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Chapter 2

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FIN 501
Edward Blinder

Chapter 2: Diversification and Asset Allocation Diversification is important because portfolios with many investments usually produce a more consistent and stable total return than portfolios with just one investment When you own many stocks, even if some of them decline in price, others are likely to increase in price (or stay at the same price) We assume that investors prefer more return to less return and second, we assume that investors prefer less risk to more risk 2.1 Expected Returns and Variances: Expected Return: average return on a risky asset expected in the future - Two states of economy = means that there are two possible outcomes - Expected Return on a security or other asset = the sum of the possible returns multiplied by their probabilities - Risk Premium = Expected Return Risk-free Rate = E ( - Using our projected returns, we can calculate the projected or expected risk premium as the difference between the expected return on a risky investment and the certain return on a risk-free investment Calculating the Variance: first determine the squared deviations from the expected return. We then simply multiply each possible squared deviation by its probability. Next we add these up, and the result is the variance - In chapter 1, we estimated the average return and the variance based on historical events and on some actual events - Here, we have projected future returns and their associated probabilities, so this information with which we must work 2.2 Portfolios: Portfolios: group of assets such as stocks and bonds held by an investor Investors tend to own more than just a single stock, bond, or other asset Portfolio return and portfolio risk are of obvious relevance Portfolio Weights: percentage of a portfolios total value invested in a particular asset - There are many equivalent ways of describing a portfolio - The most convenient approach is to list the percentages of the total portfolios value that are invested in each portfolio asset [call these percentages the portfolio weights] - Ex: if we have $50 in one asset and $150 in another, then out total portfolio is worth $200. The percentage of our portfolio in the first asset is $50/$200 = 0.25. The percentage in the second asset is $150/$200 = 0.75. The weights sum up to 1.00 since all of our money is invested somewhere. Portfolio Expected Returns: - This method of calculating the expected return on a portfolio works no matter how many assets there are in the portfolio - Suppose we had n assets in our portfolio, where n is any number at all. If we let stand for the percentage of our money in Asset i, then the expected return is: ( ) ( ( ( - The expected return on a portfolio is a straightforward combination of the expected returns on the assets in that portfolio Portfolio Variance: - Note that the return is the same no matter if a recession or a boom occurs - This portfolio has a zero variance and no risk!- This is a nice bit of a financial alchemy. We take 2 risky assets and by mixing them just right, we create a riskless portfolio. - Ex: Suppose putting 2/11 (18%) in Net-cap and the other 9/11 (82%) in J-mart (page 41) 2.3 Diversification and Portfolio Risk: The Effect of Diversification: Another Lesson from Market History - Copp and Cleary (see figure 2.1) examined diversification characteristics of the Canadian portfolios by forming portfolios of 222 randomly chosen Canadian stocks - Table 2.7: Portfolio Standard Deviation = illustrates their results of standard deviation of monthly portfolio returns - In column 3 of Table 2.7 (page 43) we see that the standard deviation for a portfolio of one security is 13.47%. If you randomly select a stock listen on the Toronto Stock Exchange and put all your money into it, your standard deviation of return would typically have been about 13% per month - Obviously, such a strategy has significant risk! If you were to randomly select 2 securities and put half your money in each, your average standard deviation would have been 11% - The important thing to notice in Table 2.7 is that the standard deviation declines as the number of securities is increased - The nearby Investment Updates box offers further historical perspective on the need for diversification [Figure 2.1: Portfolio Diversification page 44] The Principle of Diversification: - Figure 2.1: plotted the standard deviation of the return vs. the number of stocks in the portfolio - The benefit in terms of risk reduction from adding securities drops off as we add more and more - By the time we have 10 securities, most of the diversification effect is already realized, and by the time we get to 20 or so, there is little remaining benefit - In other words, the benefit of further diversification increases at a decreasing rate, so the law of diminishing returns applies here as it does in so many other places
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