclamer page for mportant legal dsclosures. Table 2 shows the correlaton between monthly deal factor returns. ote that Book to Prce, Cash Flow Yeld and Sales to Prce are all strongly postvely correlated to one another. Earnngs Yeld shows a weaker postve correlaton wth all factors, whlst Dvdend Yeld s only notably postvely correlated wth Earnngs Yeld. Table 2. Correlaton of Factor Returns Earnngs Yeld Book to Prce Cash Flow Yeld Sales to Prce Dvdend Yeld Earnngs Yeld Book to Prce Cash Flow Yeld Sales to Prce Dvdend Yeld.00 Source FTSE: FTSE Developed, monthly factor return correlaton; March 2000 to December 203. Past performance s no guarantee of future results. Returns shown may reflect hypothetcal hstorcal performance. Please see the dsclamer page for mportant legal dsclosures. FTSE Russell Factor exposure ndexes value factor 4

6 Table 3 shows the cross-sectonal correlaton of raw value factor characterstcs.e. between the valuaton measures themselves rather than between the factor returns of each valuaton measure. Ths pattern s weaker, but smlar to that observed for factor returns. Table 3. Correlaton of Factor Characterstcs Earnngs Yeld Book to Prce Cash Flow Yeld Sales to Prce Dvdend Yeld Earnngs Yeld Book to Prce Cash Flow Yeld Sales to Prce Dvdend Yeld.00 Source FTSE: FTSE Developed, mean monthly cross-sectonal factor characterstc correlaton; March 2000 to December 203. Past performance s no guarantee of future results. Returns shown may reflect hypothetcal hstorcal performance. Please see the dsclamer page for mportant legal dsclosures. 3. Sngle factor ndexes In ths secton we create factor ndexes premsed on ndvdual value factor characterstcs. We employ the ndex constructon technques set out n Factor Exposure Indexes Index Constructon Methodology, FTSE (204) [7]. Brefly, we map a normalsed valuaton measure (Z-Score) to a score n the range of zero to one usng a cumulatve normal mappng. Ths score s combned wth a stock s weghtng n an underlyng ndex to determne ndvdual stock weghtngs n the value factor ndex. The approach s tantamount to a factor tlt on an underlyng ndex, where the strength (and number) of any tlts and the degree of dversfcaton may be controlled. Smulated performance fgures n the remander of ths document are USD prce returns for the perod May 2000 to December 203, where a monthly rebalance frequency s utlsed for llustratve purposes only. FTSE Russell Factor exposure ndexes value factor 5

7 Table 4 shows the smulated hstorcal performance fgures of ndexes that result from tltng away from an underlyng market captalsaton weghted ndex towards each of the alternatve value measures. We also show the resultng ndex level factor exposure (the weghted sum of ndvdual stock value factor Z-Scores, see Appendx B) relatve to the underlyng unverse and the degree to whch each ndex loads on the deal factor ndex (see appendx A for detals of ths calculaton). Fnally, we assess ndex capacty as measured by the weghted average capacty rato (WCR) and consder the degree of dversfcaton va the average Effectve through tme (see Appendx B for both defntons). Table 4. Performance of Value Factor Indexes: FTSE Developed FTSE Developed Earnngs Yeld Book to Prce Cash Flow Yeld Sales to Prce Dvdend Yeld Geometrc Mean (%) Volatlty (%) Volatlty Reducton (%) Sharpe Rato DD (%) Two Way Turnover (%) Excess (%) Trackng Error (%) Informaton Rato Alpha (%) Alpha T-Stat Beta umber of Stocks Effectve Capacty (WCR) Rel. Factor Exposure Factor Loadng Source FTSE: FTSE Developed; captalsaton weghted underlyng ndex; USD prce returns; May 2000 to December 203. Past performance s no guarantee of future results. Returns shown may reflect hypothetcal hstorcal performance. Please see the dsclamer page for mportant legal dsclosures. Earnngs Yeld, Cash Flow Yeld and Sales to Prce have hstorcally proven superor measures of value to Book to Prce and Dvdend Yeld on most performance measures. However, a Book to Prce value ndex s the most dversfed (measured by Effectve ) and the Dvdend Yeld value ndex exhbts substantally lower levels of two way turnover. All tlted ndexes acheve a smlarly hgh loadng on the relevant deal factor ndex and exhbt substantal exposure to the factor of nterest relatve to the underlyng ndex. Chart 3 shows the smulated hstorcal cumulatve performance for each factor ndex relatve to FTSE Developed through tme. FTSE Russell Factor exposure ndexes value factor 6

