Market Risk Premium Expected

Published Date: 02 Nov 2017

Research Project Presented to

MPSTME, NMIMS

In Partial Fulfilment of the Requirement for the Degree MBA Tech

By

Tanmay Mehta

527

Year of Graduation 2013

Acknowledgements

I am indebted to many people who have helped and supported me during this project.

My deepest thanks to my mentor Prof. Alaknanda Lonare for her careful supervision and encouragement throughout the project.

I would also like to thank my friends for their useful advice and moral support.

Abstract

The market Risk Premium is one of the most researched and financial parameters controversial, and also one that generates more confusion. Much of the confusion is due to that the term "Market Risk Premium" means four very different concepts and realities each other:

1. Market Risk Premium History (PRMH) is the difference between the historical performance of the bag (of a stock index) and fixed income.

2. Market Risk Premium Expected (EEP) is the expected value of the future profitability of the bag above the fixed income.

3. Market Risk Premium Required (REP) is the incremental return an investor requires the stock market (to a diversified portfolio) above the risk-free bond (Required equity premium). It's to be used to calculate the required return to actions.

4. Market Risk Premium Implicit (PRMI) is the market risk premium required to be corresponds to the market price. Many authors and many financial professionals EEP assume equals PRMH and the REP. Then we analyze the methods proposed in the literature to measure financial and analyzes the historical differential return of Spain and the United States. The main conclusion is that it is impossible to determine "the" risk premium "market" because that number does not exist due to heterogeneous investor expectations.

Table of Contents

S.No.

Topic

Pg. No.

Title Page

1

Acknowledgements

2

Abstract

3

Table of Contents

4

1.0

Introduction

5

1.1

Statement of the Problem

5

1.2

Purpose of the Study

5

1.3

Significance of the Study

5

1.4

Methodology

6

2.0

Review of Literature

7

2.1

Concepts

7

2.2

Gap Analysis

10

3.0

Data and Methodology

11

3.1

Inter Day Volatility

11

3.2

Close to Close Volatility

11

3.3

Open to Open Volatility

11

3.4

Intra Day Volatility

12

3.5

Parkinson Model

12

3.6

Garman and Klass Model

13

4.0

Analysis of Data

14

4.1

Return

14

4.1

Volatility

18

5.0

Conclusions

20

6.0

Recommendations

21

7.0

Appendix

22

Introduction

For an investor, the market risk premium or market risk premium Required (REP) is the answer to the question: What additional return I demand to a diversified investment in equities (A stock index, for example) above the bond offering? It is a crucial parameter for every company because the answer to this question is a key reference for determining the profitability required of company stock (Ke) and the required return to any investment project. As outlined below, determine the market risk premium (required) has two problems: the first and most important is that it is the same for all inversores2, the second is which is a non-observable. We will see that the equity premium is required, as stated often, the historical performance of the stock over bonds. In this sense, Byron Wien, Morgan Stanley, recently wrote an article entitled "Risk Premium-RIP" The expectation of the return differential is the answer to a question that we all interested to know answer: What I can expect in return the bag above the fixed income the coming years? If RF is the return on risk-free bonds and E (RM) is the return expected market

Differential profitability Expectancy = [E (RM) - RF]

Example: Suppose four inverters. The four must match the risk premium if they feel the same stock index, the same calculation period, the same method of calculating the mean (arithmetic or Geometric) and the same reference rate without risk. In the table, 5.5% corresponds to the geometric mean differential return S & P 500 on U.S. government bonds to 30 years in the period 1926-2004 (See Table 5). The difference between the inverter A and B is in the expectation of differential profitability. The A self investor will invest in a diversified portfolio (and B will not invest) because his expectation Differential yield is higher (lower in the case of inverter B) to its market risk premium. The investor C not invest, and the actions required return will far exceed that of investors A and B. The D is the principal investor in many textbooks: the market risk premium and the expectation of the risk premium is equal to the historical differential return (5.5%). D The investor is indifferent between investing or not in a diversified portfolio of stocks.

different investors

A

B

C

D

Market risk premium %

4.0

4.0

8.0

5.5

differential returns %

5.5

5.5

5.5

5.5

Differential profitability expectation for the next three years %

5.5

2.0

4.0

5.5

Market premiums used by analysts and investors declined in the last 20 years of the twentieth century. In early 2005 the vast majority of investment banks and Analysts risk premiums used for Europe and USA market between 3.5% and 4.5%.

