β = 1 DOES A BETTER JOB THAN CALCULATED BETAS

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Working Paper WP-85 September, 9 β = DOES A BETTER JOB THAN CALCULATED BETAS Pablo Fernández Vicente J. Bermejo IESE Business School University of Navarra Av. Pearson, 834 Barcelona, Spain.

1 Working Paper WP-85 September, 9 β = DOES A BETTER JOB THAN CALCULATED BETAS Pablo Fernández Vicente J. Bermejo IESE Business School University of Navarra Av. Pearson, 834 Barcelona, Spain. Phone: (+34) Fax: (+34) Camino del Cerro del Águila, 3 (Ctra. de Castilla, km 5,8) 83 Madrid, Spain. Phone: (+34) Fax: (+34) Copyright 9 IESE Business School. IESE Business School-University of Navarra -

2 The CIIF, International Center for Financial Research, is an interdisciplinary center with an international outlook and a focus on teaching and research in finance. It was created at the beginning of 99 to channel the financial research interests of a multidisciplinary group of professors at IESE Business School and has established itself as a nucleus of study within the School s activities. Ten years on, our chief objectives remain the same: Find answers to the questions that confront the owners and managers of finance companies and the financial directors of all kinds of companies in the performance of their duties Develop new tools for financial management Study in depth the changes that occur in the market and their effects on the financial dimension of business activity All of these activities are programmed and carried out with the support of our sponsoring companies. Apart from providing vital financial assistance, our sponsors also help to define the Center s research projects, ensuring their practical relevance. The companies in question, to which we reiterate our thanks, are: Aena, A.T. Kearney, Caja Madrid, Fundación Ramón Areces, Grupo Endesa, Royal Bank of Scotland and Unión Fenosa. IESE Business School-University of Navarra

3 β = DOES A BETTER JOB THAN CALCULATED BETAS Pablo Fernández Vicente J. Bermejo Abstract We compute the correlations of the annual stock returns (989-8) of Dow Jones companies with a) β Rm, and with b) Rm; and find that the second correlation (assuming beta = for all companies) is higher than the first, on average, and for all companies except Caterpillar and General Motors. Rm is the return of the S&P 5. Thus, beta = works better than calculated betas! Not surprisingly, Adjusted betas (.67 calculated beta +.33) have higher correlation than calculated betas, but Adjusted betas have lower correlation than beta =. We do the exercise with 4 calculated betas every year end vs. the S&P 5, using: a) monthly data of last 5 years; b) monthly data of last years; c) weekly data of last 5 years, and d) daily data of last 5 years. We find similar results with the four betas. Despite these results, Fernández (9) reports that 97.3 % of professors who justify the betas use regressions, webs, databases, textbooks or papers (the paper specifies which ones), although many of them admit that calculated betas are poorly measured and have many problems. Only.9% of the professors justified the beta using exclusively personal judgment. Classification JEL: G, G3, G3 Keywords: beta, historical beta, calculated beta, adjusted beta, common sens. Professor, Financial Management, PricewaterhouseCoopers Chair of Finance, IESE Research Assistant, IESE IESE Business School-University of Navarra

4 β = DOES A BETTER JOB THAN CALCULATED BETAS We compute the correlations of the annual stock returns (989-8) of the Dow Jones companies with a) β Rm, and with b) Rm and find that the second correlation (assuming beta = for all companies) is higher than the first, on average, and for all companies except Caterpillar and General Motors. Rm is the return of the S&P 5. Thus, beta = works better than calculated betas! Not surprisingly, Adjusted betas (.67 calculated beta +.33) have higher correlation than calculated betas, but Adjusted betas have lower correlation than beta =. We do the exercise with 4 calculated betas every year end vs. the S&P 5, using: a) monthly data of last 5 years; b) monthly data of last years; c) weekly data of last 5 years, and d) daily data of last 5 years. Table shows the Correlation (R t, β Rm t ), the Correlation (R t, Rm t ) and their difference using four different calculated betas: a) monthly data of the last 5 years; b) monthly data of the last two years; c) weekly data of the last 5 years; d) daily data of the last 5 years. The betas are calculated every year end vs. the S&P 5 using Datastream. It may be seen that companies had Correlation (R t, Rm t ) > Correlation (R t, β Rm t ) using betas calculated with monthly data of the last 5 years. With the other calculated betas, 3, 4 and 7 companies had this result. It may also be seen that the average Correlation (R t, β Rm t ) - Correlation (R t, Rm t ) is negative in the 4 cases. Only Caterpillar and General Motors have the four differences >. Table shows the Correlation (R t, ADJβ Rm t ), the Correlation (R t, Rm t ) and their difference using the 4 different calculated betas of Table. ADJβ = Adjusted beta =.67 Raw beta It may be seen that 9 companies had Correlation (R t, Rm t ) > Correlation (R t, ADJβ Rm t ) using adjusted betas calculated with monthly data of the last 5 years. With the other adjusted betas,, and 5 companies had this result. It also may be seen that the average Correlation (R t, ADJβ Rm t ) - Correlation (R t, Rm t ) is negative in the four cases. Only Caterpillar, Chevron and General Motors have the four differences >. We calculate betas of 9 companies and exclude Kraft Foods because we only have data for them back to. IESE Business School-University of Navarra

