Appendix 1a: DTT Organisation Chart in the Netherlands 74

Appendix #

Appendix 1a: DTT Organisation Chart in the Netherlands 74

Appendix 1b: DTT Disciplines Chart 75

Appendix 1c: DTCF Matrix Chart in the Netherlands 75 Appendix 1c: DTCF Matrix Chart in the Netherlands 76 Appendix 1d: DTCF Organisational Chart in the Netherlands 77 Appendix 1e: MRP from External Parties (confidential) 78 Appendix 2a: Trade as % of Gross Domestic Product 79 Appendix 3a: Interviews at DTCF (confidential) 80 Appendix 3b: DTCF questionnaire: MRP and Alternatives 81

Appendix 4a: Assumptions Behind the CAPM 88

Appendix 4b: CAPM Tests Impossibility 89

Appendix 4c: Two Beta Definitions 90

Appendix 4d: Four Beta Applications 91

Appendix 4e: Overview of MRP Studies from Different Perspectives 93 Appendix 4f: Market Efficiency and Six Lessons 107 Appendix 4g: Arithmetic and Geometric Mean 109

Appendix 4h: Statistical Variability 110

Appendix 4i: Systematic Component in Bond Returns 111

Appendix 4j: Bond Yield and Bond Returns 114

Appendix 4k: Summary of the MRP Approaches 115

Appendix 5a: The GFD Index for Shares and Bonds 119

Appendix 5b: Arithmetic Statistics for Different Periods 120

Appendix 5c: Geometric Statistics for Different Periods 123

Appendix 5d: Arithmetic Statistics for 10-Year Periods 126

Appendix 5e: DTCF MRP Brochure for Valuation Report 129

Appendix 5f: Yearly MRP and Market Volatility 133

Appendix 1a: DTT Organisation Chart in the Netherlands General Meeting

Supervisory Board

Board of Directors Council Board

Disciplines Directors

Staff Directors

Region Directors Market Directors

5 Partnerships

Appendix 1b: DTT Disciplines Chart

Disciplines

Audit Tax

Financial advisory services

Consultancy Legal

Management

solutions HCAS SB&E advisory

services

Government solutions

Corporate finance

Transaction services

Reorganisation services

Real Estate

Financial services

Grant services

Disciplines

Audit Tax

Financial advisory services

Consultancy Legal

Management

solutions HCAS SB&E advisory

services

Government solutions

Corporate finance

Transaction services

Reorganisation services

Real Estate

Financial services

Grant services

Energy &

Utilities

Media Transport

&

Logistics Consumer

Business

Technology–

Media- Telecom

Manufacturing

Business Services

Public Sector

Financial Services &

Institutions Partner

Shadow Partner

Team participants

Partner

Shadow Partner

Team participants

Mergers &

Acquisitions

Business Valuations

Private Equity &

Structured Finance Partner

Shadow Partner

Team participants

Service Lines/

Organisation participants Industry Groups/

Organisation participants

Appendix 1d: DTCF Organisational Chart in the Netherlands

Managing Partner

Professionals Group

Partner Group/ Director

Manager

Consultant Senior Consultant

Senior manager

Risk Management

Administration Human Resource

Management Board Administration Five Staff Departments

Research Junior Consultant

Appendix 1e: MRP from External Parties (confidential)

Appendix 2a: Trade as % of Gross Domestic Product

Trade 1870 1910 1950 1995

The U.K. 41 44 30 57

France 33 35 23 43

Germany 37 38 27 46

The U.S. 14 11 9 24

Canada 30 30 37 71

Australia 40 39 37 40

Japan 10 30 19 17

Source: Brakman, Leeflang, and Sterken, 2000: 26.

Appendix 3a: Interviews at DTCF (confidential)

Appendix 3b: DTCF questionnaire: MRP and Alternatives

1. In what manner can you characterise thinking, formation and change processes behind the DTCF strategy and why?

hint: logics vs creativeness.

deliberate vs emergent ness.

revolution vs evolution.

2. On what aggregation level is the DTCF strategy determined and why?

hint: business level: inside out vs outside in.

corporate level: portfolios vs core competence.

network level: discrete vs embedded organisations.

3. From what contextual perspective is the DTCF strategy determined and why?

hint: industry level: evolution vs revolution.

organisation level: leadership vs corporate dynamics.

international level: global vs local.

4. What is the relationship between the DTCF strategic choices and its desire to conduct research concerning mrp (market risk premium = mrp) and alternatives (dividends, earnings, capital gains, corporate productivity, etc….)?

5. What is relationship between determined strategic choices at DTCF and internally observed organisational developments and needs, especially when the mrp and

alternatives research is considered? (Provide some perspective by explaining the past, current and expected future developments.)

6. What internally observed organisational needs and developments would you consider important analysing, developing, improving or changing when the mrp and alternatives research is considered?

7. What is relationship between determined strategic choices at DTCF and externally observed indirect and direct developments, especially when the mrp and alternatives research is considered? (Provide some perspective by explaining the past, current and expected future developments.)

hint: indirect factors: macro variables (economical, socio-cultural, technological, legal, demographical).

direct actors (not only for DTCF but also for the targeted industry segments as well): industry (internal rivals, potential entrants, buyers, substitutes, and suppliers).

provide answers if possible per industry segment.

for competition provide their mrp values or alternatives with sound argument and source.

Indirect factors:

Direct actors:

8. What externally observed developments and shifts would you consider important analysing in order to regain and obtain sight on the length of the different business cycles in targeted segments, especially when the mrp and alternatives research is considered? (Provide some perspective by explaining the past, current and expected future developments.)