1. Proposed methods to calculate the market risk premium

1.1. Difference between the historical returns of the stock and bond It is very common to use historical data to compare the return on investment in stocks with the return on risk-free bonds. Some conclude that the difference between the historical performance of the stock (a stock index) and the past performance of the fija3 income is a good indicator market4 premium. To support this claim is often argued that the middle market is right. Thus, although not considered as premium market risk that the shares gained more fixed income in a year determined, they are considered a good estimator of the risk premium of the market additional return of fixed income shares over several years. Another contradictions of this approach is that after a very good year for the stock market, the premium market risk will have risen and after a bad year, the market risk premium will be down although there is no reason for it. This means that equality of expectations, after a bad year the market would value plus one share that after a good year (after a year good market premium would be higher). This method, sometimes referred Ibbotson method assumes that the profitability required by investors in the past was equal to the returns received, and that the efficient market is the portfolio of all investors. As discussed below, this method yields inconsistent results, and currently is above the market risk premium that analysts use in almost all countries. However, many textbooks suggest risk premiums using this method. Brealey and Myers suggested 8.2-8.5% in the fifth edition of his book in 1996, on page 160 in its sixth edition (2000) say "Brealey and Myers have no official position on the market risk premium, but we believe that a range between 6% and 8.5% is reasonable for USA. We feel more comfortable using figures from the top of the range ". Later, on page 195, they say: "What can we say about the market risk premium? Of the historical data appears that this magnitude is between 8 and 9%, although many economists and CFOs would use a lower figure. " Ross, Westerfield and Jaffe (1999) use a risk premium of 9.2% it is, they say, past performance differential the fixed income market from 1926-19975. Van Horne (1992) recommended 3-7%, Weston, Chung and Siu (1997) recommend 7.5%. In the examples of his books, Termes (1998) used 3% for Spain and Bodie and Merton (2000) 8% for the USA. Damodaran (1994, Table 3.1, pg. 22) calculates the risk premium on Tbonds geometry for the period 1926-1990, which is 5.5% and that is the number used throughout the book as a bonus from the U.S. market. Mascarene (2004, page 271) reproduces the data on profitability Damodaran Differential geometry of the United States between 1928 and 2001, which proved to be 5.17%. Of here concludes that "the value of the risk premium that governs the U.S. market is about 5.17%, which can be considered valid for the stock markets European Union ". Adserá and Viñolas (1997) say that the risk premium is "an estimate of the future." But then they say that "usually considered that history is the best estimator of future. " They conclude that "in developed markets this figure is between 3% and 7%). Copeland, Koller and Murrin (2000, page 221) recommend using a risk premium between 4.5% and 5%. The argument used by Copeland, Koller and Murrin on page 221 is surprising: "it is unlikely that the American market is in the next century as profitable as it was in the past. If we subtract 2% bias6 the differential survivorship arithmetic between fixed income and equities, we conclude that the risk premium should be in the range 4.5-5%. " Later recognize that in the early 2000s most investment banks risk premium used between 3.5 and 5%. However, in 1995, the said second edition (see page 268): "we recommend using a risk premium from 5 to 6%, based on differential geometric returns of the S & P500 on bonds Long-term government in the period 1926-1992. We use the geometric mean for the arithmetic averages are biased ". In the first edition of 1990 said (page 196):

"Our view is that the best estimate of the risk premium is the geometric mean of the risk premium (historical) in the long term." It is obvious that in the third edition have changed their criteria. It is obvious convenience adjustment for survivorship bias. Li and Xu (2002) prove that the "survival bias" 7 does not explain the high risk premium on the stock market bonds in the U.S. stock market. Siegel (1999) states "the historical risk premium measures the difference between the return on equity and return on risk-free bonds. Many markets foreign suffered some critical period, mainly wars, usually accompanied by high inflation that evaporated in some cases the value of the bonds (for example the German hyper inflation in 1922-1923. In this period the performance of the shares was very negative, but much higher than that of the bonds was 100%). "

1.2. From equation Gordon and Shapiro

Other authors propose the calculation of the market risk premium from the Gordon and Shapiro equation that determines the price of the shares on discount dividends when they grow at an annual rate g each year:

P0 = DPA1 / (Ke-g).

Ke Solving the formula is: Ke = (DPA1/P0) + g.

The argument of the proponents of this method is as follows: Ke is profitability required to market (to a diversified portfolio), and must match the expected return by "the market"

Ke = E (RM) = RF + PM

Therefore, PM = (DPA1/P0) + g - RF

Applying this last expression to the market as a whole (DPA1/P0) is the average dividend yield of the stock, g is the expected dividend growth by "the market" and RF is the risk-free rate. Suffice to estimate growth dividends expected by "the market" to calculate the market risk premium.

Note that for these calculations to be meaningful it must be assumed that the price of actions match its value and that a dividend growth expected "The market".