5 Not surprisingly, adjusted betas (.67 Raw beta +.33) work better than Raw betas. Table 3 shows the Correlation (R t, β Rm t ), the Correlation (R t, ADJβ Rm t ) and their difference using the four different calculated betas of Table. ADJβ = Adjusted beta =.67 Raw beta It may be seen that 5 companies had Correlation (R t, ADJβ Rm t ) > Correlation (R t, β Rm t ) using adjusted betas calculated with monthly data of the last 5 years. With the other adjusted betas, 4, 4 and 9 companies had this result. It also may be seen that the average Correlation (R t, β Rm t ) - Correlation (R t, ADJβ Rm t ) is negative in the four cases. It may be seen that the average difference is higher (in absolute value) in Table than in Table 3. As in Table, only Caterpillar and General Motors have the four differences >. A) BETAS Calculated vs. the S&P 5 at Year end Using MONTHLY Data of the Last 5 YEARS Figure shows the evolution of the BETA of each company calculated vs. the S&P 5 at year end using MONTHLY data of the last 5 YEARS. Table 4 shows the difference between Correlations [ρ(r t, β Rm t ) - ρ (R t, Rm t ) from 989 to the indicated year]. It may be seen that the average difference is negative in the intervals considered. Table 5 shows the difference between Correlations [ρ(r t, β Rm t ) - ρ (R t, Rm t ) from the indicated year until 8]. It may be seen that the average difference is negative in the intervals considered. B) BETAS Calculated vs. the S&P 5 at Year end Using MONTHLY Data of the Last YEARS Figure shows the evolution of the BETA of each company calculated vs. the S&P 5 at year end using MONTHLY data of the last YEARS. Table 6 shows the difference between Correlations [ρ(r t, β Rm t ) - ρ (R t, Rm t ) from 989 to the indicated year]. It may be seen that the average difference is negative in the intervals considered. Table 7 shows the difference between Correlations [ρ(r t, β Rm t ) - ρ (R t, Rm t ) from the indicated year until 8]. It may be seen that the average difference is negative in the intervals considered. C) BETAS Calculated vs. the S&P 5 at Year end Using WEEKLY Data of the Last 5 YEARS Figure 3 shows the evolution of the BETA of each company calculated vs. the S&P 5 at year end using WEEKLY data of the last 5 YEARS. - IESE Business School-University of Navarra

6 Table 8 shows the difference between Correlations [ρ(r t, β Rm t ) - ρ (R t, Rm t ) from 989 to the indicated year]. It may be seen that the average difference is negative in the intervals considered. Table 9 shows the difference between Correlations [ρ(r t, β Rm t ) - ρ (R t, Rm t ) from the indicated year until 8]. It may be seen that the average difference is negative in the intervals considered. D) BETAS Calculated vs. the S&P 5 at Year end Using DAILY Data of the Last 5 YEARS Figure 4 shows the evolution of the BETA of each company calculated vs. the S&P 5 at year end using DAILY data of the last 5 YEARS. Table shows the difference between Correlations [ρ(r t, β Rm t ) - ρ (R t, Rm t ) from 989 to the indicated year]. It may be seen that the average difference is negative in the intervals considered. Table shows the difference between Correlations [ρ(r t, β Rm t ) - ρ (R t, Rm t ) from the indicated year until 8]. It may be seen that the average difference is negative in the intervals considered. Table contains the last column of Tables 4 to. It may be seen, again, that β = has higher correlation with returns than calculated betas for all companies except Caterpillar and General Motors Despite these results, Fernández (9) reports that 97.3% of the professors who justify the betas use regressions, webs, databases, textbooks or papers (the paper specifies which ones), although many of them admit that calculated betas are poorly measured and have many problems. Only.9% of the professors justified the beta using exclusively personal judgment (named qualitative betas, common sense betas, intuitive betas, logical magnitude betas and own judgment betas by different professors). Fernández, P. (9), Betas used by Professors: a survey with,5 answers, SSRN n IESE Business School-University of Navarra - 3