8 Table 5 shows the smulated performance fgures for a correspondng set of value ndexes, where the factor tlt s appled to an equally weghted verson of the FTSE Developed ndex. As expected, the capacty of these ndexes s lower than the market captalsaton tlted counterparts, whlst levels of dversfcaton (Effectve ) are superor. Each ndex contnues to exhbt a hgh loadng on the relevant deal factor ndex and a superor factor exposure relatve to the underlyng ndex. The relatve performance of both sets of ndexes s broadly smlar. Relatve performance s the result of the degree of factor exposure rather than underlyng ndex weghtng scheme. Chart 3. Cumulatve Relatve Performance of Value Factor Indexes: FTSE Developed 40 Relatve Cumulatve Performance /2000 / /200 /200 05/2002 / /2003 / /2004 / /2005 / /2006 / /2007 / /2008 / /2009 / /200 /200 05/20 /20 05/202 /202 05/203 /203 Earnngs Yeld Book to Prce Cash Flow Yeld Sales to Prce Dvdend Yeld Source FTSE: FTSE Developed; captalsaton weghted underlyng ndex; USD prce returns; May 2000 to December 203. Past performance s no guarantee of future results. Returns shown may reflect hypothetcal hstorcal performance. Please see the dsclamer page for mportant legal dsclosures. Table 5. Performance of Value Factor Indexes: FTSE Developed Equally Weghted FTSE Developed Earnngs Yeld Book to Prce Cash Flow Yeld Sales to Prce Dvdend Yeld Geometrc Mean (%) Volatlty (%) Volatlty Reducton (%) Sharpe Rato DD (%) Two Way Turnover (%) Excess (%) Trackng Error (%) Informaton Rato Alpha (%) Alpha T-Stat FTSE Russell Factor exposure ndexes value factor 7

9 FTSE Developed Earnngs Yeld Book to Prce Cash Flow Yeld Sales to Prce Dvdend Yeld Beta umber of Stocks Effectve Capacty (WCR) Rel. Factor Exposure Factor Loadng Source FTSE: FTSE Developed; equally weghted underlyng ndex; USD prce returns; May 2000 to December 203. Past performance s no guarantee of future results. Returns shown may reflect hypothetcal hstorcal performance. Please see the dsclamer page for mportant legal dsclosures. 4. Composte value ndexes In ths secton, we create composte value factor ndexes ncorporatng two, three, four and fve of the ndvdual value measures under consderaton. We consder only tlts away from a market captalsaton weghted underlyng ndex. Our results are robust to the use of an equally weghted underlyng ndex. For each composte value ndex, factors are selected on the bass of the most sgnfcant t-stat values n Table 2. All ndvdual valuaton measures are postvely correlated (See Tables 3 and 4). Consequently, we sum ndvdual cross-sectonal Z-Score measures of value to form a composte Z-Score or value metrc. Table 6 shows the smulated hstorcal performance, turnover, dversfcaton, capacty and relatve factor exposure of the ndexes. Table 6. Performance of Composte Value Indexes: FTSE Developed FTSE Developed EY/SP EY/SP/CY EY/SP/CY/BP EY/SP/CY/ BP/DY Geometrc Mean (%) Volatlty (%) Volatlty Reducton (%) Sharpe Rato DD (%) Two Way Turnover (%) Excess (%) Trackng Error (%) Informaton Rato Alpha (%) Alpha T-Stat Beta umber of Stocks Effectve Capacty (WCR) Rel. Factor Exposure Source FTSE: FTSE Developed; captalsaton weghted underlyng ndex; USD prce returns; May 2000 to December 203. Past performance s no guarantee of future results. Returns shown may reflect hypothetcal hstorcal performance. Please see the dsclamer page for mportant legal dsclosures. FTSE Russell Factor exposure ndexes value factor 8