The problem with this method is, again, that investor expectations are not homogeneous. If they were, it would make sense to talk about the market risk premium, because all investors have the market portfolio and the same expectations about the misma8. But not homogeneous expectations, it is apparent that they expect investors further growth will gain a market risk premium higher. Furthermore, not all investors expect dividends to grow geometrically at a constant rate.

1.3. Survey analysts and investors

Perhaps the most direct way of trying to calculate the market risk premium is make a survey of analysts or investors. An example of this method is the study of Welch (2000a). Welch made two surveys, in 1998 and 1999, several finance professors asking what was in his opinion the market risk premium. He received 226 responses and the average stood the risk premium market (measured as arithmetic mean) of government bonds in the long run around 7% (5.2% as the geometric mean). This figure is surprisingly very high. The type interest of government bonds in the long term in April 1998 was approximately 6%. The 7 inflation expected by most banks and companies to make provision was less than 2.5%. Therefore, the expected real return on government bonds to long term was 3.5%. A market risk premium of 7% means that returns expected real actions was 10.5%. At that time, the real growth forecasts GNP were around 2.5%. As the dividends paid by the American companies were less than 3% of the shares, the annual increase expected capitalization of the companies would be 1,105 divided by 1.03 to 1 = 7.3%. This means that the actual capitalization companies grow much more than the product GNP. According to these estimates, in 2048, the capitalization of the shares should be equal or greater than the U.S. gross national product. The magazine Pensions and Investments (12/1/1998) carried out a survey professional institutional investors and average risk premium was 3%. In another professionals surveyed pension funds (1997, Greenwich Associates Survey) the average risk premium was 5%.

1.4. From the IRR of expected dividends

This method is similar to the equation derived Gordon and Shapiro. According to this method, the risk premium can be calculated as the difference between the price TIR bag-expected dividends and the risk-free rate. The fundamental problem is the calculation of the expected dividends, and the premium calculated and depends on the estimated dividends.

1.5. From the inverse of PER

Proponents of this method are based on the formula that relates the capitalization (P) and heat in shares (VC) of a company with steady growth (g):

P / VC = (VSWR - g) / (Ke - g). If it is assumed that g = 0, is Ke = SWR x VC / P = BFO / P = 1/PER. If We believe this (the assumption g = 0 is to be generally very believable) results: premium market = (1/PER) - RF

Applying this to the Spanish market in October 2000, when the PER was 23 and RF was 5.5%, was that the market premium was negative, which is absurd. In October 2003, the RF PER was 16.8 and 4.35%, bringing the market premium was 1.6% (too small).

1.6. As the difference in the volatility of the stock market and long bond

This method also provides often absurd results. As test, the difference in volatility in the Spanish market, between the IBEX 35 and the benchmark 10 years has ranged between 6% and 32% in the period 1992-2004.

1.7. More recent studies

De la Dehesa (2001), the expectation refieriendo profitability indicates that differential "A recent study by economists at Goldman Sachs shows that the premium equity risk on the bonds will be maintained at an average of 2.5% over the next 20 years9 ... In the long term, historical evidence shows that Goldman analysis is right. " Pastor and Stambaugh (2001) report that between January 1834 and June 1999, the premium risk has ranged between 3.9% and 6%. They also claim that the greatest decline in risk premium market occurred in the 90s. Arnott and Ryan (2001) argue that the market risk premium is negative expected. Basan their conclusion on the low dividend yield and its expectation of small growth dividends. Arnott and Bernstein (2002) conclude about the same: the market risk premium expected is negative or zero. These two studies cover the expected risk premium, although called market risk premium expected. Lopez Lubián and Moon (2002) say that, after analyzing historical data, "it seems to estimate the market premium can be used a multiplier of risk-free rate of 0.5 -0.6 ". Fama and French (2002) estimate the risk premium for the period 1950 to 1999 between 3.4% and 4.83%. They say that these figures are much lower than the return on the fixed income market (8.28%) because the reduction of the risk premium has been an unexpected increase in quotes. In the period 1872-1999 are a risk premium (geometric) 2.55% (Using dividend growth) and 4.32% (using earnings growth). Ibbotson and Chen (2003) decomposed the profitability of the U.S. stock market in the period 1926-2000 in six different ways and say the risk premium expected geometric (Forward-looking long-term equity risk premium) is 3.97% (5.9% arithmetic). These data are approximately 1.25% lower than the historical performance of the fixed income market. Dimson, Marsh and Staunton (2003) analyze historical data between 1900 and 2002 in 16 countries (See Table 1). They state that they must use a data set as long as possible. However, conclude that the risk premium expected geometric major world markets should be of the order of 3%, substantially lower than the one in the textbook, which the polls say managers, and what is the historical average of his studio.