7 Table Raw betas vs. BETA = Correlation ( β Rmt)), Correlation ( Rmt) and its difference using four different calculated betas: a) monthly data of last 5 years; b) monthly data of last years; c) weekly data of last 5 years, and d) daily data of last 5 years. Betas calculated every year end vs. the S&P 5. Monthly data, last 5 years Monthly data, last years Weekly data, last 5 years Daily data, last 5 years R (correlation) R (correlation) R (correlation) R (correlation) β Rm Rm dif β Rm Rm dif β Rm Rm dif β Rm Rm dif 3M AT&T ALCOA AMERICAN EXPRESS BANK OF AMERICA BOEING CATERPILLAR CHEVRON CITIGROUP COCA-COLA DU PONT EXXON MOBIL GENERAL ELECTRIC GENERAL MOTORS HEWLETT-PACKARD HOME DEPOT INTEL IBM JP MORGAN CHASE JOHNSON & JOHNSON MCDONALDS MERCK & CO MICROSOFT PFIZER PROCTER & GAMBLE UNITED TECH VERIZON COM WAL MART STORES WALT DISNEY Average Máx Mín < Source: Datastream. 4 - IESE Business School-University of Navarra

8 Table Adjusted betas vs. BETA = Correlation ( Adjβ Rmt), Correlation ( Rmt) and its difference using four different calculated betas: a) monthly data of last 5 years; b) monthly data of last years; c) weekly data of last 5 years, and d) daily data of last 5 years. Betas calculated every year end vs. the S&P 5. Adjusted beta =,67 Raw beta +,33 Monthly data, last 5 years Monthly data, last years Weekly data, last 5 years Daily data, last 5 years R (correlation) R (correlation) R (correlation) R (correlation) β Rm Rm dif β Rm Rm dif β Rm Rm dif β Rm Rm dif 3M AT&T ALCOA AMERICAN EXPRESS BANK OF AMERICA BOEING CATERPILLAR CHEVRON CITIGROUP COCA-COLA DU PONT EXXON MOBIL GENERAL ELECTRIC GENERAL MOTORS HEWLETT-PACKARD HOME DEPOT INTEL IBM JP MORGAN CHASE JOHNSON & JOHNSON MCDONALDS MERCK & CO MICROSOFT PFIZER PROCTER & GAMBLE UNITED TECH VERIZON COM WAL MART STORES WALT DISNEY Average Máx Mín < 9 5 Source: Datastream. IESE Business School-University of Navarra - 5

9 Table Raw betas vs. Adjusted betas Correlation ( β Rmt), Correlation ( Adjβ Rmt) and its difference using 4 different calculated betas: a) monthly data of last 5 years; b) monthly data of last years; c) weekly data of last 5 years, and d) daily data of last 5 years. Betas calculated every year end vs. the S&P 5. Adjusted beta =,67 Raw beta +,33 Monthly data, last 5 years Monthly data, last years Weekly data, last 5 years Daily data, last 5 years R (correlation) R (correlation) R (correlation) R (correlation) β Rm ADJ.β Rm dif β Rm ADJ.β Rm dif β Rm ADJ.β Rm dif β Rm 3M AT&T ALCOA AMERICAN EXPRESS BANK OF AMERICA BOEING CATERPILLAR CHEVRON CITIGROUP COCA-COLA DU PONT EXXON MOBIL GENERAL ELECTRIC GENERAL MOTORS HEWLETT-PACKARD HOME DEPOT INTEL IBM JP MORGAN CHASE JOHNSON & JOHNSON MCDONALDS MERCK & CO MICROSOFT PFIZER PROCTER & GAMBLE UNITED TECH VERIZON COM WAL MART STORES WALT DISNEY Average Máx Mín < ADJ.β Rm dif Source: Datastream. 6 - IESE Business School-University of Navarra

