Risk and Return Note 1.docVIP

Expected Return: E(R) The expected return from investing in a security over some future holding period is an estimate of the future outcome of this security. Although the Expected Return is an estimate of an investor’s expectations of the future, it can be estimated using either ex ante (forward looking) or ex post (historical) data. If the expected return is equal to or greater than the required return, purchase the security. Regardless of how the individual returns are calculated, the Expected Return of a Portfolio is the weighted sum of the individual returns from the securities making up the portfolio: Ex ante expected return calculations are based on probabilities of the future states of nature and the expected return in each state of nature. Sum over all states of nature, the product of the probability of a state of nature and the return projected in that state. State Ps Rs Ps * Rs Good 30% 20% 0.3(0.2) Average 50% 15% +0.5(0.15) Poor 20% -4% +0.2(-0.04) 12.70% Ex post expected return calculations are based on historical data. Add the historical returns and then divide by the number of observations. Year Rt 2002 15% 2003 20% 2004 9% 2005 10% 2006 5% 11.80% Variance (Standard Deviation): σ2 (σ) Variance is a measure of the dispersion in outcomes around the expected value. It is used as an indication of the risk inherent in the security. Standard deviation is the square root of variance. Ex ante variance calculation: The expected return is subtracted from the return within each state of nature; this difference is then squared. Each squared difference is multiplied by the probability of the state of nature. These weighted squared terms are then summed together. State Ps Rs Ps * Rs (Rs – E(R))2 * Ps Good 30% 20% 0.3(0.2) 0.3(0.2-0.127)2 Average 50% 15% +0.5(0.15) +0.5(0.15-0.127)2 Poor 20% -4% +0.2(-0.04) +0.2(-0.04-0.127)2 12.70% 0.0074 8.63% Mean Variance Standard Deviation Ex post variance calculation: The average retu