Research & Analytics. Low and Minimum Volatility Indices

Transcription

1 Research & Analytics Low and Minimum Volatility Indices

2 Contents 1. Introduction 2. Alternative Approaches 3. Risk Weighted Indices 4. Low Volatility Indices 5. FTSE s Approach to Minimum Variance 6. Methodology - Overview of Objective and Constraints 7. Small Scale FTSE USA Minimum Variance Index 8. FTSE Developed Minimum Variance Index 9. Regional Results 10. Summary and Conclusions 11. Appendix Mathematical details Additional regional results Page 2 Low & Minimum Volatility Indices

3 1. Introduction Macro Environment & Volatility 10% 8% 6% 4% 2% 0% -2% -4% -6% Japan (%) 1980s 2000s Real GDP Inflation 3-1 Nominal GDP Nominal Bond Yield 8 Japan 10 yr BY vs. Nominal GDP y/y% From 8% to 1% 1 (now 0.7) -8% Jan-90 Jan-92 Jan-94 Jan-96 Jan-98 Jan-00 Jan-02 Jan-04 Jan-06 Jan-08 Jan-10 Jan-12 Japan Nominal GDP growth Y/Y GJGB10 Index 07/02/2013 US (%) US10 yr BY vs. Nominal GDP y/y% 2013 Real GDP Inflation Nominal GDP Nominal Bond Yield 7 2 (heading 3)? Page 3

4 1. Introduction Macro Environment & Volatility The decline in Nominal and Real Yields Decline in trend GDP growth expectations Persistently higher volatility? Decline in Equity return projections Joined up thinking: Dimson, Marsh & Staunton (LBS) 2013 study concluded that: low real interest rates lead to a period of low equity returns they project c 3-3.5% The US CBO has cut US potential GDP growth to: 2.2% for period vs. 3.3% for Page 4

5 2. Alternative Approaches Implementation of minimum volatility portfolio requires constraints. Max stock, sector country and turnover constraints are typical. Minimum Volatility subject to constraints is a low volatility approach. Examine simpler approaches and compare to an investable minimum volatility outcome. Approaches Risk or inverse variance weight stocks Correlations are ignored. Screen universe for a low volatility subset of stocks Capture systematic return associated with factor. Volatility reduction is incidental. Within industry screens to control tracking error Apply market cap or risk weight schemes. Min Volatility Portfolio Small scale problem using empirical covariance matrix. Large scale problem requires factor model. Assess rebalance frequency, concentration and liquidity. Page 5 Low and Minimum Volatility Indices

6 3. Risk Weighted Indices Re-weight ALL stocks by inverse of realised variance. No optimisation required. Closed form solution of Minimum Variance Portfolio when correlation is ignored (crosscorrelations are zero). Variance of daily USD returns over two years. Performance Summary Developed Europe Developed Asia Pac FTSE USA World Developed Risk Wgt Underlying Risk Wgt Underlying Risk Wgt Underlying Risk Wgt Underlying G. Mean (%p.a.) Volatility (%p.a.) Sharpe Ratio Volatility Reduction(%) DD (%) Way Turnover (%p.a.) Excess (% p.a.) Tracking Error(%p.a.) Information Ratio Alpha (% p.a.) Alpha t Stat Beta Results September 2001 to December 2011: All figures are USD total returns, except FTSE Developed Europe (Euro) Smaller volatility reduction compared to Min Variance cross-correlation is important. Relatively low tracking error and turnover a consequence of reweighting the entire universe. Page 6 Low and Minimum Volatility Indices

7 Relative Performance Volatility Reduction(%) Risk Weighted Indices: Regional & Global Risk Weighted Indices: Regional & Global 10 Risk Weight - Full Universe: Reduction in 252 Day Rolling Volatility AWDEURS AWDPAC WIUSA AWD Risk Weight - Full Universe: Relative Performance AWDEURS AWDPAC WIUSA AWD Results September 2001 to December 2011: All figures are USD total returns, except FTSE Developed Europe (Euro) Page 7 Low and Minimum Volatility Indices

