Portfolio Selection ProblemInvestment risk and returnHigher Riske Higher returnLower Risk - Lower ReturnMeasurement of return1. Single Period rate of returnHPR = where P1 = Ending price, P0 = Beginning Price and D1 = Cash dividendRupee return (R0) = 2. Multiple Period Returni. Without re-investment consideration, HPR = ii. With re-investment consideration, HPR = where R = re-investment rate of return3. Geometric Mean return () Multi- period (or compound) rate of return Geometric mean HPR gives elastic result as it considers reinvestment opportunityGM () = or, GM = [(1 + HPR1) (1 + HPR2).. (1 + HPRn) - 1Where, = the product4. Arithmetic Mean return(AM) ignores the reinvestment opportunity of fundsAM = =

Arithmetic mean HPR and Geometric mean HPR are different because1. Arithmetic mean doesnt consider time value of money but geometric mean consider the time value of money or re-investment concept2. AM and GM HPR will only be equal when the HPR are constant over the investment horizon.3. AM is suitable for one period or single period but GM is suitable for multi-period rate of return.4. AM HPR will be always greater than GM in case of variation of return.Expected rate of return, Mean rate of return and average rate of return (HPRj)If probability distribution is given, E(HPR) or = - If probability distribution isnt given, (Arithmetic mean)E(HPR) = Meaning of riskBusiness Risk: uncertain about the rate of return caused by nature of business. [ causes of business risk are uncertain about the firms sale and operating expenses]Financial risk: Risk related to firms capital structureLiquidity risk: related with the uncertainity created by the inability to sell the investment quickly for cashInterest rate risk: changes in the interest rate in marketManagerial risk: risk created due to different management policies decisionPurchasing power risk: Risk caused by inflationMeasurement of risk: Variance, standard deviation and coefficient of variation[variability of return / degree of risk]VarianceIf probability distribution of return is given,Step 1: Calculate the expected mean return, = - Step 2: Subtract the expected rate of return from each possible outcomes () to find deviation from Deviation = Step 3: Square of each deviation, multiply the result by the probability of occurrence for its related outcome and then sum their product to obtain the varianceVariance () = If probability distribution is not given,Step 1: Calculate the expected mean return,

Step 2: Subtract the expected rate of return from each possible outcome to find the deviation from Deviation: Step 3: Variance () = Standard deviation = Co-efficient of variations(CV)CVj = Measure of relative dispersion Used in comparing the risk and expected return of different assets Shows the risk per unit of return Provides basis for comparison[Higher the co-efficient of variation, higher the risk and vice-versa]It provides a meaningful basis for comparison when the expected return on two alternatives are not the same.