10 Figure BETA calculated vs. the S&P 5 at year end using MONTHLY data of the last 5 YEARS 3M AT&T ALCOA,5,5,5,5,5 AMERICAN EXPRESS BANK OF AMERICA BOEING,5,5 CATERPILLAR CHEVRON CITIGROUP,6,4,,8,6,4, COCA-COLA COLA E I DU PONT DE NEMOURS EXXON MOBIL GENERAL ELECTRIC GENERAL MOTORS HEWLETT-PACKARD,5 HOME DEPOT INTEL IBM,5,5,5,5,5 JP MORGAN CHASE & CO. JOHNSON & JOHNSON MCDONALDS MERCK & CO. MICROSOFT PFIZER,5,5,5,5 IESE Business School-University of Navarra - 7

11 Table 4 From 989 to the indicated year. Raw betas vs. BETA = Correlation ( β Rmt), Correlation ( Rmt) and its difference using betas calculated with monthly data of last 5 years. Betas calculated every year end vs. the S&P 5. Correlation( BetaRm) - Correlation( Rm). Yearly data from 989 until the year aver 3M AT&T ALCOA AMERICAN EXPRESS BANK OF AMERICA BOEING CATERPILLAR CHEVRON CITIGROUP COCA-COLA E I DU PONT DE NEMOURS EXXON MOBIL GENERAL ELECTRIC GENERAL MOTORS HEWLETT-PACKARD HOME DEPOT INTEL IBM JP MORGAN CHASE & CO JOHNSON & JOHNSON MCDONALDS MERCK & CO MICROSOFT PFIZER PROCTER & GAMBLE UNITED TECHNOLOGIES VERIZON COMMUNICATIONS WAL MART STORES WALT DISNEY Average Máx Mín < Source: Datastream. 8 - IESE Business School-University of Navarra

12 Table 5 From the indicated year until 8. Raw betas vs. BETA = Correlation ( β Rmt), Correlation ( Rmt) and its difference using betas calculated with monthly data of last 5 years. Betas calculated every year end vs. the S&P 5. Correlation( BetaRm) - Correlation( Rm). Yearly data from until the year aver 3M AT&T ALCOA AMERICAN EXPRESS BANK OF AMERICA BOEING CATERPILLAR CHEVRON CITIGROUP COCA-COLA E I DU PONT DE NEMOURS EXXON MOBIL GENERAL ELECTRIC GENERAL MOTORS HEWLETT-PACKARD HOME DEPOT INTEL IBM JP MORGAN CHASE & CO JOHNSON & JOHNSON MCDONALDS MERCK & CO MICROSOFT PFIZER PROCTER & GAMBLE UNITED TECHNOLOGIES VERIZON COMMUNICATIONS WAL MART STORES WALT DISNEY Average Máx Mín < 9 3 Rm 4% 3% % % % -% -% -3% -4% S&P 5 COMPOSITE Source: Datastream. IESE Business School-University of Navarra - 9

13 Figure BETA calculated vs. the S&P 5 at year end using MONTHLY data of the last YEARS 3,5,5,5 -,5-3M AT&T ALCOA,5,5 -,5 AMERICAN EXPRESS BANK OF AMERICA BOEING,5,5,5,5,5,5,5 CATERPILLAR CITIGROUP CHEVRON,5,5 -,5,5 GENERAL ELECTRIC GENERAL MOTORS HEWLETT-PACKARD,5,5 -,5 JP MORGAN CHASE & CO. JOHNSON & JOHNSON MCDONALDS PROCTER & GAMBLE UNITED TECHNOLOGIES VERIZON COMMUNICATIONS,5,5 3,5 3,5,5,5 3,5,5,5 -,5 - COCA-COLA COLA E I DU PONT DE NEMOURS EXXON MOBIL HOME DEPOT INTEL IBM,5 -,5 MERCK & CO. MICROSOFT PFIZER,5 WAL MART STORES WALT DISNEY - IESE Business School-University of Navarra