8 % Weight Risk Weighted Indices: Regional & Global Risk Weighted Indices: Regional & Global Similar concentration levels to Min Variance at the large cap end of the spectrum. Re-weighting of entire universe leads to less concentrated outcomes within small caps. Substantially more diversified outcomes than underlying cap weight index. FTSE Developed Concentration / Lorenz Curves 100% 90% 80% 70% 60% 50% 40% 30% 20% 10% 0% 0% 20% 40% 60% 80% 100% % Stocks FTSE AWD Min Var Underlying FTSE AWD FTSE AWD Risk Weight Industry Weights : Dec 2011 Rebalance Technology Financials Utilities Telecommunications Consumer Services Health Care Consumer Goods Industrials Basic Materials Oil & Gas 0% 5% 10% 15% 20% 25% Industry Weight(%) AWD WIUSA AWDPAC AWDEURS Page 8 Low and Minimum Volatility Indices

9 4. Low Volatility Indices: FTSE Developed Target the return characteristics of low volatility stocks. Volatility used to select stocks. Low volatility outcome is incidental - there is no specific volatility target. Apply cap and risk weights to selected universe. Factors and Construction Factors Annualised daily volatility over 2 years in USD. Selection Selection universe FTSE Developed. Lowest volatility encompassing 50% of market cap. Within industry - lowest volatility encompassing 50% of market cap. Construction Capitalisation or risk weight. Rebalance quarterly in March, June, September & December. Period September 2001 to December Page 9 Low and Minimum Volatility Indices

10 Low Volatility Indices: FTSE Developed Low Volatility FTSE Developed: Universe & Within Industry Selection Cap & Risk Weight Performance Summary 50% By Cap 50% By Cap Universe Intra-Ind Cap Wgt Risk Wgt Cap Wgt Risk Wgt Underlying G. Mean (%p.a.) Volatility (%p.a.) Sharpe Ratio Volatility Reduction(%) DD (%) Way Turnover (%p.a.) Excess (% p.a.) Tracking Error(%p.a.) Information Ratio Alpha (% p.a.) Alpha t Stat Beta Results September 2001 to December 2011: All figures are USD total returns Application of risk weights to low volatility universe - similar volatility reduction to Min Var Cap weighted versions result in relatively small volatility reductions Risk weights lead to a consequent increase in tracking error and turnover Intra-industry selection reduces tracking error Industry Weights : Dec 2011 Rebalance Technology Financials Telecommunications Consumer Services Health Care Consumer Goods Industrials Basic Materials Oil & Gas Risk weighting applied to intra-industry selection substantially increases levels of diversification Utilities Volatility differences are relatively small - inverse variance weighting is closer to equal weight 0% 10% 20% 30% Industry Weight(%) Low 50% By Cap:Intra-Ind:Risk Wgt Low 50% By Cap:Intra-Ind Low 50% By Cap: Risk Wgt Low 50% By Cap Page 10 Low and Minimum Volatility Indices

11 Volatility Reduction(%) Low Volatility Factor Indices: FTSE Developed Low Volatility FTSE Developed: Universe & Within Industry Selection By Cap Cap & Risk Weight Risk & Cap Weight: Reduction in 252 Day Rolling Volatility Low 50% By Cap Low 50% By Cap: Risk Wgt -50 Low 50% By Cap:Intra-Ind Low 50% By Cap:Intra-Ind:Risk Wgt Page 11 Low and Minimum Volatility Indices

12 5. FTSE s Approach to Minimum Variance Overall aims Volatility reduction rather than performance 20-30% average volatility reduction. Broad, diversified and investable portfolios 60% p.a. two way turnover. Straightforward, intuitive methodology no turnover constraint. Robust outcomes consistent reduction in volatility. Factor exposures - Style Primarily low beta, low residual volatility and to a lesser extent small cap. Turnover limited through a semi-annual rebalance Volatility reduction not affected by rebalance frequency. 60% two way p.a. on average. Page 12

13 FTSE s Approach to Minimum Variance Constraints and Diversification some constraints are useful Constraints act as insurance against over concentration in any particular stock, sector or country. No explicit turnover constraint. Such a constraint leads to a path dependency of resulting portfolios. Diversification constraint regularises covariance matrix. Factor or Risk Model facilitates finding a solution, but does not determine outcomes If risk model is important, why constrain factor exposures? Equally, why impose country or industry constraints? The sophistication of factor model is not key. Data Frequency and Window Results are robust to data frequency or data window selected. Page 13