9. In short, what are the major factors and actors (externally and internally), you have observed so far, leading towards the mrp and alternatives research?

Indirect factors

Direct actors

Internal actors and factors

10. What do you expect from the conducted research concerning the mrp and alternatives, in terms of desired internal organisational developments and its value?

11. How would you, as a DTCF expert, define, describe and use transparent mrp or an alternative approach?

12. How would you, as a DTCF expert, describe current application and calculation manner of the mrp at DTCF?

13. As a DTCF expert, what is the mrp or an alternative you would like to use or provide in the valuation analysis and consider truly transparent? (Please provide percentage value with a sound argument.)

Appendix 4a: Assumptions Behind the CAPM

All investors are single period decision makers who wish to maximise expected utility of terminal wealth, and whose choices among portfolios depend on the expected return and standard deviation of the probability distribution of expected returns.

All investors agree on both the expected returns and standard deviations of all assets and also agree on covariance of returns between all pairs of assets.

All investors can borrow or lend unlimited amounts of money at the risk-free interest rate.

There are no taxes.

All investments are completely divisible, can be bought and sold without delay or difficulty, and can be bought and sold without transaction costs.

No investor holds a large enough portfolio to individually affect prices of investments by buying or selling.

The quantities of all investments are fixed.

Source: Seitz and Ellison, 1999: 442.

Appendix 4b: CAPM Tests Impossibility

Some reasons why the capm is impossible to test are:

1. It relies on specification of a risk-free asset – there is some doubt whether such an asset really exists (see chapter 4).

2. It relies on analysing security returns against an efficient benchmark portfolio, the market portfolio, usually proxied by a widely used index. Because no index captures all assets it could be inefficient, compared with the full market portfolio, thus distorting empirical results.

3. The model is unduly restrictive in that it includes only securities as depositories of

wealth. A full capm should include all forms of assets, such as real estate, oil paintings

or rare coins – in fact, any asset that offers a future return. In this respect, the capm is

only a security-pricing model.

Appendix 4c: Two Beta Definitions Beta definition Application

A regression coefficient

The beta term is borrowed from linear regression. Consider a time series regression of portfolio excess return, r

(t), against some benchmark excess return, r

(t):

r

(t) = α

+ β

. r

(t) + e

(t)

for t = 1,2,...,T.

The estimated coefficients are the realized, or historical, alphas and the betas, since they are an ex post evaluation of what happened.

The regression beta is a statistical construct. It tells what happened over a certain period with a particular sample of data. The regression beta can be interpreted as the sample covariance of the portfolio and benchmark return divided by the sample variance of the benchmark return.

Predicted beta When the forward attempts are made in order to forecast beta,

Grinold uses the same notion by dividing a covariance by a variance.

Any model for predicting asset variance and covariance can be used to predict the variance of a benchmark and the covariance of any portfolio with that benchmark. The ratio of those two quantities is the portfolio’s predicted beta with respect to the benchmark. If r

and r

are the excess returns on the portfolio and the benchmark, then the formula is:

β

= Cov { r

, r

} / Var {r

}

In order to make this calculation no information about the portfolio’s expected returns is needed. The predicted beta measures exposure to benchmark risk.

Source Grinold, 1993: 28 and 29.

Appendix 4d: Four Beta Applications Beta Application

Risk exposure The predicted beta provided in appendix 4c measures exposure to benchmark risk. Like the historical beta, see appendix 4c, it can be used to break the portfolio’s excess return, r

, in to one component - β

. r

– that is perfectly correlated with the benchmark and another component (the residual return) - r

minus β

. r

– that is not

correlated with the benchmark return. The variance of the residual is denoted:

ω

= Var {r

- β

. r

}

Since the benchmark component and the residual component are uncorrelated, we can separate the portfolio's variance into benchmark and residual terms as follows:

σ

= β

. σ

+ ω

Here σ

is the variance of the benchmark portfolio. We see that beta determines the benchmark component of risk, in effect telling the investor of the riskiness of the portfolio, vis-à-vis the benchmark.

Thus, it allows the investor to distinguish between the market risk of a portfolio, and the specific company risk, which is shown by ω

.

Conditional expected returns

Beta can be used to forecast expected returns on an asset or a portfolio of assets conditional on some information about the return of any other asset or portfolio of assets. If for example, we know that the SNGALLS Index will have an excess return of 10% next year. What does that insight about the benchmark index tell us about the

expected return on ACE Dynamics? That insight may be numerically expressed in the equation:

E{r

׀r

= 10} = E{r

} + β

. [10 – E{ r

}]

In this equation, r

and r

are the unconditional expected

excess returns. This can be applied outside the bounds of finance as

well. For example, if we know July's rainfall, we can use the equation

to predict August's rainfall, provided, we have good estimates of the

co-movement (beta) between the two variables.

Unconditional expected returns

The capm is a way of obtaining unconditional expected returns. The capm breaks expected return into two parts – (1) a time premium (the risk free return) that an investor obtains for parting with the money and (2) an expected excess return (also called a risk premium) that the investor earns for taking on risk. The capm maintains that a portfolio’s expected excess returns are proportional to that portfolio’s beta with respect to the market portfolio of all assets.

The naive forecast

Many institutional investors prefer to manage their portfolios relative to an investment benchmark such as the S&P500, or the SNGALLS.

Thus, the beta that relates the returns on a security relative to the excess returns on the market, can serve as a naïve forecasting tool for determining the required rate on a portfolio relative to a certain benchmark. While the opportunity set of an informed investor

(informed for example of special information or other factors) will be expanded, for the naïve forecaster, who does not have access to any special information, the beta on market returns still serves the

purpose of arriving at an estimated required rate.