14 Table 6 From 989 to the indicated year. Raw betas vs. BETA = Correlation ( β Rmt), Correlation ( Rmt) and its difference using betas calculated with monthly data of last years. Betas calculated every year end vs. the S&P 5. Correlation( BetaRm) - Correlation( Rm). Yearly data from 989 until the year aver 3M AT&T ALCOA AMERICAN EXPRESS BANK OF AMERICA BOEING CATERPILLAR CHEVRON CITIGROUP COCA-COLA E I DU PONT DE NEMOURS EXXON MOBIL GENERAL ELECTRIC GENERAL MOTORS HEWLETT-PACKARD HOME DEPOT INTEL IBM JP MORGAN CHASE & CO JOHNSON & JOHNSON MCDONALDS MERCK & CO MICROSOFT PFIZER PROCTER & GAMBLE UNITED TECHNOLOGIES VERIZON COMMUNICATIONS WAL MART STORES WALT DISNEY Average Máx Mín < 8 3 Source: Datastream. IESE Business School-University of Navarra -

15 Table 7 From the indicated year until 8. Raw betas vs. BETA = Correlation ( β Rmt), Correlation ( Rmt) and its difference using betas calculated with monthly data of last years. Betas calculated every year end vs. the S&P 5 Correlation( BetaRm) - Correlation( Rm). Yearly data from until the year aver 3M AT&T ALCOA AMERICAN EXPRESS BANK OF AMERICA BOEING CATERPILLAR CHEVRON CITIGROUP COCA-COLA E I DU PONT DE NEMOURS EXXON MOBIL GENERAL ELECTRIC GENERAL MOTORS HEWLETT-PACKARD HOME DEPOT INTEL IBM JP MORGAN CHASE & CO JOHNSON & JOHNSON MCDONALDS MERCK & CO MICROSOFT PFIZER PROCTER & GAMBLE UNITED TECHNOLOGIES VERIZON COMMUNICATIONS WAL MART STORES WALT DISNEY Average Máx Mín < Source: Datastream. - IESE Business School-University of Navarra

16 Figure 3 BETA calculated vs. the S&P 5 at year end using WEEKLY data of the last 5 YEARS 3M AT&T ALCOA AMERICAN EXPRESS BOEING BANK OF AMERICA,5,5,5,5,5,5,5,5,5,5,5,5,4,,8,6,4, CATERPILLAR CITIGROUP CHEVRON GENERAL ELECTRIC GENERAL MOTORS HEWLETT-PACKARD JP MORGAN CHASE & CO. JOHNSON & JOHNSON MCDONALDS PROCTER & GAMBLE UNITED TECHNOLOGIES VERIZON COMMUNICATIONS,,8,6,4,,5,5,4,,8,6,4,,4,,8,6,4, COCA-COLA COLA E I DU PONT DE NEMOURS EXXON MOBIL HOME DEPOT INTEL IBM MERCK & CO. MICROSOFT PFIZER WAL MART STORES WALT DISNEY IESE Business School-University of Navarra - 3

17 Table 8 From 989 to the indicated year. Raw betas vs. BETA = Correlation ( β Rmt), Correlation ( Rmt) and its difference using betas calculated with weekly data of last 5 years. Betas calculated every year end vs. the S&P 5. Correlation( BetaRm) - Correlation( Rm). Yearly data from 989 until the year aver 3M AT&T ALCOA AMERICAN EXPRESS BANK OF AMERICA BOEING CATERPILLAR CHEVRON CITIGROUP COC- COLA E I DU PONT DE NEMOURS EXXON MOBIL GENERAL ELECTRIC GENERAL MOTORS HEWLETT-PACKARD HOME DEPOT INTEL IBM JP MORGAN CHASE & CO JOHNSON & JOHNSON MCDONALDS MERCK & CO MICROSOFT PFIZER PROCTER & GAMBLE UNITED TECHNOLOGIES VERIZON COMMUNICATIONS WAL MART STORES WALT DISNEY Average Máx Mín < Source: Datastream. 4 - IESE Business School-University of Navarra

18 Table 9 From the indicated year until 8. Raw betas vs. BETA = Correlation ( β Rmt), Correlation ( Rmt) and its difference using betas calculated with weekly data of last 5 years. Betas calculated every year end vs. the S&P 5. Correlation( BetaRm) - Correlation( Rm). Yearly data from until the year aver 3M AT&T ALCOA AMERICAN EXPRESS BANK OF AMERICA BOEING CATERPILLAR CHEVRON CITIGROUP COCA-COLA E I DU PONT DE NEMOURS EXXON MOBIL GENERAL ELECTRIC GENERAL MOTORS HEWLETT-PACKARD HOME DEPOT INTEL IBM JP MORGAN CHASE & CO JOHNSON & JOHNSON MCDONALDS MERCK & CO MICROSOFT PFIZER PROCTER & GAMBLE UNITED TECHNOLOGIES VERIZON COMMUNICATIONS WAL MART STORES WALT DISNEY Average Máx Mín < Source: Datastream. IESE Business School-University of Navarra - 5