14 6. Methodology - Overview of Objective and Constraints Objective Minimise the expected index volatility or variance the marginal risk contribution of all stocks is equal. Methodology requires only historic volatility and correlations expected returns play no role. Two years of daily observations used for correlations and volatility, with semi-annual rebalancing. Principal Component Analysis (PCA) factor model used to construct the covariance matrix. Factor Model overcomes degeneracy / dimensionality problem and facilitates solution. Underlying index: FTSE All-World Developed Index Series. Page 14

15 Methodology Constraints Constraints Stock Weight: maximum weight to avoid concentration in any particular stock. Industry Weight: maximum weight to ensure diversification. Diversification Target: ensures a minimum number of stocks in the index. Capacity Constraint: maximum weight of a constituent relative to the underlying index to promote capacity / avoid illiquidity issues. Effective Zero Weight: excludes constituents with a weight of less than 1 basis point. Constraint summary: World Developed Developed Asia Pacific USA Developed Europe Upper Stock Weight Limit Capacity Constraint Upper ICB Industry Weight Limit Diversification Target Effective Zero Weight 1.0% 1.5% 1.5% 1.5% 20x 20x 20x 20x 20% 20% 20% 20% bp 1bp 1bp 1bp Page 15

16 Country Weight (%) Methodology - Constraints Country Weight: for a given country weight in the underlying, the minimum and maximum country weights in the minimum variance portfolio lie between upper and lower bounds: Underlying Country Weight (%) Underlying Minimum Maximum Page 16

17 7. Small Scale FTSE USA Minimum Variance Index Minimise the expected index volatility the marginal risk contribution of all stocks is equal. Construction requires only volatility and correlations expected return plays no role. 2 years of daily observations and quarterly rebalancing. Intuitively the Norm constraint ensures a minimum holding. Covariance matrix with and without a factor model. Objective & Constraints Page 17 Low and Minimum Volatility Indices

18 % Weight FTSE USA Minimum Variance: With & Without Factor Model Factor model facilitates solving the problem No material difference in outcomes Volatility reduction in the order of 17%; 2 way turnover of 80% p.a. Broadly diversified outcome across industry groups Min Variance portfolio significantly more diversified than underlying FTSE USA Minimum Variance: With & Without Factor Model FTSE USA Factor Model Underlying No Factor Model Underlying G. Mean (%p.a.) Volatility (%p.a.) Sharpe Ratio Volatility Reduction(%) DD (%) Way Turnover (%p.a.) Excess (% p.a.) Tracking Error(%p.a.) Information Ratio Alpha (% p.a.) Alpha t Stat Beta FTSE USA Industry Weights : Dec 2011 Rebalance Technology Financials Utilities Telecommunications Consumer Services Health Care Consumer Goods Industrials Basic Materials Oil & Gas 0% 5% 10% 15% 20% No Factor Model Industry Weight(%) Factor Model 100% Min Variance & Underlying: Lorenz Curves 90% 80% 70% 60% 50% 40% 30% 20% 10% 0% 0% 20% 40% 60% 80% 100% % Stocks FTSE USA results September 2001 to December 2011: All figures are USD total returns. FTSE USA Min Var Underlying FTSE USA Page 18 Low and Minimum Volatility Indices

19 252 Day Rolling Volatility (%) Volatility Reduction 8. FTSE Developed Minimum Variance Index Factor model does not drive outcomes, but for larger problems is necessary Constraints are necessary to achieve investable outcome Volatility reduction is greatest during periods of high volatility day Rolling Volatility of FTSE Developed Index vs. FTSE Developed Minimum Variance Index 35% % 25% 20% 15% 10% 5% 0% 11/09/02 15/06/12, Total Return (USD) Underlying Minimum Variance Volatility Reduction Page 19

20 Performance FTSE Developed Minimum Variance Index - Performance Consistent out performance through entire period, but particularly noticeable when significant falls occur in the underlying. Absolute and Relative Performance of FTSE Developed Minimum Variance Index vs. FTSE Developed Index Underlying Minimum Variance Relative 21/09/01 15/06/12, Total Return (USD) Page 20

