Portfolio Theory and Capital Asset Pricing Model

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In the year 2000, the Swedish citizens selected their PPM funds for the first time. The Swedish government had earlier decided upon a legislative change in the pension system to cope with the upcoming future problem of pensions. The new pension system was designed to better follow the economic and demographic development (Brantmo 2001). The pension is now based upon the individuals taxable lifetime earnings. Even if you are unemployed or home with children, you are receiving money for your future pension. The highest one can earn during one year for the future pension was in 2006 equal to 333 750 SEK, which is equal to 7.5 Swedish income base amount. The pension can be divided into three different types: the guarantied pension, the income pension and the premiepension. (Försäkringskassan, Pensionssystemet, 2006)
If you have not earned any money or not a sufficient amount during your lifetime, you will receive the guarantied pension. In the year 2006, this amount is 7047 SEK per month for unmarried and 6286 SEK per month for married person. Sometimes this pension can be increased to also cover a part of the housing expenses. (Försäkringskassan, Garantipension, 2006)
There are two other types of pensions; the PPM fund and the income pension. When earning over a specific amount, the individual is not entitled to the guarantied pension, but instead receives one of these two types. The income pension is the pension one earns when, for example, working, unemployed, or home with children. The income pension system works in the following way; as the individual lends money to the people that are pensioner today, he/she then receives the money back when one becomes a pensioner him/herself. (Försäkringskassan, Inkomstpension, 2006)
The premiepension does not work like the income pension. Rather than the money being paid to today’s pensioner, it is instead invested in different kinds of equity funds of one’s choice. This money is then paid out to you when you become a pensioner. The individual must pay 2,5% of the income towards the pension every year, a maximum of 8344 SEK in 2006 (calculated based upon the maximum one can earn for pensions in 2006, 333 750 SEK). If the individual is born between 1938-1953 it will be somewhat different. This is because the system has been changed and they will be in-between. The future pension is dependent upon the return of the funds in which one has invested. Even small differences have a large effect from a long-term perspective and studies have shown that between 0-30% of the pension comes from the PPM funds. (Försäkringskassan, Premiepension, 2006)
To be as beneficial to the public as possible, PPM have agreements with the specific fund companies to have a lower fee than normal which is enforced by the government. One can also switch funds without cost12 within the system. (PPM, Avgifter, 2006)

Fund fees

There are three commonly used fees for funds in Sweden. These fees are administration fees, buying fees and selling fees. There are also performance fees which are relatively rare in Swedish mutual equity funds.

Administration fee

The most common fee is the administration fee. It is supposed to cover the cost of the administration of the fund, as well as the cost of the staffing, counselling, information distribution, and so on. The administration fee differs between different fund companies, since it matters in which branch the funds are invested, and also, for example, if counselling is included. (Fondbolagens förening, fakta om fonder och konkurrens, 2006)
From an international perspective, Sweden has relatively low fees, and it is unique in the sense that all fees are made public in their annual report. In 2004, Sweden had the lowest unweighted total expence ratio (TER) in the whole of Europe for mutual equity funds that were actively administrated, as well as the third lowest weighted13 TER on the continent. However, it is the unweighted TER that is of interest to the investor. (Fondbolagens före-ning, fakta om fonder och konkurrens, 2006)

Buying, selling and performance fee

Buying and selling fees are charged when one either buys or sells a fund. Performance fee, on the other hand, is a fee that is charged, for example, quarterly or yearly as a percentage of the over-performance. Over-performance is measured according to how a fund performs relative to a benchmark. The performance fee is a relatively rare fee in the Swedish mutual equity market and may act as an incentive for the fund administrator to perform better. (Morningstar, Ordlista, 2006)

Capital Gain Tax

The capital gain tax is just as it sounds; a tax on the gain from an asset. It is taxed as a percentage of the capital gained; currently 30% in Sweden. This tax is charged not only when selling the fund, but also when trading it.
It has been argued by Konkurrensverket that the capital gain tax hinders competition in the fund market. It acts as a kind of ‘lock-in’ mechanism which makes the investors less likely to change funds. Due to this, Konkurrensverket has suggested that the capital gain tax be ‘moved’ to the final sale date. (Konkurrensverket, Konkurrens i Sverige 2005, 2005)
This ‘lock-in’ mechanism was confirmed in a survey done by SIFO Research International14 in 2005. They found that 36% of people taking the survey would change funds more often if the capital gain tax was moved as suggested by the Konkurrensverket. (Fonbolagens förening, Var 3:e fondsparare skulle byta fonder om uppskov infördes, 2006)

Theoretical framework

A fund is constituted of several different assets and, therefore, is a form of asset portfolio. The fund administrator’s task is to manage these assets in the best possible way. With portfolio management, the administrator tries to obtain the highest possible return with the lowest possible risk.
The first section, 3.1, deals with the portfolio theory and the Capital Asset Pricing Model (CAPM). Section 3.2 continues with the risk-adjusted performance ratios and considers the Sharpe ratio.