Table 1. Past performance of the fixed income market short (30 days) and long term (10 to 30 years) in 16 countries in the period 1900-2002. Annualised performance. Source: Dimson, Mars and Staunton (2003)

Claus and Thomas (2001) also argue that the risk premium is 3% lower than the difference between the return on the stock and bond returns, and recommend using a risk premium between 3 and 4%. Grabowski and King (2003) conclude a reasonable risk premium should be long-term between 3.5% and 6%. Mayfield (2004) estimates the risk premium analytically complex concludes that the risk premium on short-term bonds is 2.4% less than the difference between the yield spread between the stock and bonds. Although it has no scientific value, we can see what market premium used in their finance classes MBA students in the United States and Europe: most teachers used in 2000 figures between 5% and 7%, although, it was to address cases of the past 20 years. Now teachers asking which is the market premium according to them, got responses ranging from 2% to 5%, in late 1999. An example:

Robert Merton, 1997 Nobel laureate in economics and finance professor at Harvard, said the author of these lines that the American market premium was around 2% in 1999. As for Spain, the Investment analysts also used in 1999-2004 market premiums between 3% and 4.5%, whereas in previous years used somewhat higher premiums. Evolution of the bag and inflation in Spain. Figure 1 compares the evolution of the overall index and the General Index of the Madrid Stock Exchange since 1940 with cumulative inflation developments. The Total Index provides the profitability total of a diversified portfolio of shares (the General Index does not take into account dividends shareholders receive). An investment of 100 pesetas in 1940 became equity (regardless of taxes) in 2004 at 193 798 pesetas (€ 1,165). Line inflation (CPI) indicates that in an average well cost 100 pesetas in 1940, was priced at 13.318 pesetas (€ 80) in 2004. The average annual return between 1940 and 2004 was 12.6% and the average annual inflation was 7.9%. Figure 2 shows the annual performance of the overall index of the Madrid Stock Exchange from 1940. The best year was 1986: the return of the shares was greater than 110%. The profitability of recent years was: 19.7% in 1999, -10.4% in 2000, -3.6% in 2001, -20.5% in 2002, 33% in 2003 and 23.1% in 2004. The worst years were 1948 (-28%), 1977 (-28%), 1976 (-26%) and 1990 (-23%). The arithmetic average annual return of these 64 years was 15.3%. The profitability geométrica10 media11 year was 12.6%. Profitability was negative in 19 of the 64 years

Figure1. Spanish Exchange. Evolution of Total Index, General Index of the Madrid Stock Exchange and inflation in Spain from 1940-2004

Figure 2. Spanish Exchange. Annual performance overall index of the Madrid Stock Exchange from 1940-2004

Figure 3 shows the average risk premium of equity income fixed the last 10 years and 20 years (calculated as the geometric mean of the difference annual return on equities less the return on bonds). Some consider to this magnitude as the risk premium. Note that this amount is very unstable over time (the Differential yield ranged from 20 years, 3% in 1993 to 8.8% in 1999) and that long periods is a negative quantity, it makes no economic sense one negative risk premium.

Figure 3. Spanish Exchange. Geometric differential return on the bond market over the past 10 20. (geometric mean of the difference between the annual performance of the overall index and the Madrid Stock Exchange annual yield bonds)

Table 2 shows the performance of the stock market, the return on fixed income, the profitability of the bag above the fixed income and profitability of the bag above inflation in different periodos12. For all parameters, we calculated the mean.

Table 2. Spanish Exchange. Total Annual Performance Index (stocks), fixed income, risk premium fixed income and inflation

Differences between the arithmetic mean and the geometric mean.

1. The geometric mean is always less than or equal to the arithmetic mean.

2. The more variables (volatile) are the returns, the greater the difference between the arithmetic mean and the geometric mean.

3. The geometric mean only depend on the price level at the beginning and end of the study period. The arithmetic mean however, tends to rise when the period used is shortened. For example, the mean arithmetic using monthly returns, is usually higher than the arithmetic mean returns using year.

4. The difference between the two series geometric mean is not equal to the geometric mean of the difference. By contrast, the average of the difference of two series, the difference is equal to the arithmetic mean of each of the series.

Table 3 shows the volatility of the stock (in the profitability of the overall index), fixed income and inflation in the same periods.

Table 3. Spanish Exchange. Total Annual Volatility Index (stocks), fixed income and inflation

4. Return on equity and fixed income in USA

In this section we analyze the behaviour of the stock and bonds in USA.