21 FTSE Developed Minimum Variance Index Comparative Statistics A semi-annual rebalance (March and September) yields comparable results to the quarterly rebalance, but at markedly lower levels of turnover. Volatility reduction of 28%. Significantly lower draw down. Diversification minimum variance index holds approximately two-thirds of underlying stocks. UNDERLYING MINIMUM VARIANCE Semi-Annual Quarterly Geometric Mean (%) Volatlility (%) Volatlility Reduction (%) Sharpe Ratio DD (%) Mean Number of Stocks Two Way Turnover (%) Excess (%) Tracking Error (%) Information Ratio Alpha (%) Alpha T-Stat Beta All statistics are on an annual basis 21/09/01 15/06/12, Total Return (USD) Page 21

22 FTSE Developed Minimum Variance Index Country and Sector Weights USA UK Switzerland Sweden Spain Singapore Portugal Austria New Zealand Norway Netherlands Korea Japan Italy Israel Ireland Hong Kong Greece Germany France Finland Denmark Canada Belgium Australia Active Country Weight (%) Technology Financials Utilities Telecommunications Consumer Services Health Care Consumer Goods Industrials Basic Materials Oil & Gas Industry Weight (%) Minimum Variance Underlying All data as at March 2012 rebalance Page 22

23 % of Weight FTSE Developed Minimum Variance Index Concentration 100% 90% 80% 70% 60% 50% 40% Lorenz curves for March 2012 rebalance indicate that the minimum variance portfolio is substantially less concentrated than the underlying cap weighted index. 30% 20% 10% 0% 0% 20% 40% 60% 80% 100% % of Stocks Underlying Min Variance All data as at March 2012 rebalance Page 23

24 % Implemented % Rebalanced FTSE Developed Minimum Variance Index Liquidity Liquidity considerations: assumed US$1bn portfolio size at March 2012 rebalance 79% (97%) of the minimum variance portfolio can be implemented at less than 10% (50%) of average daily traded volume (ADTV). 82% (96%) of the minimum variance portfolio can be rebalanced at 2%(8%) of ADTV. Cap weighted indices typically offer substantial implementation advantages % Share of ADTV % Share of ADTV Underlying Min Variance Underlying Min Variance Page 24

25 Volatility Reduction 9. Regional Results Volatility Reduction Volatility reductions of the order of 20-30% on average are achieved for all regions. 50% 252-day Rolling Volatility Reduction of Regional Minimum Variance Index vs. Cap Weighted Index 45% 40% 35% 30% 25% 20% 15% 10% 5% 0% World Developed Asia Pacific USA Europe 11/09/02 15/06/12, Total Return (USD) except Total Return (EUR) for Europe Page 25

26 Relative Performance Regional Results Performance Although performance is not specifically targeted, all regions outperform their cap weighted counterparts Relative Performance of Regional Minimum Variance Index vs. Cap Weighted Index World Developed Asia Pacific USA Europe 21/09/01 15/06/12, Total Return (USD) except Total Return (EUR) for Europe Page 26

27 Regional Results Comparative Statistics Volatility reduction is consistent across all regions. Draw down is also substantially reduced. Diversification minimum variance index represents around two-thirds of underlying across regions. World Developed Developed Asia Pacific USA Developed Europe Underlying Min Var Underlying Min Var Underlying Min Var Underlying Min Var Geometric Mean (%) Volatlility (%) Volatlility Reduction (%) Sharpe Ratio DD (%) Mean Number of Stocks Two Way Turnover (%) Excess (%) Tracking Error (%) Information Ratio Alpha (%) Alpha T-Stat Beta World, Asia Pacific and Europe rebalanced March and September. USA rebalanced June and December. All statistics are on an annual basis 21/09/01 15/06/12, Total Return (USD) except Total Return (EUR) for Developed Europe Page 27

28 Regional Results Factor Exposures Sub market beta and small cap tilt. Value tilt outside Europe. Significant alpha over period after style, size and market adjustment except Japan. Factor Loadings By Region Alpha by Region WIJPN WIJPN AWEBLOCS AWEBLOCS AWDEXUKS AWDEXUKS AWDEURS AWDEURS WIUSA WIUSA AWDPACXJ AWDPACXJ AWDPAC AWDPAC AWD AWD Value-Growth Small-Large Market Factor loadings from monthly regression spanning Jan 2003 to June 2012 Page 28 Annualised Alpha Alpha t stat