19 Figure 4 BETA calculated vs. the S&P 5 at year end using DAILY data of the last 5 YEARS,,8,6,4,,4,,8,6,4,,8,6,4,,8,6,4,,8,6,4, 3M AT&T ALCOA CATERPILLAR CITIGROUP CHEVRON GENERAL ELECTRIC GENERAL MOTORS HEWLETT-PACKARD JP MORGAN CHASE & CO. JOHNSON & JOHNSON MCDONALDS PROCTER & GAMBLE UNITED TECHNOLOGIES VERIZON COMMUNICATIONS,8,6,4,,7,6,5,4,3,,,8,6,4, AMERICAN EXPRESS BOEING BANK OF AMERICA,8,6,4, COCA-COLA COLA E I DU PONT DE NEMOURS EXXON MOBIL HOME DEPOT INTEL IBM,8,6,4, MERCK & CO. MICROSOFT PFIZER WAL MART STORES WALT DISNEY 6 - IESE Business School-University of Navarra

20 Table From 989 to the indicated year. Raw betas vs. BETA = Correlation ( β Rmt), Correlation ( Rmt) and its difference using betas calculated with daily data of last 5 years. Betas calculated every year end vs. the S&P 5. Correlation( BetaRm) - Correlation( Rm). Yearly data from 989 until the year aver 3M AT&T ALCOA AMERICAN EXPRESS BANK OF AMERICA BOEING CATERPILLAR CHEVRON CITIGROUP COCA-COLA E I DU PONT DE NEMOURS EXXON MOBIL GENERAL ELECTRIC GENERAL MOTORS HEWLETT-PACKARD HOME DEPOT INTEL IBM JP MORGAN CHASE & CO JOHNSON & JOHNSON MCDONALDS MERCK & CO MICROSOFT PFIZER PROCTER & GAMBLE UNITED TECHNOLOGIES VERIZON COMMUNICATIONS WAL MART STORES WALT DISNEY Average Máx Mín < Source: Datastream. IESE Business School-University of Navarra - 7

21 Table From the indicated year until 8. Raw betas vs. BETA = Correlation ( β Rmt), Correlation ( Rmt) and its difference using betas calculated with daily data of last 5 years. Betas calculated every year end vs. the S&P 5 Correlation( BetaRm) - Correlation( Rm). Yearly data from until the year aver 3M AT&T ALCOA AMERICAN EXPRESS BANK OF AMERICA BOEING CATERPILLAR CHEVRON CITIGROUP COCA-COLA E I DU PONT DE NEMOURS EXXON MOBIL GENERAL ELECTRIC GENERAL MOTORS HEWLETT-PACKARD HOME DEPOT INTEL IBM JP MORGAN CHASE & CO JOHNSON & JOHNSON MCDONALDS MERCK & CO MICROSOFT PFIZER PROCTER & GAMBLE UNITED TECHNOLOGIES VERIZON COMMUNICATIONS WAL MART STORES WALT DISNEY Average Máx Mín < Source: Datastream. 8 - IESE Business School-University of Navarra

22 Table Last column of tables 4 to It may be seen, again, that β = has higher correlation with returns than calculated betas for all companies except Caterpillar and General Motors Last column of table n aver aver aver aver aver aver aver aver 3M AT&T ALCOA AMERICAN EXPRESS BANK OF AMERICA BOEING CATERPILLAR CHEVRON CITIGROUP COCA-COLA E I DU PONT DE NEMOURS EXXON MOBIL GENERAL ELECTRIC GENERAL MOTORS HEWLETT-PACKARD HOME DEPOT INTEL IBM JP MORGAN CHASE & CO JOHNSON & JOHNSON MCDONALDS MERCK & CO MICROSOFT PFIZER PROCTER & GAMBLE UNITED TECHNOLOGIES VERIZON COMMUNICATIONS WAL MART STORES WALT DISNEY Average Máx Mín < IESE Business School-University of Navarra - 9

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