Source Grinold, 1993: 30 and 31.

Appendix 4e: Overview of MRP Studies from Different Perspectives

MRP Study Market, data and period Instrument(s) Model(s) Research Outcome

Lacy H. Hunt and David M.

Hoisington (2003).

Annual data from the SP500, longest treasury bond, earnings, gross domestic product, and inflation.

Periods:

1871 - 2001

1900 - 2001

1926 - 2001

1871 - 1925

1846 - 2001

1871 - 1945

No standard deviation value is

Equities = (dividends + earnings), treasury bonds, gross domestic product, price- earnings ratio and inflation.

Equities, dividends, earnings, and gross domestic product.

Equities less bond:

4.3% 1871 - 2001

5.1% 1900 - 2001

5.4% 1926 - 2001

2.8% 1871 - 1925

6.8% 1846 - 2001

2.7% 1871 - 1945

SP500 Dividend yield less bond:

0.3% 1871 - 2001

-0.3% 1900 - 2001

-1.3% 1926 - 2001

2.4% 1871 - 1925

-2.6% 1846 - 2001

2.7% 1871 - 1945

Capital gains differential:

4.1% 1871 - 2001

5.4% 1900 - 2001

6.7% 1926 - 2001

0.4% 1871 - 1925

9.4% 1846 - 2001

2.9% 1900 - 2001

2.8% 1926 - 2001

0.8% 1871 - 1925

3.7% 1846 - 2001

0.5% 1871 - 1945

Bonds:

5.0% 1871 - 2001

4.9% 1900 - 2001

5.3% 1926 - 2001

4.5% 1871 - 1925

5.6% 1846 - 2001

4.5% 1871 - 1945

Beginning period P/E ratio

11.7% 1871 - 2001

12.8% 1900 - 2001

10.1% 1926 - 2001

11.7% 1871 - 1925

18.7% 1846 - 2001

11.7% 1871 - 1945

Beginning period dividend yield

5.5% 1871 - 2001

4.0% 1846 - 2001

5.5% 1871 - 1945

Beginning period treasury bond yield

4.2% 1871 - 2001

2.0% 1900 - 2001

3.7% 1926 - 2001

4.2% 1871 - 1925

2.2% 1846 - 2001

4.2% 1871 – 1945

MRP Study Market, data and period Instrument(s) Model(s) Research Outcome

Robert D. Arnott and Peter L.

Bernstein (2002)

Equity annual and monthly data:

William G. Schwert (1802 – 1925)

Robber Shiller (1871 - 2001)

Ibbotson Associates (1926 - 2000) S&P500 Yields and Total Returns

Long term government bonds:

Global Financial Data (1800 - 2001), National Bureau of Economic Research, 10 year Government bond yields

Ibbotson Associates (1926 - 2000) Long Term Government

Stocks, dividends, bonds, gross domestic product and inflation.

Equity risk premium (total market return – risk free rate)

The observed real stock returns, and the excess return for stocks relative to bonds, over the last 75 years has been extraordinary, due largely to important nonrecurring developments.

The investors of 75 years ago would have had no objective basis for expecting the real returns or excess returns that stocks subsequently delivered. It is worth noting that their objective measure for the risk premium was unusually high in 1926, helping to set the stage for the

outstanding stock returns of the past 75 years.

The investors would rarely have had an objective basis for expecting lofty real returns or excess returns, such as those that we have had the good fortune to earn from stocks over the past 75 years.

It is dangerous to shape future expectations based on extrapolating these lofty historical returns. In so doing, an investor is tacitly

assuming that valuation levels that have doubled, tripled and quadrupled, relative to the underlying

Research (1801 – 2001) (annual until 1801;

interpolated for monthly estimates.

Ibbotson Associates (1926 - 2000) Ibbotson monthly data was given primary (two-thirds) weighting from 1926 to 1950, since NBER data was annual through 1950.

Gross Domestic Product:

National Bureau of Economic Research (1801 – 2001)

Gross National Product, annually through 1920.

Gross Domestic Product, quarterly from 1921 - 2001.

Period: 1810 - 2001.

spending.

On the hopeful side, they have demonstrated, that the “normal” level of the risk premium is modest (around 2.4%), and therefore that current market valuations do not need to return to levels that can deliver the 5% “risk premium” (excess return) that the Ibbotson data would suggest. If there is reversion to the mean, then the difference between 2% and zero still requires nearly a halving of stocks relative to bonds to restore balance, but that’s a less daunting picture than would be required to facilitate a reversion to a 5%

“risk premium” that many observers believe is normal.

It is also possible that the modest difference between a 2.4% “normal” risk premium, and the negative risk premiums that have prevailed in recent quarters, permitted the bubble. It is possible that “reversion to the mean” might not ever happen, in which case we see stocks sputter along delivering bond-like returns, at a higher risk than bonds, for a long time to come.

The consensus, that a “normal” risk premium is around 5%, was shaped by a deeply rooted naivete in the investment community, where most participants have a career span reaching no further back than the monumental 25-year bull market from 1975 to 1999. This kind of mindset is a mirror image to the attitudes of the chronically

Today, investors are loathe to recall that the real total returns on stocks were negative over most 10-year spans during the two decades from 1963 to 1983, or that the excess return of stocks relative to bonds was negative as recently as the ten years ended August 1993.27 When reminded of such experiences, today’s investors retreat behind the mantra that things will be different this time. But no one can genuflect before the notion of the long run and deny that there will again be such circumstances in the decades ahead.

