CHAPTER THREE: INTRODUCTION TO PORTFOLIO THEORY pps

CHAPTER THREE: INTRODUCTION TO PORTFOLIO THEORY 06/08/2011 1 8 - 2 Portfolios • A portfolio is a collection of different securities such as stocks and bonds, that are combined and considered a single asset • The risk-return characteristics of the portfolio is demonstrably different than the characteristics of the assets that make up that portfolio, especially with regard to risk. • Combining different securities into portfolios is done to achieve diversification. 06/08/2011 8 - 3 Diversification Diversification has two faces: 1. Diversification results in an overall reduction in portfolio risk (return volatility over time) with little sacrifice in returns, and 2. Diversification helps to immunize the portfolio from potentially catastrophic events such as the outright failure of one of the constituent investments. (If only one investment is held, and the issuing firm goes bankrupt, the entire portfolio value and returns are lost. If a portfolio is made up of many different investments, the outright failure of one is more than likely to be offset by gains on others, helping to make the portfolio immune to such events.) 06/08/2011 8 - 4 Expected Return of a Portfolio Modern Portfolio Theory The Expected Return on a Portfolio is simply the weighted average of the returns of the individual assets that make up the portfolio: The portfolio weight of a particular security is the percentage of the portfolio’s total value that is invested in that security. )( n 1i    iip ERwER [8-9] 06/08/2011 8 - 5 Expected Return of a Portfolio Example Portfolio value = $2,000 + $5,000 = $7,000 r A = 14%, r B = 6%, w A = weight of security A = $2,000 / $7,000 = 28.6% w B = weight of security B = $5,000 / $7,000 = (1-28.6%)= 71.4% %288.8%284.4%004.4 ) %6(.714)%14(.286)( n 1i     iip ERwER 06/08/2011 8 - 6 Range of Returns in a Two Asset Portfolio In a two asset portfolio, simply by changing the weight of the constituent assets, different portfolio returns can be achieved. Because the expected return on the portfolio is a simple weighted average of the individual returns of the assets, you can achieve portfolio returns bounded by the highest and the lowest individual asset returns. 06/08/2011 8 - 7 Modern Portfolio Theory - MPT • Prior to the establishment of Modern Portfolio Theory (MPT), most people only focused upon investment returns…they ignored risk. • With MPT, investors had a tool that they could use to dramatically reduce the risk of the portfolio without a significant reduction in the expected return of the portfolio. 06/08/2011 8 - 8 Expected Return and Risk For Portfolios Standard Deviation of a Two-Asset Portfolio using Covariance ))()((2)()()()( , 2222 BABABBAAp COVwwww   [8-11] Risk of Asset A adjusted for weight in the portfolio Risk of Asset B adjusted for weight in the portfolio Factor to take into account comovement of returns. This factor can be negative. 06/08/2011 8 - 9 Expected Return and Risk For Portfolios Standard Deviation of a Two-Asset Portfolio using Correlation Coefficient ))()()()((2)()()()( , 2222 BABABABBAAp wwww   [8-15] Factor that takes into account the degree of comovement of returns. It can have a negative value if correlation is negative. 06/08/2011 8 - 10 Grouping Individual Assets into Portfolios • The riskiness of a portfolio that is made of different risky assets is a function of three different factors: – the riskiness of the individual assets that make up the portfolio – the relative weights of the assets in the portfolio – the degree of comovement of returns of the assets making up the portfolio • The standard deviation of a two-asset portfolio may be measured using the Markowitz model: BABABABBAAp wwww  , 2222 2 06/08/2011 [...]