PMT_StudyNotes_Extra - DRAFT CHAPTER 4 PORTFOLIO THEORY Chapter 4 discusses the theory behind modern portfolio management Essentially portfolio

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DRAFT 1 CHAPTER 4: PORTFOLIO THEORY Chapter 4 discusses the theory behind modern portfolio management. Essentially, portfolio managers construct investment portfolios by measuring a portfolio’s risks and returns. An understanding of the relationship between portfolio risk and correlation is critical to understanding modern portfolio theory. A grasp of variance, standard deviation, the Markowitz model, the risk-free rate, and the Capital Asset Pricing Model (CAPM) are also needed. Calculating Portfolio Returns The expected return of a portfolio is simply the weighted average of returns on individual assets within the portfolio, weighted by their proportionate share of the portfolio at the beginning of the measurement . Example 1: Oliver’s portfolio holds security A, which returned 12.0% and security B, which returned 15.0%. At the beginning of the year 70% was invested in security A and the remaining 30% was invested in security B. Calculate the return of Oliver’s portfolio over the year. R p = (.6x12%)+(.3x15%) = 12.9% Example 2: Oliver’s portfolio holds security A, which returned 12.0%, security B, which returned 15.0% and security C, which returned –5.0%. At the beginning of the year 45% was
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DRAFT 2 invested in security A, 25.0% in security B and the remaining 30% was invested in security C. Calculate the return of Oliver’s portfolio over the year. R p = (.45x12%)+(.25x15%)+(.3x(-5%)) = 7.65% Calculating Portfolio Risk While there may be different definitions of risk, one widely-used measure is called variance. Variance measures the variability of realized returns around an average level. The larger the variance the higher the risk in the portfolio. Variance is dependent on the way in which individual securities interact with each other. This interaction is known as covariance. Covariance essentially tells us whether or not two securities returns are correlated. Covariance measures by themselves do not provide an indication of the degree of correlation between two securities. As such, covariance is standardized by dividing covariance by the product of the standard deviation of two individual securities. This standardized measure is called the correlation coefficient . Example 3: Oliver’s portfolio holds security A, which returned 12.0% and security B, which returned 15.0%. At the beginning of the year 70% was invested in security A and the remaining 30% was invested in security B. Given a standard deviation of 10% for security A, 20% for security B and a correlation coefficient of 0.5 between the two securities, calculate the portfolio variance. AB B A B A B B A A p w w w w ρ σ σ σ σ σ 2 2 2 2 2 2 + + = (1)
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DRAFT 3 Portfolio Variance = (.7 2 x10 2 )+(.3 2 x20 2 )+(2x.7x.3x10x20x.5) = 127 Portfolio standard deviation is the square root of the portfolio variance. % 27 . 11 127 = = p σ (2) Equivalently: Portfolio Standard Deviation = (127) .5 =11.27% The above example is for a portfolio that consists of two assets. You will find an example of a three asset portfolio in the practice questions at the end of this chapter.
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This note was uploaded on 04/28/2010 for the course ECON FINC3017 taught by Professor Xelloss during the Spring '10 term at University of St Andrews.

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PMT_StudyNotes_Extra - DRAFT CHAPTER 4 PORTFOLIO THEORY Chapter 4 discusses the theory behind modern portfolio management Essentially portfolio

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