Indeed, these crises are more likely than most of us would like to believe.

All gathered evidence gathered demonstrates that the normal risk premium is not 5%, but is much closer to a modest 2.4%. A 2.4% risk premium has historically served to entice investors to accept equity market risk. A negative risk premium, as appears to prevail today, is a symptom of irrational valuation.

As a consequence, investors greedy enough or naïve enough to expect a 5% risk premium, and overweight equities accordingly, may well be doomed to deep disappointments in the future as the realized risk premium falls far below this inflated expectation.

MRP Study Market, data and period Instrument(s) Model(s) Research Outcome

Ibbotson Associates, Inc,

(2002)

For the Netherlands MSCI index is used with reinvested dividends and capital gains.

Long-term bond yields are derived from the most recent ten-year government bond noted at International Monetary Fund.

Period: 1970-2001.

Equities and bonds.

Equity risk premium model.

Provided values are arithmetic means without standard deviation value:

In local currency: 7.7 % (1970 - 2001).

In dollars: 8.5% (1970 - 2001).

Marc H. Goedhart, Timothy M. Koller,

and Zane. D.

Williams (2002)

In the U.S. analysed yearly data from the S&P500 (1963 - 2001).

In the U.K. analysed market data (1965 –2001).

Current real long-term bond yields for the U.S. and the U.K. for the same time periods.

Equities, long- term bonds, inflation, gross domestic product, dividends, and earnings.

Forward looking model based on projections implied by current stock prices relative to earnings, cash flows, and expected future growth.

In the U.S. real equity risk premium is:

5% (1962 – 1979).

3.6% (1990 – 2000).

In the U.K. real equity risk premium is:

4,3% (1962 – 1979).

3% (1990 – 2000).

MRP Study Market, data and period Instrument(s) Model(s) Research Outcome

Roger G. Ibbotson and Peng Chen Yale University

(2001).

Annual data from Wilson and Jones, SP 500 and the U.S.

government bond.

Period: 1926 -2000

Stocks, bonds, bills, and inflation.

Combination of equity risk premium and demand side models

Geometric mean

Equity premium historical perspective

Geometric 5.24% 1926 - 2000

Equity premium forecast with forward looking earnings model

Geometric 3.97% 1926 - 2000

Equity premium forecast with forward looking dividend model

Geometric 0.24% 1926 – 2000

Equity premium forecast with forward looking gross domestic product model

MRP Study Market, data and period Instrument(s) Model(s) Research Outcome

Eugene F. Fama and Kenneth R.

French, University of Chicago (2001).

Annual data from the SP500 in the U.S. market.

Monthly data from the commercial paper.

Periods:

1872 - 2000

1872 - 1950

1951 – 2000

Equities = (dividends + earnings),

commercial paper and inflation.

Equity risk

premium, dividend and earnings growth model.

Real returns equities an standard deviation:

5.57%; 0,1851 (1872 - 2000);

4.40%; 0,1957 (1872 - 1950);

7.43%; 0,1673 (1950 - 2000).

Real returns dividends:

3.54%; 0,1300 (1872 - 2000);

4.17%; 0,1602 (1872 - 1950);

2.55%; 0,0562 (1950 - 2000).

Real returns earnings:

No data (1872 - 2000);

No data (1872 - 1950);

4.32%; 0,1402 (1950 - 2000).

Inflation data:

2.16%; 0,0751 (1872 - 2000);

0.99%; 0,0911 (1872 - 1950);

4.00%; 0,0311 (1950 - 2000).

MRP Study Market, data and period Instrument(s) Model(s) Research Outcome

Justin Pettit, Ivan Gulic and April

Park (2001)

The study is based on the monthly returns based on the S&P500 index and the U.S.

Treasury long bonds from 1926 – 2000.

Stocks, bonds, and inflation.

Equity risk premium (total market return – risk free rate)

The market risk premium over the long-term bond is about 5% and an adjusted risk premium of 6,5

%: 1950 – 2000.

Elroy Dimson, Paul Marsh and Mike Staunton (2000).

Annual data from different databases where various countries were analysed.

Period: 1900 –2000

For the Netherlands CBS-data sets were used 1900 -2000.

Dutch bond returns are represented by consols: 1900 – 1914.

The Eichholtz-Koedijk-Otten bond index: 1915 – 1973.

The Morgan and Stanley bond data 1974 -2000.

Stocks, bonds, bills, and inflation.

Equity risk premium (total market return – risk free rate)

Arithmetic and geometric mean with the standard deviation value:

Arithmetic mean 1900-2000:

The Netherlands 6.72%; 0,21

Geometric mean 1900-2000:

The Netherlands 4.7%; 0,21

MRP Study Market, data and period Instrument(s) Model(s) Research Outcome

William G.

Schwert, University of Chicago (1990).

Monthly data:

Smith and Cole: 1802 - 1862

Macaulay: 1863 - 1871

Cowles: 1872 - 1885

Dow Jones: 1885 - 1925

CRSP NYSE: 1926 - 1987

Daily data:

Dow Jones: 1885 - 1928

SP of NYSE: 1928 – 1962

Portfolio returns with added monthly dividend yields from:

Cowles: 1871 - 1938

CRSP: 1926 – 1987.

Equities, dividends and capital gains.