... Number of Stocks in Portfolio 06/08/2011 8 - 25 250 300 Diversification Domestic Diversification Table 8-3 Monthly Canadian Stock Portfolio Returns, January 1985 to December 1997 Number of Stocks in Portfolio Average Monthly Portfolio Return (%) Standard Deviation of Average Monthly Portfolio Return (%) Ratio of Portfolio Standard Deviation to Standard Deviation of a Single Stock Percentage of Total Achievable... Risk, Return and Portfolio Theory 06/08/2011 23 Diversification • We have demonstrated that risk of a portfolio can be reduced by spreading the value of the portfolio across, two, three, four or more assets • The key to efficient diversification is to choose assets whose returns are less than perfectly positively correlated • Even with random or naïve diversification, risk of the portfolio can be reduced... Canadian Sto cks: Ho w M uch is Eno ugh?" Canadian Investment Review (Fall 1 999), Table 1 06/08/2011 8 - 26 Total Risk of an Individual Asset Equals the Sum of Market and Unique Risk • Standard Deviation (%) Average Portfolio Risk Diversifiable (unique) risk [8-19] Nondiversifiable (systematic) risk Number of Stocks in Portfolio [8-19] 06/08/2011 This graph illustrates that total risk of a stock is... dominated by superior portfolios that line on the line above E D Standard Deviation (%) 06/08/2011 variance portfolio (lowest risk combination) 8 - 20 Efficient Frontier The Two-Asset Portfolio Combinations 8 - 10 FIGURE Expected Return % A B C E The actual choice will depend on her/his risk preferences D Standard Deviation (%) 06/08/2011 Rational, risk averse investors will only want to hold portfolios such... • As the portfolio is divided across more and more securities, the risk of the portfolio falls rapidly at first, until a point is reached where, further division of the portfolio does not result in a reduction in risk • Going beyond this point is known as superfluous diversification 06/08/2011 8 - 24 Diversification Domestic Diversification 8 - 11 FIGURE Average Portfolio Risk January 1985 to December... because it affects the degree to which diversification can be achieved using various assets • Theoretically, if two assets returns are perfectly positively correlated, it is possible to build a riskless portfolio with a return that is greater than the risk-free rate 06/08/2011 8 - 15 Diversification of a Two Asset Portfolio Demonstrated Graphically The Effect of Correlation on Portfolio Risk: The Two-Asset... portfolio risk (σ) and the correlation coefficient – The slope is not linear a significant amount of diversification is possible with assets with no correlation (it is not necessary, nor is it possible to find, perfectly negatively correlated securities in the real world) – With perfect negative correlation, the variability of portfolio returns is reduced to nearly zero 06/08/2011 8 - 17 Expected Portfolio. .. economic ‘system’) and unique, companyspecific risk that is eliminated from the portfolio through diversification Total risk  Market (systemati risk  Unique (non - systematic) risk c) 8 - 27 International Diversification • Clearly, diversification adds value to a portfolio by reducing risk while not reducing the return on the portfolio significantly • Most of the benefits of diversification can be achieved... is expanded to include investments beyond the domestic capital markets, additional risk reduction is possible (See Figure 8 -12 found on the following slide.) 06/08/2011 8 - 28 Diversification International Diversification 8 - 12 FIGURE 100 Percent risk 80 60 40 U.S stocks 20 International stocks 11.7 0 0 10 20 30 Number of Stocks 06/08/2011 8 - 29 40 50 60 Summary and Conclusions In this chapter you... Summary and Conclusions In this chapter you have learned: – How to measure different types of returns – How to calculate the standard deviation and interpret its meaning – How to measure returns and risk of portfolios and the importance of correlation in the diversification process – How the efficient frontier is that set of achievable portfolios that offer the highest rate of return for a given level . CHAPTER THREE: INTRODUCTION TO PORTFOLIO THEORY 06/08/2011 1 8 - 2 Portfolios • A portfolio is a collection of different securities such as stocks and bonds, that are. the portfolio Factor to take into account comovement of returns. This factor can be negative. 06/08/2011 8 - 9 Expected Return and Risk For Portfolios Standard Deviation of a Two-Asset Portfolio. achieve portfolio returns bounded by the highest and the lowest individual asset returns. 06/08/2011 8 - 7 Modern Portfolio Theory - MPT • Prior to the establishment of Modern Portfolio Theory