Session 6&amp;7 - Portfolio Theory Background Reading_2010

Session 6&7 - Portfolio Theory Background Reading_2010...

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S6 & S7: Portfolio Theory – Background Reading 1 The Markowitz Portfolio Theory Objectives: discuss the ranking and selection of portfolios of risky assets discuss the allocation of funds between the optimal portfolio of risky assets and the risk-free asset Learning Outcomes: compute the expected return and risk of i) a portfolio of risky assets, ii) a balanced portfolio that combine risk free lending/borrowing with the portfolio of risky assets determine the composition of i) an efficient portfolio ii) a minimum variance portfolio iii) the optimal portfolio of risky assets iv) the optimal balanced portfolio

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S6 & S7: Portfolio Theory – Background Reading 2 What is Portfolio Theory? Portfolio theory is about the choice of assets to be included in a portfolio and allocation of funds among the selected assets with an aim to provide investors the best combination of expected return and risk . Regarding assets, there are two main categories: risky assets with uncertain returns such as stocks and bonds risk free assets with certain returns such as bank bills, treasury notes or zero coupon bonds issued by governments with maturities that match the investors’ holding period, Regarding the choice of assets for example, Should investors avoid very risky assets / markets with large variations in returns? Between two risky assets with very similar return patterns such as Qantas and Virgin Blue, should investors include both in the portfolio? Regarding the allocation of funds for example, how much money should investors spend on each risky assets included in the portfolio? borrow to invest or set aside for risk free lending?
S6 & S7: Portfolio Theory – Background Reading 3 Portfolio Analysis – Measuring Expected Portfolio Return Consider a portfolio that is made up of two risky assets: BHP: \$2000 + CBA: \$3000 = \$5000 The expected year-end values of the stocks are: BHP: \$2500 + CBA: \$3300 = \$5800 Common sense approach to compute E(R P ), the expected return on the portfolio: E(R P ) = (2500 + 3300)/(2000 + 3000) – 1 = 16% p.a. Alternative approach: Portfolio weights: w BHP = 2000/5000 = 0.4 w CBA = 3000/5000 = 0.6 Asset Expected return: E(r BHP ) = 2500/2000-1 = 25% E(r CBA ) = 3300/3000-1 = 10%  i n i i P r E w R E 1 where w i is the proportion of funds allocated to the i th asset and E ( r i ) is the expected return on the i th asset. Thus E(R P ) = 0.4 x 25% + 0.6 x 10% = 16% p.a.

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S6 & S7: Portfolio Theory – Background Reading 4 Portfolio Analysis – Criterion of Risk Measurement The risk of a portfolio containing n assets, should measure the degree of uncertainty in achieving the expected return and this is best reflected by the standard deviation of returns of the portfolio, P . The larger the standard deviation, the riskier is the asset and the larger is the range of possible outcome around the mean (i.e., the expected return). Thus investors would be less certain of the likelihood that the expected return will eventuate.
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This note was uploaded on 06/12/2011 for the course ASB 1001,2522, taught by Professor Nicole during the One '09 term at University of New South Wales.

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Session 6&7 - Portfolio Theory Background Reading_2010...

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