Portfolio monthly returns with the mean value and standard deviation:

0.0071%; 0,0455 (1802 - 1987)

Capital gains monthly returns omitting estimated dividend yields with the mean value and standard deviation:

0.0088%; 0,0797 (1802 - 1870)

Portfolio daily returns with the mean value and standard deviation:

0.0395; 1,019 (1885 - 1987)

Appendix 4f: Market Efficiency and Six Lessons

If markets are efficient in the weak sense, then it is impossible to make consistently superior profits by studying past returns, prices will follow random – walk. If markets are efficient in the semi strong sense, then the prices will adjust immediately to public information. If markets are efficient in the strong sense, then the prices will reflect all available information from both the company and the economy [Brealey and Myers, 2000: 358 and 370].

A market is efficient when market prices fully reflect information about the securities.

Since new information about securities, by definition, will be random, price changes also must be random. In other words, day-to-day price changes cannot be predicted. A direct implication of market efficiency is that it will not be easy to find positive npv financing or investment opportunities. In short, it will not be possible to find under-priced or

overpriced securities. A fierce competition between investors eliminates profit

opportunities and causes debt and equity issues to be priced fairly [Brealey and Myers, 2000: 352 and 353].

Lesson 1: Markets have no memory

This stresses weak form efficiency and clearly implies that attempts at timing the market for bond or stock issue are unlikely to result in value maximizing decisions. Historic prices and recent trends are not much help in forecasting the market trend. It is

unfortunately true that many managers try to time the market by picking the best time to issue securities.

Lesson 2: Trust market prices

It is not possible for most investors to consistently find bargains or under-priced

securities in the market. Market prices reflect the collective wisdom of all the investors and analysts and therefore will be the best estimates of the value of the securities. In other words, it is unreasonable and unwise to assume that one can predict the prices better than the market itself.

Lesson 3: Read the entrails

Market prices tell us a lot about the future. Security prices typically reflect what investors

expect to happen in the future. For example, the difference between short-term and

long-term interest indicates the expected changes in interest rates. The return offered by

a company’s bonds and the variability of its common stock prices are good indicators of

the probability of its going bankrupt. Market reactions to corporate announcements such

as mergers, acquisitions, and restructuring give managers fair indication of the valuation

effect of these actions. A very good measure of the market reaction is the abnormal

return, which is the net return on the stock surrounding the event after taking into

account the normal or expected return. (Abnormal return = actual return - expected

return, where the expected return is measured as a + b r

).

Lesson 4: There are no financial illusions:

Investors are concerned with the firm’s cash flows and are unlikely to be impressed by accounting gimmicks or other cosmetic changes, which do not enhance the cash flows.

Therefore, a firm cannot expect to increase its value by merely cosmetic changes such as stock splits or by manipulating the earnings reported to shareholders.

Lesson 5: The do-it-yourself alternative

Investors will not pay others for anything that they can create or do themselves at a lower cost. An implication of this lesson is that corporate combinations pursuing

diversification for risk reduction is unlikely to be valued highly in the market as investors can duplicate this strategy at lower costs by buying shares of companies in different industries.

Lesson 6: Seen one stock, seen all

Unlike branded products, stocks do not have unique qualities; investors buy a stock if the expected return it offers is fair compensation for the risk it entails. This means that stocks, which offer similar return-risk trade off, are near perfect substitutes for each other or the demand for any given stock is highly elastic. The implication is that large blocks of a stock can be sold at close to the market price as the market is convinced that you have no private information. Scholes’ study of secondary offerings confirmed that large offerings had only a very small effect on the price.

Source: Brealey and Meyers, 2000: 368 – 375.

Appendix 4g: Arithmetic and Geometric Mean

Brealey and Myers [2000: 157] provide the following example. Suppose the price of Big Oil’s common stock is 10 euro. There is an equal chance that at the end of the year the stock will be worth 9, 11 or 13 euro. Therefore the return could be -10%, +10%, or 30%

where we assume Big Oil’s will pay no dividends. The expected return is 1/3 (- 10 + 10 + 30) = 10%. If we rerun the process in reverse and discount the expected cash flow by the expected rate of return, we can obtain the value of Big Oil’s common stock: present value = 11/1.10 = 10 euro.

The expected return of 10% is therefore correct rate at which to discount the expected cash flow. It is also the opportunity cost of capital for investments, which have the same degree of risk as Getronics. It is called the opportunity cost because it is the return foregone by investing in the project rather than investing in securities [Brealey and Myers, 2000: 17].

Now suppose that we observe the returns on Big Oil’s common stock over a large number of years. If the odds are unchanged, the return will be -10 % in a third year of the years, +10 % in a further third, and + 30 % in the remaining years. The arithmetic average of these yearly returns is (- 10 + 10 + 30)/ 3 = 10%. The arithmetic mean of the returns correctly measures the opportunity cost of capital for investments of similar risk to Getronics.

The geometric mean of Big Oil’s common stock would be (0.9 x 1.1 x 1.3)

– 1 =

0,088% or 8,8%, which is less that the opportunity cost of capital. Investors would not be

willing to invest in a project offering 8,8% return if an investor could get 10% expected

return in the capital markets. The npv of such project would be: - 10 + (10,88/ 1,1) = -

0,10.

Appendix 4h: Statistical Variability

Brealey and Myers [2000: 188 and 189] provide an example of the distribution of possible returns from two investments.

Figure 4h: Probability of Project Returns

Figure 4h pictures the distribution of possible returns from two investments. Both offer an expected return of 10 %, but A has much the wider spread of possible outcomes. Its standard deviation is 15 percent; the standard deviation of B is 7,5%. Most investors dislike uncertainty and would therefore prefer B to A.

- 40 - 20 0 20

Return in % Probability

40 60

- 40 - 20 0 20

Return in % Probability

40 60

Investment A

Investment B

Appendix 4i: Systematic Component in Bond Returns

Booth explained direct implications for the bond market. If investors hold diversified portfolios, what does the increased bond market risk mean for their overall portfolio?