29 % Implemeted % Rebalanced Liquidity Considerations: Assumed 1Bn USD Portfolio Size Liquidity Considerations: Assumed 1Bn USD Portfolio Size % (95%) of the Min Variance portfolio can be implemented at < 10% (50%) of ADTV Cap weighted indices typically offer substantial implementation advantages Screened risk weighted indices typically exhibit liquidity issues & high turnover FTSE Developed Implementation: Proportion of Index Implemented By Share of ADTV % Share of ADTV Min Var Risk Wgt Low 50% By Cap Intra-Ind: Cap Wgt Low 50% By Cap Intra-Ind: Risk Wgt Rebalance from June 2011 to December 2011; implementation as of December 2011 Page FTSE Developed Rebalance: Proportion Rebalanced By Share of ADTV % Share of ADTV Min Var Risk Wgt Low 50% By Cap Intra-Ind: Cap Wgt Low 50% By Cap Intra-Ind: Risk Wgt

30 24 Month Correlation Correlation With Alternatively Weighted Indices Minimum variance is relatively uncorrelated with other indices Twenty-four month rolling correlation of excess returns (USD TRI) 100% 80% 60% 40% 20% 0% -20% -40% -60% -80% 2003/ / / / / / / / /08 DBI Developed EDHEC Developed RAFI Developed 1000 RAFI All World 3000 Page 30

31 10. Summary and Conclusions Pure risk weighted outcomes and cap weighted volatility screens yield smaller volatility reductions Where optimisation is to be avoided and volatility reduction is the only objective Risk Weight the 50% by Cap of stocks with the lowest volatility Where optimisation is to be avoided and tracking error is a concern Cap weight the 50% by Cap of stocks with the lowest volatility within industries Min Variance and risk weighted volatility screens achieve similar large reductions in volatility Similar tracking error and comparable levels of diversification Min Variance has lower turnover Liquidity profiles of risk weighted volatility screens are inferior Screening cut-offs are arbitrary Min Variance approach is the preferred and most direct route to volatility reduction Page 31 Low and Minimum Volatility Indices

32 FTSE Global Minimum Variance Index Series FTSE Developed Minimum Variance FTSE USA Minimum Variance FTSE Japan Minimum Variance FTSE Developed Europe Minimum Variance FTSE Developed Europe ex UK Minimum Variance FTSE Developed Eurobloc Minimum Variance FTSE Developed Asia Pacific Minimum Variance FTSE Developed Asia Pacific ex Japan Minimum Variance All indices are calculated on a total return basis Page 32

33 Appendix Page 33 FTSE Minimum Indices

34 Minimum Variance: Mathematical details Objective and Constraints Objective: Minimise portfolio variance, σ 2 = N i=1 N j=1 w i C ij w j where w i is the weight of the i th stock and C ij is the covariance matrix constructed using the following Principle Component Analysis (PCA) of an N N empirical correlation matrix derived from two years of daily total returns (containing T business days). Let λ 1,.., λ K be the K eigenvalues of the empirical correlation matrix that are bigger than 1 + N/T + 2 N/T and let Λ1,, ΛK be their associated eigenvectors each with N elements. Let D nm be the K K diagonal matrix with D nn = λ n and P nj be the K N matrix whose n th row is given by Λn. One then constructs the N N PCA correlation matrix as φ = PDP T. The diagonal elements of φ are additionally constrained to be equal to one. The PCA covariance matrix is then defined by: C ij = δ i δ j φ ij where δ i is the standard deviation or volatility of the i th stock. Constraints: Long Only Constraint: w i 0 i Fully Invested: N i=1 w i = 1 Upper Stock Limit: w i w max i Country Constraint: Bounded by Max[ 0.9 X 5.0, 0.0] and Min[1.1 X + 5.0, 100.0] where X is the country weight in the underlying. Industry Constraint: Maximum weight contribution of a particular Industrial Group is less than or equal to 20%. N 2 Diversification Target: i=1 w i = 1/H. Maximum Weight Multiple: The maximum weight multiple of the underlying market capitalisation weight in the Minimum Variance Index is 20 times. Effective Zero Weight Threshold: Any optimised stock weight that is less than 1 basis point is treated as having a zero weight. Page 34

35 FTSE Developed Asia Pacific Minimum Variance Index Country and Sector Weights Singapore New Zealand Korea Technology Financials Utilities Telecommunications Consumer Services Health Care Japan Consumer Goods Industrials Hong Kong Australia Active Country Weight (%) Basic Materials Oil & Gas Industry Weight (%) Minimum Variance Underlying All data as at March 2012 rebalance Page 35