4.1. profitability

Figure 4 shows the annual performance of the stock market (stocks), fixed income without 3-month risk (T.bills) and the risk-free rate at 30 years (T.bonds) from 1926.

Figure 4. Annual performance of the U.S. stock market (stocks), fixed income 3 months (T.bills) and income 30 year fixed (T.bonds).

4.2. volatility

Figure 5 shows the annual volatility, calculated with data from the last 10 years, the actions, inflation, bonds and long-term government bonds in the short term. The first conclusion that can be drawn from this figure is that the volatility of the shares in the recent years has been, on average, lower than the volatility of the shares of the previous periods: in the years 1935 to 1945, in the years 1955 to 1965 and in the years 1972 to 1983 the volatility was higher than in the nineties. The volatility that has had long-term bonds (T.Bonds) has been significant, especially in the late 80s, a period in which the volatility of the long bond period was higher than that of the shares. The volatility of short-term fixed income (T.Bills) has been significantly lower and almost always remained below the volatility of the inflation.

Figure 5. Annual volatility of the U.S. stock market (stocks), fixed income 3 months (T.bills), fixed income 30 (T.bonds) and inflation. Volatility calculated using annual data for the last 10 years.

Figure 6. Annual volatility of S & P500. Annualized volatility calculated using monthly data of the last year.

Figure 6 shows the volatility of the stock of the S & P 500 Index using monthly data. We can also observe how the volatility of the nineties has not been higher than the volatility prior period. Figures 5 and 6 show that the volatility in the U.S. stock market in the recent years is not only higher than the volatility of the past, as some claim, but it is rather inferior14. May. Return on fixed income market in USA

5.1. Period 1926-2004

Figure 7 shows the geometric mean of the last 20 years of the annual gap between the annual return of the stock and the risk-free rate 3 months (T-bills) and corresponding to the risk-free rate at 30 years (T-bonds) from 1948-2004.

Figure 7. Geometric mean over the last 20 years of the risk premium on T-bills and risk premium over T-bonds.

Figure 8 shows the average of the last 10 years of the annual gap between the annual return of the stock and bond corresponding to the risk-free 3 months (return Differential T-Bills) from 1938-2004 to compare with the level of interest rates in the short within each year. Note that the risk premium has been greater in years with interest rates low. It is also appreciated that when rates rise, the differential return descends and vice versa. This is logical: we have seen that the stock usually rises when interest rates fall.

Figure 8. Annual performance of fixed income to three months (T.bills) and average over the last 10 years risk premium over T-bills.

Table 4 shows the performance of the stock market, the return on short-term fixed income and return on long-term fixed income in different periods. For all parameters, there has been calculated the arithmetic mean and the geometric mean.

Table 5 shows the performance of the stock over the corresponding fixed income short-term (risk premium bills) and the profitability of the bag above the corresponding to the long-term fixed income (bonds differential profitability) in different periods. To all parameters we calculated the arithmetic mean and the geometric mean.

Table 4. American Stock Exchange. Average (arithmetic and geometric) in different periods of profitability shares annual, fixed income 3 months (T.bills) and 30-year bond (T.bonds).

Table 5. American Stock Exchange. Average (arithmetic and geometric) in different periods of profitability differential action on the 3-month bond (T-Bills) and on 30-year bonds (T-Bonds).

Figure 9 shows the average annual geomética the difference between the annual return bag and the risk-free rate 3 months (T-Bills), and the annual difference between the annual return of the bag and the corresponding fixed income long-term risk-free (T-Bonds) of all years to 2004. Figure 10 shows the same information but calculating the risk premium from 1926 to the year indicated. The informative data is the geometric mean of profitability differential on T-Bonds.

Figure 9. American Stock Exchange. Average annual differential returns (geometric) since indicated to 2004 of the fixed income shares to 3 months (T-Bills), on 30-year bonds (T-Bonds) and on inflation.

Figure 10. American Stock Exchange. Average annual differential returns from 1926 to the year indicated income shares set to 3 months (T-Bills), on 30-year bonds (T-Bonds) and on inflation.

5.2. Period 1802 -1925

Schwert (1990) and Siegel (1998) studied the relationship between equities and fixed income U.S. before 1926. The data on which they base their studies are less reliable than data Recently, but nevertheless are interesting. Table 6 shows their conclusions. can be seen that the risk premium in the period 1802-1925 was substantially lower profitability differential in subsequent years. It also shows that inflation was substantially lower in the years before 1926. By contrast, the real return on bonds was significantly higher in the years before 1926.

Table 6. American Stock Exchange. Average (arithmetic mean) in different periods of the differential Profitability income shares set to 3 months (T-Bills) and on 30-year bonds (T-Bonds).