That is, how much of the increased interest rate risk is diversifiable? From the

conducted research, the bond market uncertainty has had a systematic as well as an unsystematic component [Booth, 1998: 20 and 21] (see Figure 4i).

Figure 4i: Beta for the Long-Term Bond, Source: Stern Stewart Research 2001.

Pettit, Gulic, and Park [2001: 5] have provided facts where the long-term government bond returns are positively correlated with the stock market since the early 1970s. While bond returns are realized only if the bond is sold, this covariability does imply a degree of systematic risk. Depending on the measurement period, the beta of long bonds has varied over the past five decades from –0.1 to over 0.4. Analysis of monthly returns suggests 0.25 is a reliable estimate of the current beta of long government bonds. The 0.25 beta value is subjective because that value represents an average value of trailing 30 – year betas. The long-term average is used because the shorter periods are overly sensitive to the specific months selected.

Booth’s research has acknowledged mentioned results. As the investment horizon shortens price volatility dominates income volatility. In daily data, as an extreme, almost all the volatility is from price changes [Booth, 1998: 20 and 21]. To estimate a risk-less rate, the current yield on the long bond must be reduced by the systematic component of that yield. The estimate of the systematic component the bond beta (0.25) is

multiplied not by the actual historical risk premium, but by a higher, adjusted mrp – one

that reflects the fact that mrp’s have been understated since the early 1970s by the

overstatement of the risk-less rate [Pettit, Gulic, and Park, 2001: 5].

The point of calculating a bond beta is to better quantify how much systematic risk has migrated to the risk-free rate, to improve the application of the capm in cases where the company beta is either very high or very low – say, a beta outside of the 0.8 to 1.2 range. For most cases, this refinement is immaterial, but for many technology stocks with hight betas, it is significant [Pettit, Gulic, and Park, 2001: 6].

In practice, the investors use as a proxy for the risk-free rate any number of government bond rates, each with its own strengths and weaknesses. An investor who uses bill rates argues that the shorter duration and lower correlation of the bill with the stock market make it truly risk-less. However, because bill rates are more susceptible to supply/

demand swings, central bank intervention, and yield curve inversions, bills provide a less reliable estimate of long-term inflation expectations and do not reflect the return required for holding a long-term asset. For valuation, long-term forecasts, and capital budgeting decisions, the most appropriate risk-free rate is derived from long-term government bonds. Long-term government bonds capture long-term inflation

expectations, are less volatile and subject to market movements, and are priced in a liquid market [Pettit, Gulic, and Park, 2001: 5].

The measuring error of the systematic risk component in long-term bonds can be measured as follows:

1. Theory: r

= r

+ ß

* (r

– r

)

2. Theory: r

= r

+ ß

* (r

– r

) = r

+ a

3. Practice: r

= (r

+ a) + ß

* [r

– (r

+ a)]

where (r

+ a) = r

= bond return

Calculated required rare of return on investment (i) is as follows:

4. r

= r

+ ß

* (r

– r

) + (a – ß

)

where (a – ß

) is the measuring error.

Therefore the measuring error is:

^

^

The measuring error is small when:

(1 – ß

) * ( ß

) is small and zero when ß

= 0 or when ß

= 1.

With these aspects in mind, it is possible to provide measuring error of the risk free

asset [Eije von, 2003].

Appendix 4j: Bond Yield and Bond Returns

Fabozi and Fabozi [1989: 37, 38, and 39] provide an answer for the relationship

between the bond yields and its return calculation. The yield is the interest rate that will make the present value of the cash flows equal to the price (or initial investment). The yield to maturity is computed in the same way as the yield (internal rate of return); the cash flows are those that the investor would realise by holding the bond to maturity. For a semi-annual pay bond, the yield to maturity is found by first computing the periodic interest rate, y, that satisfies the following relationship:

P = ∑ C/(1+y)

+ M/(1+y)

where: P is the price of the bond; C is the semi-annual coupon interest; M is the maturity value; and, n is the number of periods (number of ½ years).

For a semi-annual pay bond, doubling the periodic interest rate or discount rate (y) gives the yield to maturity. The yield number which satisfies bond price equation is called the bond equivalent yield. The number of years is not used because an investor needs a yield value that may be compared with alternative coupon bonds.

The yield to maturity considers not only the current coupon income but also any capital gain or loss that the investor will realise by holding the bond to maturity. In addition, the yield to maturity considers the timing of the cash flows. The following relationship should be recognised among the coupon rate, current yield and yield to maturity.

Bond selling at Relationship

Par Coupon rate = current yield = yield to maturity

t=1 n

Appendix 4k: Summary of the MRP Approaches

MRP Approach Measuring period Statistics Strengths Weaknesses

Historical difference MRP approach Academicals use long history data providing an mrp measure, where is assumed that the past returns on the market will follow a random walk process.

Application of the mrp in the business practice varies across business segments.

The lower bond of the mrp reflects the intrinsic firm value.

The mrp variation among the lower and higher premium is reflected in the buy and sell situations.

Arithmetic mean;

Geometric mean;

Standard deviation;

Standard error;

Variance;

Lognormal distribution;

Normal distribution;

Bond beta;

Sharp ratio en other possible ratios.

Early periods acceptable if proved sufficiently long to achieve statistical reliability, while avoiding potentially less relevant early market returns.

The mrp development could be explained by the means of the six factors providing the qualitative support.

Data availability provides easiness in the mrp calculation. Statistical connotations provide quantitative mrp information.

Possibility of providing nominal and real returns for a desired capital budgeting period.