10 As the number of factors decreases, performance metrcs mprove. Ths s the result of creatng composte measures contanng ncreasngly less relevant factors. In partcular the nformaton rato rses monotoncally as the number of factors decrease and s roughly 50% hgher for the two-factor composte than for the fve factor composte ndex. ote also, that turnover falls, but not qute monotoncally, as the number of factors s reduced. We base the choce of factors on whch to form a composte measure of value on the followng consderatons: Book to Prce and Dvdend Yeld hstorcally have a detrmental effect on the performance and turnover of composte value measures. Earnngs Yeld exhbts a relatvely strong correlaton wth Dvdend Yeld, both n terms of factor returns and factor characterstcs. Cash Flow Yeld s relatvely hghly correlated wth Book to Prce n terms of factor returns and factor characterstcs. Ths suggests that Dvdend Yeld and Book to Prce may be gnored, snce Earnngs Yeld and Cash Flow Yeld are relatvely good proxes for them. Consequently, we are left wth a choce between a two or three-factor composte measure of value: In performance, turnover and capacty terms the two-factor composte measure s slghtly superor to the three-factor composte. In dversfcaton and factor exposure terms the three-factor composte measure s slghtly superor to the two-factor composte. Gven ths analyss s very much based n sample and the smlarty of two and three factor composte ndexes n terms of ndex characterstcs, we have a mnor preference for a three-factor constructon. Ths s a cautous choce whch ensures greater factor dversty. Ths choce has the further advantage that our composte factor has a greater orentaton towards factors that are less susceptble to manpulaton (Cash Flow Yeld and Sales to Prce) than to those that are (Earnngs Yeld). The results to date ncorporate monthly ndex rebalances. From a practcal perspectve a lower rebalance frequency s requred. We llustrate that the smulated hstorcal performance characterstcs of our composte three-factor value ndex s ndependent of the rebalance frequency and rebalance cycle. Table 7 reports results for a quarterly rebalance, a sem-annual March and September rebalance, a sem annual June and December rebalance and an annual September rebalance, where the three-factor value tlt s appled to the captalsaton weghted FTSE Developed ndex. Table 7. Performance of Composte Value Index: Rebalance Frequency and Cycle FTSE Developed Monthly Quarterly Sem-Ann Mar & Sep Sem-Ann Jun & Dec Annual Geometrc Mean (%) Volatlty (%) Volatlty Reducton (%) Sharpe Rato DD (%) Two Way Turnover (%) Excess (%) FTSE Russell Factor exposure ndexes value factor 9

11 FTSE Developed Monthly Quarterly Sem-Ann Mar & Sep Sem-Ann Jun & Dec Annual Trackng Error (%) Informaton Rato Alpha (%) Alpha T-Stat Beta umber of Stocks Effectve Capacty (WCR) Rel. Factor Exposure Source FTSE: FTSE Developed; captalsaton weghted underlyng ndex; USD prce returns; May 2000 to December 203. Past performance s no guarantee of future results. Returns shown may reflect hypothetcal hstorcal performance. Please see the dsclamer page for mportant legal dsclosures. All ndex characterstcs, ncludng capacty, dversfcaton levels and the degree of factor exposure are robust to the frequency and tmng of the rebalance. The rebalance frequency has a substantal mpact on turnover. An annual rebalance mnmses turnover; we make the pragmatc decson to rebalance annually n September order to synchronse ndex rebalances wth revews of the underlyng ndex unverse and other factor (Qualty) ndexes. For comparson, an annual September revew appled to the same composte value factor, but from an equally weghted verson of the FTSE Developed results n a mean excess return of.62%p.a., two-way turnover of 5.74% p.a., an average effectve of 459, an average WCR of 0.23 and average factor exposure of arrowng of broad value ndexes The composte value ndexes examned so far are broad, retanng all underlyng ndex consttuent stocks. The aggregate ndex level factor exposure may be mproved, by removng from the broad ndex, stocks wth the smallest contrbuton to ndex level factor exposure. Specfcally, we calculate the factor contrbuton of each stock n the broad ndex (broad value ndex weght * Z-Score). We then sequentally remove stocks wth the smallest factor contrbuton and recalculate the Effectve, capacty and exposure of the resultng ndex. Ths s repeated untl the narrow ndex dversfcaton target (67% of the broad ndex); or the narrow ndex capacty target (WCR 2.5x the broad ndex); or the factor exposure objectve (2x the exposure of the broad ndex relatve to the underlyng) s acheved. As the dversfcaton target s reduced, the resultng narrow ndex becomes ncreasngly concentrated and a greater exposure to the value factor s acheved. At around two thrds of the broad ndex Effectve, we acheve notceable mprovements n factor exposure wthout compromsng the dversfcaton levels exhbted by the ndex. FTSE Russell Factor exposure ndexes value factor 0

