# Finance 9

 computing returns Two ways to determine how much you have earned on each of your investments1. Dollar return2. Percentage return Dollar return the amount of profit or loss from an investment denoted in dollarsCapital gain or loss + Income (Ending value – beginning value) + value Percentage return find it more useful to characterize investment earnings as this so that we can easily compare one investment’s return to other alternative’s returns – The dollar return characterized as a percentage of money invested- Because it’s standardized, we can use % returns for almost any type of investment. average returns a measure summarizing the past performance of an investment- Use this to examine performance over timeAverage return = sum of all returns/ number of returns Average returns shown are more precisely called arithmetic average returns- These are appropriate for statistical analysis- However, they don’t accurately illustrate the historical performance of a stock or portfolio. geometric mean return the mean return computed by finding the equivalent return that is compounded for N periods Performance of asset classes • Historically, stocks have performed better than either bonds or cash• Annual variability defines risk. Volatility – financial theory suggests that investors should look at an investment’s historical return to assess how much uncertainty to expect in the future high variability = high degree of future uncertainty standard deviation a measure of past return volatility, or risk, of an investment total risk the volatility of an investment, which includes current portions of firm-specific risk and market risk. calculate… standard deviation as the square root of the variance, and this figure represents the securities or portfolios total risk. standard deviation computation starts with the average return over the periodPROCESS Larger SD indicates greater return volatility – or high risk- Although analysts and investors use a stock return’s standard deviation as an important and common measure of risk, its laborious to compute by hand. higher risk investments offer higher returns over time- But short-term fluctuations in the value of higher risk investments can be substantial. using S&P 500 index to look at two large firms – Have measures of total risk – SD – twice as large as the SD on the stock market returns.- Does not mean they are two of the most risky firms.- It means the differences in standard deviations between individual companies and entire market have more to do with diversification.- Owning 500 companies generates much less risk then just owning one. coefficient of variation (CoV) a measure of risk to reward (SD/average return) earned by an investment over a specific period of time. • Amount of risk per unit of return• Smaller CoV indicates a better risk-reward relationship portfolios a combination of investment assets held by an investor- Reduces many sources of stock risk diversification reduces risk. The process of putting money in different types of investments for the purpose of reducing the overall risk of the portfolio stock’s risk has two components 1. Risks that are both specific to that company and common to other companies in the same industry.2. General risk that all firms face based upon economic strength both domestically and globally. 1 We call this firm specific risk: the portion of total risk that is attributable to firm or industry factors. – Firm-specific risk can be reduced through diversification. 2 We call this market risk: the portion of total risk that is attributable to overall economic factorsTotal risk = firm-specific + market risk diversifiable risk another term for firm-specific risk- can reduce firm-specific risk by diversifying- If RadioShack announces lower-than-expected profits, its stock price will decline. But it won’t affect Mattel stock’s price. pooling the market risk can pool it by adding more stocks- provides offsetting, reduced firm specific risks overall- total risk falls rapidly as we add the first few stocks… then diminishes nondiversifiable risk another term for market risk modern portfolio theory A concept and procedure for combining securities into a portfolio to minimize risk.- Describes how to combine stocks to achieve the lowest total risk possible for a given expected return. AKA how to achieve the highest expected return for the desired risk level. optimal portfolio the best portfolio of securities for the investor’s level of risk aversion. dominating portfolios – We say one portfolio dominates the other if it has higher expected return for the same or less risk, or the same or higher expected return with lower risk.- Dominating portfolios appear higher and to the left in the figure. efficient portfolios the set of portfolios that have the max expected return for each level of risk- If we showed all efficient portfolios, they would appear as a line that connects the upper side of the bullet shape. efficient frontier the combination of all efficient portfolios. These dominate all other possible stock portfolios.- The shape of the efficient frontier implies that diminishing returns apply to risk-taking in the investment world. How does diversification work? If two stocks are subject to exactly the same kinds of events such that their returns always behave the same way over time, then we have no need to own both stocks. Pick the one that performs better. diversification comes when two stocks are subject to different kinds of events such that their returns differ over time.- combining stocks with similar characteristics does not provide much diversification and thus risk reduction the way that stocks co-move over time determines how much diversification and thus risk reduction we can achieve by combining them.- correlation correlation a measurement of the co-movement between two variables that ranges between -1 and +1. portfolio return comes directly form the returns of the portfolio securities and the proportion of the portfolio invested in each security.
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