Variables can be defined with great accuracy. The choice among variables must be defined clearly within the context of applied practice examples.

The arithmetic mean provides ex-ante perspective. The geometric mean provides ex-post perspective.

The capm assumptions.

There is no theoretically correct period making the chosen history period arbitrary.

Reduced number of observations can provide to irrelevant or even inaccurate mrp value.

The choice among measuring variables varies across mrp studies providing different mrp values.

Semi-market assumption.

MRP Approach Measuring period Statistics Strengths Weaknesses

Dividend growth model As in the basic approach there is no theoretically correct period for the dividend growth model.

Academicals use identical long history data as in the mrp basic approach.

Additionally a comparison study is made among the calculated values.

Application of the dividend growth model varies across business examples. Here some banks and financial institutions apply the dividend growth model.

Identical for the basic mrp approach. The estimate from the dividend growth model is more precise; both models have lower standard errors than the estimate from the average market return.

In the dividend growth model the aggregate risk aversion is on average roughly similar for two different historical periods (1872-1949 and 1950-1999).

However, the Sharpe ratio for the equity premium from the average market return almost doubles for the same period.

The estimate of the expected stock return from the dividend growth model is less than the income return on investment, so the message is that investment is on average profitable unlike in the average market return.

If an investor is interested in the long-term expected growth of wealth, the dividend growth model is probably best, and the average stock return and the earnings growth estimate of the expected return are upward biased. The estimate from the dividends provides therefore a better ex- ante estimate.

If an investor is interested in the unconditional expected annual simple return, the 1951 – 2000 period estimates from the dividend growth model is downward biased. The bias is large when the average growth rate of dividends is used to estimate the expected rate of capital gain, but it is small for the average growth rate of earnings.

The historical dividend growth underestimates growth in productivity because of the trend away from paying dividends. Lower payout ratios and lower dividend yields do not mean lower productivity or reduced return to investors. Dividend growth has declined over the years due to share buybacks, change in investor preference, corporate merger and acquisition activity, and corporate reinvestment – not due to reduced corporate productivity.

The dividend growth model also adds the current dividend yield with the historical dividend rate to arrive at the forecast. The constructed relationship is incorrect because of the relationship between the dividend yield and the dividend growth rate.

The final weakness is related to the current P/E ratio, which is twice as high as the historical average. The current P/E ratio implies higher than average future

MRP Approach Measuring period Statistics Strengths Weaknesses

Earnings growth model As in the basic approach there is no theoretically correct period for the earnings growth model.

Academicals use identical long history data as in the mrp basic approach.

Additionally a comparison study is made among the calculated values.

Application of the earnings growth model varies across business examples based on various estimation and forecasting institutions.

Identical for the basic mrp approach. The estimate from the earnings growth model is more precise than the estimate from the average return. Since earnings growth is more volatile than dividend growth, the standard error of the expected return from the earnings growth model is higher than the estimate from the dividend growth model.

In the earnings growth model the aggregate risk aversion is on average roughly similar for two different historical periods (1872-1949 and 1950-1999). The Sharpe ratio for the equity premium from the average market return almost doubles for the same period (see previous approach).

The estimate of the expected stock return from the earnings growth model is identical to the dividend growth model so the investment is on average profitable.

In the earnings growth model, the historical growth in corporate earnings has been in line with the growth of overall economic productivity. This aspect make the earnings growth model a superior predictor of corporate profitability and future earnings growth.

The average stock return and the earnings growth estimate of the expected return are upward biased. The bottom line inference does not depend on whether one is interested in the expected annual simple return or long term expected wealth. The bias-adjusted expected return estimates for the 1951 - 2000 period from dividends and earnings are lower than bias-adjusted estimates from realised returns.

MRP Approach Measuring period Statistics Strengths Weaknesses

Forward-Looking Dividend and Earnings Growth Model

As in the basic approach there is no theoretically correct period for the forward looking dividend and earnings growth model.

Academicals use identical long history data as in the mrp basic approach. The forecast of the equity risk premium is done trough the supply side models by using the historical information.

Application of the forward-looking dividend and earnings models varies across business examples based on various estimation assumptions, which are dependent on various forecasting institutions.

Identical as in the basic mrp approach. When the forward-looking dividend and earnings growth model are properly modelled they can prevent violations of the Miller and Modigliani theorem.

First, the growth in corporate productivity as measured by earnings is in line with the growth of overall economic productivity.

Second, P/E increases account for only a small portion of the total return of equity.

The bulk of the return is attributable to dividend payments and nominal earnings growth (including inflation and real earnings growth).

Third, the increase in factor share of equity relative to the overall economy can be fully attributed to the increase in the P/E ratio.

Historical divided growth underestimates historical earnings growth because of the decrease in the payout ratio. The differences between the dividend and the earnings model are therefore related to the decrease of in the historical in the historical payout ratios, the low current payout ratio and the high P/E ratio. The second difference is due to the lowered payout ratios. Applying a low rate forward would mean that even more earnings would be retained in the future than in the historical period. The first two differences are direct violations of the Miller and Modigliani theorem. The firm’s dividend payout ratio only affects the form in which shareholders receive their returns, (i.e.

dividend or capital gains), but not their total return. Firms today likely have such low payout ratios in order to reduce the tax burden of their investors. Instead of paying dividends, many companies reinvest earnings, buy back shares or use their cash to purchase other companies.

The third difference is due to the expectations of higher than average earnings growth predicted by the high current P/E ratio. The high P/E ratio can be caused by mis-pricing, low required rate of return, and high expected future earnings growth rate. Mis-pricing is eliminated by assumption of market efficiency. Bu assuming a constant equity risk premium trough the past and future periods will eliminate a low required rate.

