Portfolio Theory with Application to Rolls Royce

Table of Contents

List of Tables

List of Figure

List of Abbreviations

1. Introduction

2. Portfolio Theory

3. Capital Asset Pricing Model

4. The Company – Rolls-Royce plc.
4.1. Rolls-Royce Business Segments
4.1.1. Civil Aerospace
4.1.2. Defence Aerospace
4.1.3. Marine
4.1.4. Energy
4.2. Corporate Objectives

5. The Application to Rolls-Rolls plc.
5.1. Financial Information
5.2. Diversification
5.3. Capital Asset Pricing Model

6. Critique

7. Conclusion

References

Word Count

List of Tables

Table 1: Sales by Division (real) 1999 – 2002

Table 2: Divisional Sales (%) 1999 – 2003

Table 3: Divisional Correlations of Sales

List of Figures

Figure 1: Equivalent Offsetting Fluctuations in Return

Figure 2: Available Protfolio Risk-Return Combinations

Figure 3: Systematic and Unsystematic Risk

Figure 4: The Capital Asset Pricing Model

Figure 5: Rolls-Royce Time Line 1884 – 2000

Figure 6: Rolls-Royce Business Profile

Figure 7: Undelying Profit

Figure 8: Margins per Division

Figure 9: Sales of Civil and Marine Division

Figure 10: Calculation of Cost of Capital

List of Abbreviations

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1. Introduction

“Modern portfolio theory is the philosophical opposite of traditional stock picking.“^[1] It provides a tool with which it is possible to reduce the risks in business and private investments. At the same time it is the basis for the Capital Asset Pricing Model (CAPM).

This short assey introduces both the theoretical framework of Modern Portfolio Theory (MPT) and the CAPM which are then applied to Rolls-Royce plc. As this is just an overview the reader must be aware that this outline doesn´t go too deep.

2. Portfolio Theory

MPT – or portfolio theory – was introduced in 1952 by Harry Markowitz^[2]. It explores how risk averse investors construct portfolios in order to optimise expected returns for a given level of market risk . The theory quantifies the benefits of diversification. Out of a universe of risky assets, an efficient frontier of optimal portfolios can be constructed. Each portfolio on the efficient frontier offers the maximum possible expected return for a given level of risk.^[3]

To most investors, the logic of diversification is intuitively obvious: "Don't put all your eggs in one basket." Diversification helps spread risk between countries, currencies or markets. It makes sure that the investor is able to benefit from opportunities from around the world. It provides him with a means of hedging bets against crises^[4] and unexpected events (stock market crashes or natural disasters).^[5]

For this reason international diversification makes very good sense. A globally diversified portfolio represents less risk than a diversified domestic portfolio If you have shied away from investing abroad, you have actually been subjecting your portfolio to greater risk.

Diversification reduces risk and is “designed to even out the bumps”^[6] (see figure 1). MPT shows that even a random mix of investments is less risky than putting all your money in a single stock^[7].

Assuming that a portfolio contains two risky assets: one that pays off if the sun shines, another that pays off if it doesn't. A portfolio that contains both assets will always pay - rain or shine. Thus, adding one asset to another can reduce the overall risk of our all-weather portfolio.

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Figure 1 : Equivalend Offsetting Fluctuations in Return

The crucial insight of MPT is that the risk of an individual asset is of little importance to the investor. What matters is its contribution to the portfolio's risk as a whole. This is meant by diversification. But this is only valid under the assumption that both the sun and rain assets are perfectly negatively correlated which is not often the case in reality.

The weighting in a portfolio plays a crucial part. A few observations can be made for the all-wheather portfolio. They are essential for the understanding of MPT^[8]. The line from A to F builds the opportunity set representing the possible combinations. The combination at point C dominates over point E, since point C offers a better return for the same risk. The combinations between D and F are less attractive than those between A and D. Therefore, the rationale investor chooses a portfolio in the segment between A and D^[9] in order to maximise the return.

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Figure 2 : Available Portfolio Risk-Return Combinations

(Source: adapted from Pike and Neale, page 318)

In general, investors are assumed to be risk-averse. A risk-averse person is one who when faced with assets which promise to provide the same return will choose the asset with the lowest risk. In order for investors to accept higher risk, they seek compensatio with the potential for earning a higher return and vice-versa.

“In order to increase portfolio returns, investors have to take on greater risk. Injecting stocks into a portfolio for higher returns therefore translates to a bumper ride. To smooth out the bumps, investors would do well to (a) diversify globally and (b) hold a portfolio of stocks for long enough periods. You may not win a Nobel Prize, but you will be on the right road to investment success.”^[10]

3. Capital Asset Pricing Model

The CAPM distinguishes between the unsystematic or specific risk and the systematic or market risk. Already Small Portfolios eliminate the majority of the specific risk, but to remove all of it, a portfolio comprising all the traded securities has to be built. This so called ´Market Portfolio` plays the main part in the CAPM. Besides, every investor has the chance to invest in risk free assets, such as government bonds. For investing in risky assets, investors expect a risk premium. The expected return on a share is the sum of the return on a risk free asset and the market risk premium, multiplied by β.

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Figure 3 : Systematc and Unsystematic Risk

(Source: adapted from Pike and Neale, page 335)

[...]

^[1] www.moneychimp.com/articles/risk

^[2] with his paper "Portfolio Selection" (1952)

^[3] www.moneychimp.com/articles/risk

^[4] such as war or oil shortages

^[5] taken from Markowitz: Portfolio Selection, page 19 ff

^[6] see: Pike; Neale: Corporate Finance and Investment; page 310

^[7] It is also interesting to note that risk falls steeply as you begin to diversify. With a holding of around 40 stocks, all the benefits from diversification have been almost nearly achieved.

^[8] Figure 2 shows the risk and return relation if the assets are weighted differently

^[9] which is called the efficient frontier

^[10] www.cyberhaven.com/investors/portfolio.html