1. 1 Investors are concerned with two principal properties inherent in securities: The return that can be expected from holding a security. The risk i.e. the return that is achieved will be less than the return that was expected. Investors want to maximize expected returns subject to their tolerance risk. Basics: Risk and Return

2. 2 Realized returns are after the fact return that was earned. It is a historical data. = Realized Return generated by the ith stock in time period t. Realized Return Vs Expected Return

3. 3 Expected Return on the other hand is our expectation from future. It is the return from an asset that investors anticipate they will earn over future period. It is a predicted return. It may or may not occur. = Expected Return on asset i = Probability of ith state to occur. = Expected Return for the ith stock

4. 4 Arithmetic Mean Vs Geometric Mean Arithmetic Mean The arithmetic average, customarily designated by the symbol X-bar ( ) or the sum of each the values being considered divided by the total number of values.

5. 5 Geometric Mean The geometric average return measures compound, cumulative returns over time. It is used in investments to reflect the realized change in wealth over multiple periods. The geometric average is defined as the nth root of the product resulting from multiplying a series of returns together where: R = total return n = number of periods

6. 6 RISK (Variability in Returns) Systematic RiskUnsystematic Risk

7. 7 Measurement of Risk Standard Deviation The formula for Expected (ex-ante) Where n = a possible outcome X = the expected outcome. P = the probability (or likelihood) of the difference between n and X occurring.

8. 8 Historical (ex-post) = = Realized Return generated by the ith stock in time period t. = Average Return of ith stock.

9. 9 CV = The coefficient of variation shows the risk per unit of return, and it provides a more meaningful basis for comparison when the expected returns on two alternatives are not the same. COEFFICIENT OF VARIATION

10. 10 COEFFICIENT OF VARIATION ProjectsExpected ReturnRiskCV X60%15%25.00% Y8%3%37.50% If we calculate the Coefficient of Variation here, then we find Project Y actually has more risk per unit of return than Project X, in spite of the fact that X's stan­dard deviation is larger. Therefore, even though Project Y has the lower standard deviation, according to the coefficient of variation it is riskier than Project X.

11. 11 Beta is a measure of the systematic risk of a security that cannot be avoided through diversification. Therefore, Beta measures non- diversifiable risk. BETA where = Beta of security with market = Covariance between security and market = Variance of market returns