The high P/E ratio is interpreted as the market expectation of higher earnings growth. Despite the record earning

Monthly Index Developments 1952 - 2002

0 2000 4000 6000 8000 10000 12000 14000 16000 18000 20000

12 /3 1/ 1 9 5 0 12 /3 1/ 1 9 5 5 12 /3 1/ 1 9 6 0 12 /3 1/ 1 9 6 5 12 /3 1/ 1 9 7 0 12 /3 1/ 1 9 7 5 12 /3 0/ 1 9 8 0 12 /3 0/ 1 9 8 5 12 /2 8/ 1 9 9 0 12 /2 8/ 1 9 9 5 12 /2 9/ 2 0 0 0

Index Shares Index Bond

Appendix 5b: Arithmetic Statistics for Different Periods

The measuring variables are: mr = market return; rf = risk free returns; and, mrp = market risk premium. These are annualised arithmetic returns where the reduced amount of history will provide a greater standard error and standard deviation (see different time periods below). The confidence interval used for the mrp measurement is 95%. The first period is 1951-2002 where a relatively low standard error (0,003417) of the mean is observable in comparison with the 1991-2002 period (0,07742). The data is based on the Global Financial Data Inc. shares and bonds index.

Period 1951-2002

One-Sample Statistics

52 ,1533 ,22570 ,03130

52 ,0686 ,07477 ,01037

52 ,0848 ,24643 ,03417

MR RF MRP

N Mean Std. Deviation

Std. Error Mean

One-Sample Test

4,899 51 ,000 ,1533 ,0905 ,2162

6,617 51 ,000 ,0686 ,0478 ,0894

2,482 51 ,016 ,0848 ,0162 ,1534

MR RF MRP

t df Sig. (2-tailed)

Mean

Difference Lower Upper

95% Confidence Interval of the

Difference Test Value = 0

Period 1961-2002

One-Sample Statistics

42 ,1403 ,22347 ,03448

42 ,0761 ,08035 ,01240

42 ,0642 ,24411 ,03767

MR RF MRP

N Mean Std. Deviation

Std. Error Mean

One-Sample Test

t df Sig. (2-tailed)

Mean

Difference Lower Upper

95% Confidence Interval of the

Difference Test Value = 0

Period 1971-2002

One-Sample Statistics

32 ,1613 ,23406 ,04138

32 ,0864 ,08399 ,01485

32 ,0749 ,25440 ,04497

MR RF MRP

N Mean Std. Deviation

Std. Error Mean

One-Sample Test

3,898 31 ,000 ,1613 ,0769 ,2457

5,817 31 ,000 ,0864 ,0561 ,1167

1,666 31 ,106 ,0749 -,0168 ,1667

MR RF MRP

t df Sig. (2-tailed)

Mean

Difference Lower Upper

95% Confidence Interval of the

Difference Test Value = 0

Period 1981-2002

One-Sample Statistics

22 ,1829 ,23879 ,05091

22 ,0950 ,08777 ,01871

22 ,0879 ,25651 ,05469

MR RF MRP

N Mean Std. Deviation

Std. Error Mean

One-Sample Test

3,593 21 ,002 ,1829 ,0770 ,2888

5,075 21 ,000 ,0950 ,0560 ,1339

1,607 21 ,123 ,0879 -,0258 ,2016

MR RF MRP

t df Sig. (2-tailed)

Mean

Difference Lower Upper

95% Confidence Interval of the

Difference Test Value = 0

Period 1991-2002

One-Sam ple Statistics

12 ,1662 ,24830 ,07168

12 ,0841 ,08700 ,02512

12 ,0822 ,25778 ,07442

MR RF MRP

N Mean Std. Deviation

Std. Error Mean

One-Sample Test

2,318 11 ,041 ,1662 ,0084 ,3239

3,348 11 ,007 ,0841 ,0288 ,1394

1,104 11 ,293 ,0822 -,0816 ,2460

MR RF MRP

t df Sig. (2-tailed)

Mean

Difference Lower Upper

95% Confidence Interval of the

Difference Test Value = 0

For the total measuring period the following statistical measures are provided that are explaining characters for the market risk premium histogram outcome.

Statistics

52 52 52 52

0 0 0 0

,1533 ,0686 ,0848

,03130 ,01037 ,03417

,1150 ,0685 ,0800

,32 ,02 -,38^a

,22570 ,07477 ,24643

,05094 ,00559 ,06073

,375 1,069 ,167

,330 ,330 ,330

1,03 ,39 1,10

-,29 -,05 -,38

,74 ,34 ,72

7,97 3,57 4,41

Valid Missing N

Mean

Std. Error of Mean Median Mode Std. Deviation Variance Skewness

Std. Error of Skewness Range

Minimum Maximum Sum

RM RF MRP YEARS

Multiple modes exist. The smallest value is shown a.

The mrp mean histogram outcome shows a positively skewed distribution for the annual market risk premium values. The median value (0,08%) is slightly lower than the mean value (0,0848%). The mrp distribution is in the 1951 – 2002 period is therefore not normally distributed. When the lognormal distribution is used, the SPSS program has provided identical results. Remarkably, the normal distribution has proved reliable for the mrp analysis (see chapter 4 and 5).

,66 ,51 ,36 ,21 -,08 ,06

-,23 -,38

The mrp distribution in The Netherlands

Global Financial Data Inc. Shares and Bonds Index 6

5

4

3

2

1

0

Std. Dev = ,25 Mean = ,08 N = 52,00