12 Table 8 detals the result of applyng ths process to the annually rebalanced broad composte value ndex derved from the captalsaton weghted FTSE Developed Index. Table 8. Performance of a arrow Composte Value Index FTSE Developed Broad arrow Geometrc Mean (%) Volatlty (%) Volatlty Reducton (%) Sharpe Rato DD (%) Two Way Turnover (%) Excess (%) Trackng Error (%) Informaton Rato Alpha (%) Alpha T-Stat Beta umber of Stocks Effectve Capacty (WCR) Rel. Factor Exposure Source FTSE: FTSE Developed; captalsaton weghted underlyng ndex; USD prce returns; May 2000 to December 203. Past performance s no guarantee of future results. Returns shown may reflect hypothetcal hstorcal performance. Please see the dsclamer page for mportant legal dsclosures. The resultng number of stocks n the narrow ndex s on average approxmately 7% of the FTSE Developed ndex, but the dversfcaton and capacty constrants are satsfed. The narrow ndex dsplays substantally greater levels of exposure to the composte value factor, resultng n an ncrease n the factor premum, as measured by excess return. However, there s a correspondng ncrease n turnover. A comparson of Tables 7 and 8 ndcates that a narrow composte value ndex rebalanced annually exhbts almost double the levels of factor exposure (and value premum) compared to broad ndexes that are rebalanced more frequently. Turnover levels of the narrow, annually rebalanced ndex are comparable or lower to broad ndexes rebalanced more frequently. Chart 4 shows the composte value factor exposure through tme for the FTSE Developed, annually rebalanced broad and narrow composte value ndexes and a monthly rebalanced narrow ndex. The monthly rebalance provdes an ndcaton of the upper lmt to value exposure that s achevable. Chart 4 ndcates that there s lttle justfcaton for more frequent rebalances n order to mantan the value exposure of the ndex. We therefore conclude that an annually rebalanced narrow ndex s approprate. FTSE Russell Factor exposure ndexes value factor

13 To ensure the results are robust to the tmng of the annual rebalance, we examne the outcomes of annual rebalances that follow dfferent rebalance cycles (January to January, February to February, etc). Chart 5 confrms that smulated rsk adjusted performance outcomes.e. Sharpe Ratos and Two-Way Turnover outcomes are nsenstve to the tmng of the annual rebalance. Chart 4. FTSE Developed Value Exposure through Tme Value Exposure / /2000 0/200 06/200 /200 04/ / / /2003 2/ /2004 0/ / /2005 0/ /2006 / / / / /2008 2/ /2009 0/ /200 08/200 0/20 06/20 /20 04/202 09/202 02/203 07/203 2/203 FTSE Developed Broad arrow (Annually) arrow (Monthly) Source FTSE: FTSE Developed captalsaton weghted underlyng ndex; March 2000 to December 203. Past performance s no guarantee of future results. Returns shown may reflect hypothetcal hstorcal performance. Please see the dsclamer page for mportant legal dsclosures. Chart 5. FTSE Developed; Annual Rebalance Cycle, Sharpe Rato and Two-Way Turnover Sharpe Rato Two-Way Turnover (%) Jan Feb Mar Apr May Jun Jul Aug Sep Oct ov Dec 40 Sharpe Rato Two-Way Turnover Source FTSE: FTSE Developed; captalsaton weghted underlyng ndex; annual rebalance n dfferent months; May 2000 to December 203. Past performance s no guarantee of future results. Returns shown may reflect hypothetcal hstorcal performance. Please see the dsclamer page for mportant legal dsclosures. FTSE Russell Factor exposure ndexes value factor 2