36 % of Weight % Rebalanced FTSE Developed Asia Pacific Minimum Variance Index - Concentration and Liquidity Assumption: US$1 bn portfolio 100% 90% 80% % 60% 60 50% 40% 30% 20% 10% 0% 0% 20% 40% 60% 80% 100% % of Stocks Underlying Min Variance % Share of ADTV Underlying Min Variance All data as at March 2012 rebalance Page 36

37 FTSE Developed USA Minimum Variance Index Sector Weights Technology Financials Utilities Telecommunications Consumer Services Health Care Consumer Goods Industrials Basic Materials Oil & Gas Industry Weight (%) Minimum Variance Underlying All data as at June 2012 rebalance Page 37

38 % of Weight % Rebalanced FTSE Developed USA Minimum Variance Index Concentration and Liquidity Assumption: US$1 bn portfolio 100% 90% 80% 70% 60% % 40% 30% 20% 10% 0% 0% 20% 40% 60% 80% 100% % of Stocks % Share of ADTV Underlying Min Variance Underlying Min Variance All data as at June 2012 rebalance Page 38

39 FTSE Developed Europe Minimum Variance Index - Country and Sector Weights UK Sweden Spain Portugal Austria Norway Netherlands Italy Ireland Greece Germany France Finland Denmark Belgium Technology Financials Utilities Telecommunications Consumer Services Health Care Consumer Goods Industrials Basic Materials Oil & Gas Industry Weight (%) Active Country Weight (%) Minimum Variance Underlying All data as at March 2012 rebalance Page 39

40 % of Weight % Rebalanced FTSE Developed Europe Minimum Variance Index Concentration and Liquidity Assumption: US$1 bn portfolio 100% 90% 80% 70% % 60 50% 40% 40 30% 20% 10% 0% 0% 20% 40% 60% 80% 100% % of Stocks % Share of ADTV Underlying Min Variance Underlying Min Variance All data as at March 2012 rebalance Page 40

41 Contact details Peter Gunthorp Managing Director, Research & Analytics Tel no: Andrew Dougan Associate Director, Research & Analytics Tel no: Disclaimer This presentation does not constitute an offer or invitation to buy or sell any investment or participate in any investment activity, nor any advice concerning the acquisition or disposal of securities. This presentation has not been approved by a person authorised under the Financial Services and Markets Act 2000 ( FSMA ) for the purposes of section 21 of FSMA. Accordingly this presentation and the information contained within it is only made to, and for the use of, persons whom FTSE believes to be investment professionals within the meaning of article 19(5) of the Financial Services and Markets Act 2000 (Financial Promotion) Order 2005 or U.S. institutional investors and major U.S. institutional investors, as provided by Rule 15a-6 under the U.S. Securities Exchange Act of These slides should not be relied upon by anyone else. If you have not received this presentation directly from FTSE, do not use or rely on it or forward it to anyone else. All information is provided for information purposes only and is derived from historical data and information deemed to be reliable and generally available to the public in its primary form. Nothing in this presentation constitutes financial or investment advice, nor any advice concerning the acquisition or disposal of securities. You should exercise your discretion in your use of the FTSE Global Minimum Variance Index Series (the Index ) and if you do not have the relevant professional expertise in relation to investments of the kind the Index relates to, before using the Index you should consult an investment professional who does for advice. FTSE makes no claim, prediction, warranty or representation whatsoever, expressly or impliedly, either as to the results to be obtained from the use of the Index or the fitness or suitability of the Index for any particular purpose to which it might be put. No responsibility or liability can be accepted by FTSE for any errors or for any loss from the use of this presentation. All figures and graphical representations in these slides refer to past performance and are sourced by FTSE. Past performance is not a reliable indicator of future results. All rights in the Index vest in FTSE. FTSE is a trade mark of the London Stock Exchange Group companies and is used by FTSE under licence. This publication is not intended for dissemination to the public or distribution by subscription and recipients of this publication shall not disseminate or distribute it in any way. No part of this publication may be reproduced, stored in a retrieval system or transmitted by any other form or means whether electronic, mechanical, photocopying, recording or otherwise without the prior permission of FTSE.. Page 41

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