One conclusion that can be drawn after studying all these periods is that the differential profitability has fluctuated greatly over the past, it is almost impossible to say what has been its mean value and of course much more difficult to predict the future from data historical. A closer look at the data presented here, allows us to formulate the following comments:

1. The stock returns varies so much that the expected risk premium can not be estimated from historical data (historical data Although we have over 70 years).

2. The data show that the risk premium has varied greatly over time. This may be because the risk premiums investors have used over the years have changed substantially.

3. The use of long periods of time is intended to eliminate the deviations as result of economic cycles, technological advances, political changes, wars, etc.. But want to extend the results between countries whose circumstances are different, or make comparisons between them, our perceptions may be wrong. Thus, in the 1926-2004 period U.S. financial markets suffered some financial crisis, but the U.S. economy was not exposed to other types of events that took place in other countries, such as a war fought at home. April. Inflation has changed dramatically in the years following the gold standard. One consequence of the abandonment of the gold standard was that unexpected inflation came to mean much more risk important. June. Comparison of Spanish and American bags

6.1. Evolution of stock market indices

Figure 11 compares the evolution of the overall index of the Madrid Stock Exchange since 1940 with that of the U.S. stock market. An investment of 100 pesetas in 1940 in Spanish shares became (Ignoring taxes) in 2004 to 193,798 pesetas. An investment of $ 100 in 1940 U.S. stocks turned (ignoring taxes) in 2004 at $ 139,938. A investment of $ 100 in 1940 in American government bonds became (neglecting taxes) in 2004 at $ 2,211. Figure 11. Evolution of Total Index of the Madrid Stock Exchange, the S & P 500 (U.S. Shares) and the long bond term in the USA.

Although Figure 11 you can suggest to the reader that there is a high correlation between the stock Spanish and American, this is not entirely true. The correlation between annual returns Spanish stock and the annual return of the U.S. stock between 1941 and 2004 was only 18.6% 15. Figure 12 shows the annual performance of the U.S. stock market and the Spanish stock exchange since 1940.

Figure 12. Annual performance of the Spanish Stock Market (Total Index of the Madrid Stock Exchange) and stock U.S. (S & P 500)

6.2. Correlation between the two countries bags

Figure 13 shows how it has grown gradually the correlation between the returns of Spanish and American stock markets. From a negative correlation in the 50s and in many of the 60s and 70s, has gone to a very high correlation in recent years.

Figure 13. Correlation between USA and Spain bags

Correlation of the annual returns of the past 10 years

UBS (2004) also notes that the correlations between stocks and bonds in different countries have increased significantly, particularly since March 2000. This indicates that the correlations (between March 2000 and December 2004) S & P 500 - DAX and S & P 500 - FTSE was 0.97. The correlation S & P 500 - Topix was 0.94. The correlations between the IRR of government bonds to 10 years were also great: 0.93 between USA and Germany, 0.85 between USA and Japan, 0.91 between USA and UK.

6.3. The effect of inflation in both countries

In order to compare the evolution of Spanish and American bags were not enough Figures 11 and 12: we must take into account the effect of inflation in both countries. Figure 14 shows the Annual inflation developments in both countries. Almost every year inflation was higher U.S. inflation Spanish. Figure 15 shows the path of inflation, that is, how each year costing the goods whose price was 100 (pesetas or dollars depending on the country) in 1940. It notes that goods costing 100 pts. in 1940 were worth 13,318 ptas. (80 €) in 2004, while real that cost $ 100 in 1940 was worth $ 1,364 in 2004. Average inflation was in Spain for USA 7.9% and 4.2%.

Figure 14. Annual inflation in the U.S. and Spain

Figure 15. Path of inflation in Spain and the USA

Figure 16 incorporates inflation developments in American and Spanish indexes. Thus U.S. stock index deflated about 100 in 1940 to 10,263 in 2004, while the index Spanish deflated bag goes from 100-1455 in 2004. The figure also shows that the index of government bonds in the long term many years American was below 100 and that from 1992 reached a value above 100.

Figure 16. Evolution of Total Index of the Bolsa de Madrid Spanish deflated by inflation, and the S & P 500 (U.S. Shares) and long-term bonds in the U.S., deflated by inflation in USA.

The fundamental risk that bond investors have long-term is the risk that the inflation exceeds the value they expect when they buy bonds. A higher inflation than price of long-term bonds. Figure 17 shows the average appreciation over the last 10 years of the bags Spanish American and above inflation. The Spanish stock market has had periods has revalued unless inflation: in the early '50s, around the year 60 and in the period between 1974 and 1983. However, it also has periods when it has revalued well above inflation as were mid 50s, early 70, the late 80s and after 1993.