14 Chart 6 shows the smulated hstorcal performance through tme for the FTSE Developed and broad and narrow composte value ndexes. Chart 6. FTSE Developed: Cumulatve Performance, Broad and arrow Value Indexes Cumulatve Performance /2000 / /200 /200 05/2002 / /2003 / /2004 / /2005 / /2006 / /2007 / /2008 / /2009 / /200 /200 05/20 /20 05/202 /202 05/203 /203 FTSE Developed Broad arrow Source FTSE: FTSE Developed; captalsaton weghted underlyng ndex; USD prce returns; May 2000 to December 203. Past performance s no guarantee of future results. Returns shown may reflect hypothetcal hstorcal performance. Please see the dsclamer page for mportant legal dsclosures. 6. Conclusons We examne fve common measures of value (Earnngs Yeld, Book to Prce, Cash Flow Yeld Sales to Prce and Dvdend Yeld); rejectng two and usng three to create a smple composte value factor. The composte measure conssts of an equally weghted combnaton of absolute measures of Earnngs Yeld and Cash Flow Yeld and a country relatve measure of Sales to Prce. Over the perod May 2000 to December 203 broad value ndexes were constructed by applyng a composte value tlt to both a captalsaton weghted and equally weghted versons of the FTSE Developed ndex. A broad value factor ndex rebalanced annually n September results n: A value premum of approxmately.9% p.a. (.6% p.a. equal weght). Sgnfcant and persstent value exposure relatve to the underlyng ndex. Comparable levels of dversfcaton to the underlyng ndex. Index capacty of 74% (67% equal weght) of the underlyng ndex. Approxmate annual two-way turnover of 29% p.a. (52% p.a. equal weght). Subsequently, we form a narrow value ndex and acheve ncreased levels of exposure to the composte value factor: A value premum of approxmately 3.5% p.a. (captalsaton weghted). 77% mprovement n factor exposure compared to the broad ndex. Dversfcaton levels of 69% of the broad ndex. Index capacty of 56% of the broad ndex. Annual two-way turnover of 48% p.a. FTSE Russell Factor exposure ndexes value factor 3

15 Appendx A. Regresson Analyss Cross-sectonal Regresson Consder the cross-sectonal regresson: J R = α + δ β + e f + ε j j j= k= K k k where R s the return of the th of stocks, e k s the exposure of the th stock to k th of K factors, δ j s ndustry (country) exposure of the th stock to j th of J ndustres (countres), wth δ = j 0 f f j j and α s an ntercept, β j s the factor return of j th ndustry (country), f k s the factor return of k th factor and ε s the resdual. For each stock the ndustry exposures J meet the condton: δ = whch acts as a constrant on our regresson. Ths s j= j ncorporated n the followng way. Let Rˆ be the return predcted by the model and W be some weghtng scheme for stocks wth w =. Then employng a weghted regresson through mnmzaton = 2 of ( ) mples that w R Rˆ = wr = = = wrˆ Further we can explot freedom to set α = wr. Takng the weghted sum of both = sdes of our regresson and smplfyng now yelds: J w δ β + w ef = 0 j j = j= = k= Reversng sums gves J wˆ β + f we = 0 j k j= k= = K k K k k where ŵ j s the weght n the j th sector. Ths last equaton s solved by settng: we = 0 and ŵ 0 k β = j j = J j= The frst of these equatons can be satsfed redefnng the factor exposure by normalsaton thus: eˆ = ( e µ )/ σ where µ = we k k k k k = k and σ = w ( e 2 2 k = k µ) k. Each normalsed factor exposure has mean zero and standard devaton of one. The second equaton can be satsfed by wrtng the return to ndustry (country) one as: β = wˆ J ˆ j j= 2 w β j FTSE Russell Factor exposure ndexes value factor 4