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Portfolio Theory and Capital Asset Pricing Model

The portfolio theory was first developed by Markowitz (1952). In this article, he showed how one could acquire a higher return in a portfolio of stocks than in an individual stock, the former also with a lower risk. This article is the foundation of all investments techniques we have today. Markowitz (1991) says, “My work on portfolio theory considers how an optimizing investor would behave, whereas the work by Sharpe and Lintner on the CAPM is concerned with economic equilibrium assuming all investors optimize in the particular manner I proposed.” (Markowitz, 1991, p. 469) From the work of Markowitz, the Modern Portfolio Theory was developed by authors like Sharpe, Lintner, and Mossin, among others. These authors have independently brought forward evidence of the relationship between expected returns and the risk. Therefore this model is often also called the Sharpe-Lintner-Mossin capital asset pricing model. (Elton & Gruber, 1995)
In this theory the portfolio has two risks; systematic risk (often called market risk) and unsystematic risk (also known as specific risk). The thought behind this is that the investor can diversify the portfolio in such a way as to eliminate the unsystematic risk; one can ‘spread out’ the risk enough for it not to matter. The systematic risk, on the other hand, is impossible to diversify away, and it is also for this risk that investors are expected to demand a higher return.
The CAPM model attempts to depict the general equilibrium of the relationship between expected returns and risk. This is the most basic model and it requires numerous assumptions. When completed, it is a simplistic and understandable model for the capital markets. However, the various assumptions used in the model also make it unreliable and unsuitable for prediction of the market situation today and how one should invest. (Elton & Gruber, 1995)
In figure 3.1, one can see the expected return on the y-axis and the standard deviation as risk on the x-axis. The risk-free rate is given by the capital market line (CML) which is a straight line and the straightness of the line will not change as the market risk changes. (Alexander, Sharpe & Bailey, 2001)
Point M, where the efficient frontier is tangent to the CML, is the most efficient point, in terms of risk and return, in the market. It is where every investor wants to invest and if all assumptions of this model would be fulfilled, this would be a stable equilibrium. The second most efficient investment is every point on the CML because here one can diversify away the unsystematic risk. (Alexander et al., 2001)
When the assumptions are fulfilled and every investor holds the market portfolio, they are only interested in the market risk. The market risk is the only thing that will affect their expected return through the slope of the capital market line. The slope of the capital market line is affected by all the assets in the market. When a high risk asset (high standard deviation) enters the market, the effect on the capital market line is greater than if an asset with a small risk would enter. Basically, it is dependent on the assets covariance to the market portfolio. These riskier assets must logically then yield a greater return to appeal the investors (Alexander et al., 2001).

Risk-adjusted Performance and the Sharpe ratio

There are three different risk-adjusted performance measures that are commonly used; Sharpe index, Jensen’s alpha and Treynor index.
Jensen’s Alpha compares the average return with the expected return according to the CAPM model (Jensen, 1968). The Treynor index is different from the Sharpe ratio in the sense that the Treynor (1965) index is based on systematic risk, while the Sharpe (1966) ratio is based on the total risk of the fund (Alexander et al. 2001).
However, the Sharp ratio will be used in this paper because it is probably the most well-known risk measure used in the industry.
The Sharpe ratio, also called the reward-to-variability ratio, is a ratio that tells the investor how much return a fund gives compared to the risk it has (Simons, 1998). The ratio, named after William Sharpe (1966), uses the standard deviation of portfolio returns as the total risk measure.
The Sharpe ratio is based on the trade-off between risk and return. The higher the ratio, the more the fund gives in return per risk. This means that any investor, regardless of how risk tolerant he or she is, should invest in the fund with the best combination of risk and return. That is the most ‘efficient’ fund (Simons, 1998).
The Sharpe ratio is most useful for investors who are investing all their money in one fund. Simons (1998) claims that, if CAPM explained previously holds, “then the market portfolio is, in fact, the portfolio with the highest Sharpe ratio” (Simons, 1998, p. 45).
The Sharpe ratio should be used and compared for funds that are on the same market, otherwise it may be misleading. This is because it does not take correlations between funds returns into consideration. How high the Sharpe index is varies based upon which market the fund focuses. (Simons, 1998).

Table of contents :

1 Introduction
2 Background
2.1 Risk and Return
2.2 Banks
2.3 PPM
2.4 Fund fees
2.5 Capital Gain Tax
3 Theoretical framework
3.1 Portfolio Theory and Capital Asset Pricing Model
3.2 Risk-adjusted Performance and the Sharpe ratio
4 Empirical Analysis
4.1 Limitations
4.2 Data
4.3 Method
4.4 Result
5 Discussion
5.1 Regression 1
5.2 Regression 2
5.3 Regression 3
5.4 Regression 4
5.5 Previous research and the critique on banks
5.6 Caveats
6 Conclusion
6.1 Further Studies


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