Figure 17. Inflation risk premium on Spanish stock markets and U.S. (average last 10 years)

6.4. volatility

Figure 18 shows the Spanish stock market volatility of the U.S. stock market and the inflation in Spain and the United States. All volatilities have been calculated using data annual 10. It notes that the Spanish stock market volatility has generally been higher than the American stock market volatility. Was also higher volatility of inflation in Spain to the volatility of inflation in the United States but has tended to equalize in the last 15 years.

Figure 18. Stock market volatility and inflation in Spain and USA. (Volatility calculated with annual data last 10 years)

July. Differential return on bonds in different countries Table 7 shows the risk premium (defined as the difference between the mean geometric stock returns and the geometric mean of the return on bonds long term) in different countries. See you in Germany and Italy, the difference was negative in that period, which is another proof that there is no point called "risk premium" to the difference between the historical performance of stocks and fixed income without riesgo16. Obviously, the return differential was greater in countries with the best performance of the shares during the period.

Table 7. Magnitude of the risk premium in different countries

The utility of Table 7 is purely informative: not used to determine the risk premium each market. It makes no sense to say that the risk premium (defined as profitability Additional actions required to fixed income) of Spain in the period 1970-1996 was 0.31%, while in the Netherlands was 4.65% and 3.72% U.S..

8. Risk premium U.S. and Spanish bags from the equation Gordon and Shapiro Also you can try to calculate the implied premium in the market from the equation Gordon Shapiro. Shapiro Gordon equation simply says that the stock price (capitalization) is the present value of the expected cash flows for stocks (ECF) updated to actions required return (Ke):

P = Present value [ECF, Ke]

Ke is equal to the risk-free rate plus the market risk premium. Ke = RF + risk premium. To calculate the risk premium, known stock prices, all you need to know is flows which are expected for stocks. One way to do this exercise is to use the expected dividends (and redemptions) according to forecasts by analysts (take the average). For the five years following the year in which the calculation is done take the analysts' estimates. Data are available with analyst estimates only since 1985. Before this date dividends are taken really was. From year 6 assumes that dividends grow with the rate of government bonds in the long term. Figure 19. Implied risk premium in the U.S. stock market using the Gordon Shapiro formula growth in two stages. Estimated growth of dividends and repurchases: the first 5 years: estimates analysts (before 1985, real growth) from year 6: T.bond rate.

Figure 19 shows the implied risk premium. According to this figure was an increase the implied risk premium oil crises in the years 72 and 81, and then decreases to around 3% in 1999. The point of this figure is not so much the specific magnitude, as the fact that from the 80 observed a decrease mercado17 risk premium. Glassman and Hassett (2000), calculated in his book "Dow 36,000" that the risk premium American market in 1999 was 3% 18. Claus and Thomas (1999) reached the same conclusion. Jeremy Siegel, Wharton professor and author of "Stocks for the long term," he says, "although it may actions appear to have more risk than government bonds in the long term, this is not true. The safest investment in the long term (from the point of view of preserving the purchasing power of investor) were the stocks, not bonds. " This has been essential for Analysts and investors use market premiums below the historical performance of the stock fixed income.

The decline in market premium also explains, at least in part, why the bags have been so profitable in the 90s. Market premiums used for valuations in the years eighty to ninety were higher than those used today. Two factors behind this are the reduction in investor risk through diversification and reducing interest rates. On the other hand, we must bear in mind that in the second half of the twentieth century, the profitability of shares has exceeded expectations: the global real return average share in 1900-1950 was 5.1%, whereas in 1951-2002 was 8.4% 9. Recent comparison of the evolution of the stock in Spain, Germany, Japan and USA

Figure 20 shows the comparison of interest rates in the long term (interest rate 10-year bonds) in Spain, Germany, Japan and USA. It may look like through 1996, the interest rate of bonds in Spain was significantly higher than other countries. However, from that date interest rates long term Spain, USA, and Germany have been estimated to currently stand at around 4%. Japan, despite having followed the same trend as the other countries (interest rates have fallen since December 1991) had interest rates always lower than those of Spain, Germany and USA.

Figure 20. Types of long-term interest in Spain, Germany, Japan and the U.S.

