Risk & Return Fundamentals

1. Risk & Return Fundamentals Risk: Risk and uncertainty are terms used to describe situations where the outcomes of decisions are not known with complete certainty. Risk is defined as the chance that the actual outcome will be unequal to the expected outcome. As a general proposition, the greater the chance of low returns, the greater the risk of the investment. Two important points must be remembered. • Some risk is present in any decision, and • Since risk cannot be avoided completely, the best strategy to account for its effect is to recognize it formally, measure as best as possible and then make choices based on decision rules that incorporate the risk measure.

2. Classification of risk: Systematic Risk: Risk that cannot be avoided or minimized and that is out of control of an individual or a business enterprise. Unsystematic Risk: Risk that cannot be avoided but can be minimized by making intellectual decision based on best judgment relying on relevant information and that is to some extent under the control of an individual or a business enterprise. Business Risk: Risk related to overall business activities of a particular business enterprise that is mostly out of control of that business enterprise. Financial Risk: Risk related to using of fund for forming and running business operations or making investments by a particular party that is under the control of that party.

3. Measures of Risk: Risk refers to the dispersion of a variable. It is commonly measured by the variance or the standard deviation. The variance of a probability distribution is the sum of the squares of the deviations of actual returns from the expected return, weighted by the associated probabilities. Standard Deviation – absolute measurement of total risk Coefficient of Variation - relative measurement of total risk Beta Coefficient - absolute measurement of systematic risk

4. Risk Preference: The three basic risk preference behaviors- Risk-Averse: The attitude toward risk in which an increased return would be required for an increase in risk. Risk-Indifferent: The attitude toward risk in which no change in return would be required for an increase in risk. Risk-Seeking: The attitude toward risk in which a decreased return would be accepted for an increase in risk.

5. Return: Percentage form of earnings from an investment or asset including normal income and capital gain or loss is called return. Return may be the following three types: Risk-free rate of return: Rate of return can be earned by making investment in government securities of a country is known as risk-free rate of return. Nominal rate of return: Rate of return calculated by ignoring existing level of inflation is known as nominal rate of return. Real rate of return: Rate of return determined by considering/adjusting existing level of inflation is known as real rate of return.

6. Calculating Expected Return for a Security: The expected return of a single security is the expected value of the weighted average of all possible return outcomes, where each outcomes is weighted by its respective probability of occurrence. It is calculated as- Where, = the expected return on a security = the ith possible return = the probability of the ith return = the number of possible returns

7. Calculating Risk for a Security: To calculate the total risk associated with the expected return of a security, the variance or the standard deviation is used. The variance and its square root, standard deviation, are measures of the spread or dispersion in the probability distribution; that is the key measure the dispersion of a random variable around its mean. The larger this dispersion, the larger the variance or standard deviation. Calculation of the variance or standard deviation- The variance of returns = The standard deviation of return =

8. Portfolio Return and Risk: When we analyze investment return and risk, we must be concerned with the total portfolio held by an investor. Individual security returns and risks are important, but it s the return and risk to the investor’s total portfolio that ultimately matters. Portfolio Expected Return: The expected return on any portfolio is easily calculated as a weighted average of the individual securities’ expected returns. The percentages of a portfolio’s total value that are invested in each portfolio assets are referred to as portfolio weights, which we will denote by w.

9. The expected return on any portfolio P can be calculated as Where, = the expected return on the portfolio = the portfolio weight for the ith security = 1.0 = the expected return on the ith security = the number of different securities in the portfolio

10. Example: consider a three stock portfolio consisting of stocks A, B and C with expected returns of 12%, 20% and 17%, respectively. Assume, that 50% of investable funds is invested in security A, 30% in B, and 20% in C. calculate the expected return of this portfolio. = 0.5 (12%) + 0.3 (20%) + 0.2 (17%) = 15.4% Regardless of the number of assets held in a portfolio, or the proportion of total investable funds placed in each asset, the expected return on the portfolio is always a weighted average of the expected returns for individual assets in the portfolio.

11. Portfolio Risk: The risk of the portfolio is measured by the variance (or standard deviation) of the portfolio’s return, exactly as in the case of each individual security. Typically, portfolio risk is stated in terms of standard deviation which is simply the square root of the variance. It is at this point that the modern portfolio theory emerge, which can be stated as follows: Although the expected return of a portfolio is a weighted average of its expected returns, portfolio risk (as measured by the variance or standard deviation) is not a weighted average of the risk of the individual securities in the portfolio. Symbolically. But

12. Modern Portfolio Theory (MPT): In the 1950s, Harry Markowitz, considered the father of modern portfolio theory (MPT), developed the basic portfolio principles that underline modern portfolio theory. MPT is a theory of portfolio selection. It is some times referred to as mean-variance optimization, because portfolios are built on the basis of optimizing the expected return-risk tradeoff.

13. Markowitz Portfolio Theory: Before Markowitz, investors dealt loosely with the concepts of return and risk. Investors have known intuitively for many years that it is smart to diversify; that is, not to “put all of your eggs in one basket”. Markowitz, however, was the first to develop the concept of portfolio diversification in a formal way- he quantified the concept of diversification. He showed quantitatively why and how portfolio diversification works to reduce the risk of a portfolio to an investors. Markowitz theory actually was developed to answer a basic question: Is the risk of portfolio equal to the sum of the risks of the individual securities comprising it?

14. Markowitz was the first to develop a specific measure of a portfolio risk and to derive the expected return and risk of a portfolio based on covariance relationships. Portfolio risk is not simply a weighted average of the individual security risks. Rather, we must account for the interrelationships among security returns in order to calculate portfolio risk, and in order to reduce portfolio risk to its minimum level for any given level of return. Reason behind it, poor performance by some securities may be offset by strong performance in other securities. So to develop an equation to calculate the risk of a portfolio as measured by the variance and standard deviation, we must account for two factors: • Weighted individual security risk • Weighted co movements between securities’ return.

15. Measuring Co movements in securities: Covariance is the absolute measure of the co movements between security returns used in the calculation of the of portfolio risk. We can easily illustrate how security returns move together by considering the correlation coefficient. The Correlation Coefficient: The correlation coefficient (pronounced “rho”) is a statistical measure of the relative co movements between security returns. It measure the extent to which the return on any two securities are related. It is a relative measure of association that is bounded by +1 and -1, with = +1.0 = perfect positive correlation = -1.0 = perfect negative correlation = 0.0 = zero correlation