Abstract The objective of this work is to optimize portfolios and to evaluate their performances. CAPM and APT models are important models that use statistical measures in order to achieve the objective. Throughout this work we improved our knowledge regarding portfolio theory and its application. Literature and Data For information we used the book Investments and Portfolio Management by Bodie, Kane and Marcus as well as material given during the lectures. We used Microsoft Excel to elaborate data and the sources were given during the labs.
Introduction: The goal is to explore and compare different methods such as CAPM, APT and portfolio theory. Methodology: In this assignment we exploit theories such as the Portfolio Theory, Mean-Variance Theory and the CAPM. So, we are assuming all the hypotheses that these theories assume. Among all, we are assuming that average return is a good measure of return and the risk could be calculated with the standard deviation. When we use CAPM, we are implying that the only risk is the Beta with the market (systematic risk) because we can reduce the risk of each asset to zero, with a well-diversified portfolio. In APT, we assume there are other important risks related to other factors. So, the main difference between APT and CAPM is that while CAPM only considers the market as the factor, APT considers more factors. There are other important differences, but these are out of the scope of this work. a) The assets we choose are all listed at the Stockholm Stock Exchange
(OMX30) and are the following: ABB, Assa Abloy, Electrolux, Ericsson, H&M, Kinnevik, Nokia, SEB, SCA and Volvo. Most of these companies are industrial manufacturing companies with a long history. Kinnevik (investment company) and SEB (banking and finance) are in the financial sector. H&M is a retail-clothing company. We used monthly returns during 5 years, from January 2006 to December 2010. 2
We choose ten companies with following average return, variance and
It is easy to notice that ABB and Electrolux have the highest average
returns while Nokia has the lowest return. Ericsson and Nokia have a negative average return. We use standard deviation as a measure of risk, according to mean-variance theory. A high standard deviation implies a high deviation from the average return; a low standard deviation implies a low deviation from the average return. SEB and Volvo have the highest standard deviation, while H&M has the lowest. Firstly, we created an evenly weighted portfolio. The portfolio has the following features:
Average Return is 0,6%, with a standard deviation of 6%. It seems to be a non-attractive portfolio, because of the very low return with a high risk. In order to compare portfolios we could use the Sharpe Ratio, which is a performance measurement. It is calculated as subtracting the risk free rate from the portfolio return and dividing the result by the standard deviation. We use the average return of 3-months T-Bills to compute the risk free rate.
This is a relative measure, so we should compare it with the Sharpe Ratio of a different weighted portfolio, in order to see if we get a better return to risk. By multiplying the monthly average return by 12, we obtain the following annual returns:
The following graph shows the stocks´ performances over this 5-year period compared to the OMX (a proxy for the Swedish Market).
We choose to observe a portfolio composed by Kinnevik and Volvo. We
choose these companies because the firms are operating in two different sectors. Volvo is an international company, which produces trucks and equipment while Kinnevik is an investment company. Average Returns, Standard Deviations and Covariance of these companies are the following:
Covariance between two or more assets is very important because it allows us to get a diversification effect. Covariance is the...