d. You should recognize that basing a decision solely on expected returns is appropriate only for risk-neutral individuals. Because your client, like virtually everyone, is risk averse, the riskiness of each alternative is an important aspect of the decision. One possible measure of risk is the standard deviation of returns. (1.) Calculate the standard deviation for each alternative. T-Bills Alta Inds. Repo Men American Foam Market Port. Standard Deviation 0% 21.9% (2.) What type of risk is measured by the standard deviation? Price-fluctuations of a given asset. e. Suppose you suddenly remembered that the coefficient of variation (CV) is generally regarded as being a better measure of stand-alone risk than the standard deviation when the alternatives being considered have widely differing expected returns. Calculate the missing CVs, and fill in the blanks on the row for CV. Does the CV produce the same risk rankings as the standard deviation? T-Bills Alta Inds. Repo Men American Foam Market Port. CV 0.00 Rankings Expected Return Standard Deviation CV % Investment % Investment % Investment 8.00% T-Bills 0.00% T-Bills 0.00 T-Bills f. Suppose you created a 2-stock portfolio by investing $50,000 in Alta Industries and $50,000 in Repo Men. (1.) Calculate the expected return, Standard deviation, Coefficient of variation (CVp) for this portfolio. (2.) How does the risk of this 2-stock portfolio compare with the risk of the individual stocks if they were held in isolation? PORTFOLIO RETURNS The expected return on a portfolio is simply a weighted average of the expected returns of the individual assets in the portfolio. Consider the following portfolio. Portfolio weight Expected Return Stock Estimate Portfolio Return Alta Inds. 0.5 17.4% Recession 3.00% Repo Men 0.5 1.7% Below Avg. 6.35% Average 10.00% rp 9.6% Above Average 12.50% Standard Dev. 3.3% Boom 15.00% CV 0.35 g. Suppose an investor starts with a portfolio consisting of one randomly selected stock. What would happen (1) to the risk and (2) to the expected return of the portfolio as more and more randomly selected stocks were added to the portfolio? What is the implication for investors? Draw a graph of the two portfolios to illustrate your answer. PORTFOLIO RISK Perfect Negative Correlation Stock W Stock M Portfolio WM Year Returns Returns (Equally weighted avg.) 2006 40% -10% 15% 2007 -10% 40% 15% 2008 35% -5% 15% 2009 -5% 35% 15% 2010 15% 15% 15% Avg return 15% 15% 15% Std deviation 22.64% 22.64% 0.00% Correlation Coefficient -1.00 These two stocks are perfectly negatively correlated--when one goes up, the other goes down by the same amount. We could use Excel's correlation function to find the correlation, but when exact positive or negative correlation occurs, an error message is given. We demonstrate correlation in a later section. Perfect Positive Correlation. Now suppose the stocks were perfectly positively correlated, as in the following example: Stock M Stock M' Year Returns Returns Portfolio MM' 2006 -10% -10% -10% 2007 40% 40% 40% 2008 -5% -5% -5% 2009 35% 35% 35% 2010 15% 15% 15% Average return 15% 15% 15% Standard deviation 22.64% 22.64% 22.64% Correlation Coefficient 1.00 With perfect positive correlation, the portfolio is exactly as risky as the individual stocks. Partial Correlation. Now suppose the stocks are positively but not perfectly so, with the following returns. What is the portfolio's expected return, standard deviation, and correlation coefficient? Stock W Stock Y Year Returns Returns Portfolio WY 2006 40% 28% 34% 2007 -10% 20% 5% 2008 35% 41% 38% 2009 -5% -17% -11% 2010 15% 3% 9% Average return 15% 15% 15% Standard deviation 22.64% 22.57% 20.63% Correlation coefficient 0.67 Here the portfolio is less risky than the individual stocks contained in it. We found the correlation coefficient by using Excel's "CORREL" function. Click the wizard, then Statistical, then CORREL, and then use the mouse to select the ranges for stocks W and Y's returns. The correlation here is about what we would expect for two randomly selected stocks. Stocks in the same industry would tend to be more highly correlated than stocks in different industries. Adding more stocks to a portfolio The standard deviation of the portfolio would decrease because the stocks being added are not perfectly correlated. The expected return of the portfolio would remain relatively constant. h. (1.) Should portfolio effects impact the way investors think about the risk of individual stocks? (2.) If you decided to hold a 1-stock portfolio and consequently were exposed to more risk than diversified investors, could you expect to be compensated for all of your risk; that is, could you earn a risk premium on that part of your risk that you could have eliminated by diversifying? Market Risk The part of a security's stand alone risk that cannot be diversified away. Stand-Alone Risk = Market Risk + Diversifiable Risk Diversifiable Risk The part of a security's stand alone risk that can be diversified away. i. How is market risk measured for individual securities? How are beta coefficients calculated