16 or equvalently by defnng a new exposure to ndustry operator: δˆ j = wˆ / wˆ f and j δ j 0 f and j j f = Factor and sector returns are calculated from actual returns R, new exposure functon to ndustres (countres), δˆ j and normalsed exposures to factors ê k, n the usual way. Ideal Factor Indexes and Factor Loadngs We defne the returns to an deal factor ndex X as the set of monthly factor returns f t X obtaned through the cross-sectonal regresson when we gnore ndustres (countres), retan the market ntercept and choose our value factor as a sngle factor. For a gven ndex wth monthly excess returns R t, the factor loadng F of that ndex on the th factor, s gven by tme seres regresson: R = α + F * f + ε t t where a s the ntercept and ε s the resdual. FTSE Russell Factor exposure ndexes value factor 5

17 Appendx B. Capacty, Dversfcaton and Factor Exposure Capacty Let ŵ be the weghts of the ndex for whch we are computng capacty and W the weghts of the underlyng Market Captalsaton weghted ndex. Then the weghted capacty rato (WCR) s gven by: WCR = w ˆ * wˆ w = Ths rato s bounded below by one and the larger the value, the poorer the capacty. Let M be the market captalsaton of th stock. Then the weghted average market captalsaton rato (WAMCR) s gven by: Wˆ M = * WAMCR = M W * M = Ths rato s bounded below by zero and the larger ts value, the better the capacty. Both defntons maybe used to assess the capacty of an ndex although we prefer WCR as t does not suffer from the defcency of mplyng that an ndex consstng of one stock wth market captalsaton M has the same capacty as an ndex of stocks each wth market captalsaton M. Dversfcaton The dversfcaton measure used n ths document s: Effectve = M = Wˆ 2 where Effectve s the effectve number of stocks n the ndex, M the actual number of stocks and ŵ the weght of th stock n the ndex. Factor Exposure The Factor Exposure of an ndex s defned to be: = Factor Exposure Wˆ * Z = where ŵ are the weghts of the ndex and Z s the cross-sectonal factor Z-Score. FTSE Russell Factor exposure ndexes value factor 6

18 References. Asness, C.S., Moskowtz T.J., and Pedersen L.H. Value and Momentum Everywhere, Journal of Fnance, v. 68, June 203, pp Basu, S., Investment Performance of Common Stocks n Relaton to ther Prce-Earnngs Ratos: A Test of the Effcent Market Hypothess, Journal of Fnance, v. 3, June 977, pp Danel, K. and Ttman, S., Evdence on the Characterstcs of Cross Sectonal Varaton n Stock Returns, Journal of Fnance, v. 52, March 997, pp Fama, E. F., and French, K.R. The Cross-Secton of Expected Stock Returns, Journal of Fnance, v. 47, June 992, pp Fama, E. F., and French, K.R. Common Rsk Factors n the Returns on Bonds and Stocks, Journal of Fnancal Economcs, v. 33, February 993, pp Fama, E. F., and French, K.R. Sze and Book-to-Market Factor n Earnngs and Returns, Journal of Fnance, v. 50, 995, pp Factor Exposure Indexes Index Constructon Methodology, FTSE (204) FTSE Russell Factor exposure ndexes value factor 7

