Explain how expected return and returns variance are used to describe the return distribution for a security or portfolio of securities

Calculating Return on Investment on a single stock or portfolio of Stocks: Definition: Return on investment on a single or portfolio of stocks is the increase in total value of investment over a defined period. Return on Investment = ({Total Return Value of Security at end of Maturity + Dividend}/{Initial value of Investment in Security} )– 1 Formula:The above formula is true for Perfect Markets. Perfect Markets: Perfect Markets are those that have the following characteristics All investors have same information about securities There is no taxes on gaining wealth through sale of securities No restrictions on buying and selling of securities Purchasing and selling of securities do not affect the market price of securities No costs in buying and selling of securities Note: Perfect Markets is only in theory and can never happen in real scenario where securities are always considered risky assets How Risk are Described: Risk can be described in terms of the probability distribution of returns over a period If returns follow normal distribution, risk can be described in terms of expected mean return and the variance or standard deviation of returns FRM AIM: Explain how expected return and returns variance are used to describe the return distribution for a security or portfolio of securities - Part II Expected Return: Average of return over periods E(Rp)= sum_{0}^{n}WiE(Ri)  Standard Deviation: Also known as volatility Describes the spread of returns over the many periods Larger the standard deviation, greater the risk about the returns Denoted by Sigma Normal Distribution: Can be used to describe the probabilities of outcomes of returns using just the mean and the standard deviation Used for calculate returns distribution in many applications Used to determine the probability of returns above or below a certain level of return Cumulative z-table is used to calculate the probability that a return will be below or above a predefined level