Figure 21 shows the evolution of the stock indices of the four countries. The starting point of all is the level index IBEX 35 December 1991: 2,633 points. It can be seen that the IBEX 35, the S & P 500 and the DAX 30, have followed parallel paths: all they have experienced significant appreciation. The behavior of the Japanese stock market (the Nikkei 225) has been completely different: not only it has risen in most of the period had a lower level than it was in December 1991. Table 8 shows the correlation matrix between the increase in interest rates different countries and the returns of the indices. The correlations between stock indices Spanish, German and American, were higher than the correlations of these indices with the bag Japanese. Also worth noting that the correlation between the performance of the indices and the rate increase was greater (in absolute value) in Spain (-33.4%) than in the other countries. (7.9%, 26.4% and 0.4%). Regarding the correlation between the rate increases was greater, logically, the correlation between Spain and Germany between Spain and the United States. without

But there has been a strong correlation between increased rates in Germany and the United States. The correlation between increased rate between Spain and in Japan was practically zero.

Table 8. Correlation Matrix. Monthly data from 1991 to 2004.

In a controversial article Porter (1992) said that the U.S. economy increased less than that of Japan and Germany during the 80s because the cost of capital (and the risk premium that analysts and managers used) was higher in the United States. How does the reader of this argument? Thus Figure 21 as many of the previous figures enable verification that the prices stock markets, with the exception of Japan, rose greatly in the nineties to subsequently dropped in 2000, 2001 and 2002. In 2000 it used to give two explanations for the rise Quotes of the nineties: the first, which had decreased market risk premium, and the second, it was overrated the bolsa19.

10. Conclusion: Is there a market risk premium?

One of the assumptions underlying the CAPM, and most financial models, expectations is homogeneous: all investors have the same expectations of profitability and riesgo20 for all assets. In that case all investors would consist of debt portfolios without risk and portfolio with the same percentage composition the market (the bag). But it is obvious that investors have the same expectations, not all investors have portfolios of identical composition and not all investors have a portfolio composed of all actions of the market.21.

We know the market risk premium (market risk premium required) preguntándosela, although many times the market risk premium is not an explicit parameter for many investors, but implicit, manifested in the price you are willing to pay for the acciones22. However, it is impossible to determine the market risk premium because that number does not exists. Even if we knew the risk premiums of each investor, it would be meaningless to speak of the risk premium "market". This is based on aggregation theorems of microeconomics, which are actually non-aggregation theorems. A model that works perfectly on an individual level, may not work at the aggregate level (market) 23. For CAPM, this means that although the CAPM may be an appropriate model to explain investment decisions of each investor, it is valid for the whole market because investors do not have the same expectations of return and risk for all actions. The value of each share by each investor is the value current expected cash flows discounted at a rate (which depends on the expected beta and premium market risk of the investor). Different investors have different expectations of flows and different expectations of risk (expected beta and market risk premium). If all investors have the same expectations of flows and risk, then yes make sense to talk about risk premium "market" (required market risk premium), because it would equal to the expected beta for each investor. However, expectations are not homogéneas24 and features very distintas25 investors.

Identical risk expectations means that all investors agree on the expected volatility future profitability every action and correlation between stock returns. 21 A good article on the nonexistence of homogeneous expectations is Levy and Levy (1996). Example 22. An investor is willing to pay today 100 pesetas for a perpetual annual flow 6 pesetas guaranteed by the State (risk free rate). This implies that the risk-free rate is 6%. However, only willing to pay 80 pesetas other perpetual annual flow 6 pesetas in year 1 and growing at 3% per year, which expected from a diversified portfolio of shares. This means that the profitability required to market is 10.5% (6/80 +0.03). Consequently the market premium of this inverter is 4.5% (10.5% - 6%). 23 As Mas-Colell, Whinston and Green (1995, page 120) says: "It is true that the preferences of a representative consumer have normative content although aggregate demand can be generated from said representative consumer. There may occur even a representative consumer but not has social welfare function (social welfare function) that allows finding a representative consumer normative. " Lintner (1969) argued that the existence of heterogeneous expectations does not alter the validity of the CAPM in simple scenarios. He claimed that if investors have heterogeneous expectations about returns and covariances, then the market portfolio is not necessarily efficient, and therefore can not be made tests the validity of the CAPM.

The following table shows the forecasts made in late 1997 by several analysts estadounidenses26 about the level of the Dow Jones at the end of 1998. It also shows its recommendation for the composition of a portfolio:% Equity means the equity proportion recommending (The rest in bonds). Significant is the dispersion of forecasts (between 6,100 and 10,250) and the dispersion of the ratio of RV in the portfolio. One would expect that those who pursue higher revaluation of the Dow Jones, recommend a higher proportion of RV, but as you can observed, not always the case. The Dow Jones was 7,908 points on December 31, 1997 and 9181 points on 30 December 1998. We emphasize that the problem of the market risk premium is that expectations investors are not homogeneous. If they were, it would make sense to talk about the market risk premium because all investors have the market portfolio.