19 For more nformaton about our ndexes, please vst ftserussell.com. 205 London Stock Exchange Group companes. London Stock Exchange Group companes ncludes FTSE Internatonal Lmted ( FTSE ), Frank Russell Company ( Russell ), MTS ext Lmted ( MTS ), and FTSE TMX Global Debt Captal Markets Inc ( FTSE TMX ). All rghts reserved. FTSE, Russell, MTS, FTSE TMX and FTSE Russell and other servce marks and trademarks related to the FTSE or Russell ndexes are trademarks of the London Stock Exchange Group companes and are used by FTSE, MTS, FTSE TMX and Russell under lcence. All nformaton s provded for nformaton purposes only. Every effort s made to ensure that all nformaton gven n ths publcaton s accurate, but no responsblty or lablty can be accepted by the London Stock Exchange Group companes nor ts lcensors for any errors or for any loss from use of ths publcaton. ether the London Stock Exchange Group companes nor any of ther lcensors make any clam, predcton, warranty or representaton whatsoever, expressly or mpledly, ether as to the results to be obtaned from the use of the FTSE Russell Indexes or the ftness or sutablty of the Indexes for any partcular purpose to whch they mght be put. The London Stock Exchange Group companes do not provde nvestment advce and nothng n ths document should be taken as consttutng fnancal or nvestment advce. The London Stock Exchange Group companes make no representaton regardng the advsablty of nvestng n any asset. A decson to nvest n any such asset should not be made n relance on any nformaton heren. Indexes cannot be nvested n drectly. Incluson of an asset n an ndex s not a recommendaton to buy, sell or hold that asset. The general nformaton contaned n ths publcaton should not be acted upon wthout obtanng specfc legal, tax, and nvestment advce from a lcensed professonal. o part of ths nformaton may be reproduced, stored n a retreval system or transmtted n any form or by any means, electronc, mechancal, photocopyng, recordng or otherwse, wthout pror wrtten permsson of the London Stock Exchange Group companes. Dstrbuton of the London Stock Exchange Group companes ndex values and the use of ther ndexes to create fnancal products requre a lcence wth FTSE, FTSE TMX, MTS and/or Russell and/or ts lcensors. The Industry Classfcaton Benchmark ( ICB ) s owned by FTSE. FTSE does not accept any lablty to any person for any loss or damage arsng out of any error or omsson n the ICB. Past performance s no guarantee of future results. Charts and graphs are provded for llustratve purposes only. Index returns shown may not represent the results of the actual tradng of nvestable assets. Certan returns shown may reflect back-tested performance. All performance presented pror to the ndex ncepton date s back-tested performance. Back-tested performance s not actual performance, but s hypothetcal. The back-test calculatons are based on the same methodology that was n effect when the ndex was offcally launched. However, back-tested data may reflect the applcaton of the ndex methodology wth the beneft of hndsght, and the hstorc calculatons of an ndex may change from month to month based on revsons to the underlyng economc data used n the calculaton of the ndex. FTSE Russell 8

20 About FTSE Russell FTSE Russell s a leadng global provder of benchmarkng, analytcs and data solutons for nvestors, gvng them a precse vew of the market relevant to ther nvestment process. A comprehensve range of relable and accurate ndexes provdes nvestors worldwde wth the tools they requre to measure and benchmark markets across asset classes, styles or strateges. FTSE Russell ndex expertse and products are used extensvely by nsttutonal and retal nvestors globally. For over 30 years, leadng asset owners, asset managers, ETF provders and nvestment banks have chosen FTSE Russell ndexes to benchmark ther nvestment performance and create ETFs, structured products and ndex-based dervatves. FTSE Russell s focused on applyng the hghest ndustry standards n ndex desgn and governance, employng transparent rules-based methodology nformed by ndependent commttees of leadng market partcpants. FTSE Russell fully embraces the IOSCO Prncples and ts Statement of Complance has receved ndependent assurance. Index nnovaton s drven by clent needs and customer partnershps, allowng FTSE Russell to contnually enhance the breadth, depth and reach of ts offerng. FTSE Russell s wholly owned by London Stock Exchange Group. For more nformaton, vst To learn more, vst emal ndex@russell.com, nfo@ftse.com; or call your regonal Clent Servce Team offce: EMEA +44 (0) orth Amerca Asa-Pacfc Hong Kong Tokyo Sydney +6 (0) FTSE Russell