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5%20-%20Portfolio%20Theory - BANK 3004 Portfolio and Fund...

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BANK 3004 Portfolio and Fund Management Page 1 of 7 Topic 5 Portfolio Theory © H. Bassan, 2009 Topic Overview In this topic, we consider how the composition of a risky portfolio may best be determined. That is, we will effectively consider the optimal trade-off between risk and expected return. The construction of optimal portfolios is based on the organising principle of modern portfolio theory efficient diversification, which maintains that any risk-averse investor will search for the highest expected return for any level of portfolio risk. We obtain key insights into both the investment process and the benefits of diversification based on a model of portfolio selection, first published in 1952 by Harry Markowitz, a 1990 Nobel Prize winner. We start our journey by considering the capital allocation decision how much of a portfolio to place in safe but low return money market securities versus risky but higher return assets (such as shares). That is, we ask how an investor decides how much to invest in the risky asset as compared to the risk-free asset. We take the composition of “the risky asset” as given firs t and obtain the risk-return combinations for a portfolio with a risky asset and a risk- free asset. The individual investor’s portfolio choice is based on the risk averseness of the investor measured using a utility formula. Then, we examine how to construct the efficient frontier (representing a set of portfolios that minimise portfolio risk for each level of expected return). Finally, the optimal risky portfolio an investor’s best combination of risky assets and risk -free asset and its construction are investigated. Since we will now be interested in the risk and expected return combinations for portfolios, we should be able to calculate and understand the meaning of standard deviation and return as well as covariance and correlation coefficients. We have already considered these measures, as relevant, for individual securities as well as portfolios in Topic 2. A review of that topic is appropriate now. Learning Objectives After studying this topic, you should be able to: 1. Calculate the risk and return statistics for portfolios (a review of Topic 2). 2. Explain the concept of utility and its link with risk aversion. 3. Explain the capital allocation decision and its importance. 4. Explain the meaning and characteristics of the risk-free asset. 5. Compute and show graphically how to combine the risk-free asset and a portfolio of risky assets to obtain the investment opportunity set (capital allocation line). 6. Explain how and when diversification works. 7. Construct and explain the meaning of the efficient frontier and its importance. 8. Construct the optimal risky portfolio given an input list.
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