Risk and Return Chapter 5

Objectives Understand the relationship between risk and return Define risk and return and show how to measure them by calculating expected return, standard deviation, and coefficient of variation. Discuss the different types of investor attitudes toward risk. Explain risk and return in a portfolio context, and distinguish between individual security and portfolio risk. Distinguish between avoidable ( unsystematic) risk and unavoidable (systematic) risk; and explain how proper diversification can eliminate one of these risks.

Return: Income received on an investment plus any change in market price, usually expressed as a percentage of the beginning market price of the market price of the investment. Income plus price appreciation Investment return therefore is the financial outcome from an investment. Investment return is typically measured as a percentage of the total amount of money invested.

Risk Risk refers to the chance that some unfavourable event/s will occur. In the specific context of managerial finance, risk refers to the possibility of unfavourable occurrences, which would lead to a reduction in future returns or even to a loss. Investment risk is related to the possibility of earning a return less than the expected return. The greater the probability of negative or low return, the riskier the investment. The variability of returns from those that are expected.

Using Probability Distribution to Measure Return A probability distribution is defined as a set of outcomes with probability of occurrence attached to each outcome Measure the probability of the occurrence of different states of economy. – Deep recession, Mild recession, Average, Mild boom, Strong boom. Calculate Expected Return.

Measuring Return State of EconomyProbability of Occurrence Return Deep recession0.05-2% Mild recession0.209% Average economy0.5012% Mild boom0.2015% Strong boom0.0526% Expected Return = - 2%x0.05+9%x %x %x %x0.05 =12%

Analysing Stand-alone Risk Variance: Variance is a measure of dispersion of possible outcomes around the expected value, I.e., the expected rate of return. The larger the variance, the greater the dispersion and hence higher the risk.

Analysing Stand-alone Risk Standard deviation: Standard deviation =  [0.05(-2-12) (9-12) (12-12) (15-12) (26-12) 2 ] = +4.8%

Using standard deviation as a measure of risk enables us to draw two important conclusions about the distribution of outcomes. i.The larger the standard deviation, the greater the dispersion of actual return from the expected return and hence the higher the stand-alone risk. i.If the distribution of outcomes is continuous and approximately normal, then we can say that  68.3% of all outcomes will fall within one SD  95% within 2SD  99.7% (almost all) within 3SD Analysing Stand-alone Risk

Coefficient of variation: CV measures the risk per unit of return. Example: Project X has a 30% expected return with a 10% standard deviation. Project Y has a 10% expected return with a 5% standard deviation. How do you compare the decision between investment in these two projects? Analysing Stand-alone Risk

Project X: 10/30 = 33% Project Y 5/10 = 50% Analysing Stand-alone Risk Coefficient of Variation Actual Return Project Y therefore, has higher risk per unit of return than project X. It can be argued that project Y is riskier than project x despite having a lower standard deviation than project X.

Subjective vs. Objective Probability Distributions.

Types of Risk Stand-alone Risk – When all your money is invested in one business activity. Market Risk – When your money is invested in different business activities.

Stand-alone Risk Systematic/Non-diversifiable – This part of stand-alone risk cannot be eliminated. – Caused by uncontrollable events that affect the entire economy, e.g., inflation, recession, war, flood, etc. Unsystematic/diversifiable – This part of stand-alone risk can be reduced if money is invested in different types of assets. – Affects only certain company or industries. – Caused lawsuits, strikes, unsuccessful marketing programmes, technological changes, etc.

If an individual holds a large number of stocks in a portfolio, the important issue is the overall aggregate risk of the portfolio because combining assets into portfolios reduces risk as losses or less- than-expected returns will be offset by more-than-expected returns on some other assets.

Portfolio Management Portfolio management therefore involves an investment that combines market risk and unsystematic risk so losses (lower return) on some investments are partially or fully recovered by the gains (higher return) on some other investments.

Portfolio Risk & Return Mean-variance Model Conceptualisation with the 2-asset portfolio Portfolio return Portfolio risk

Portfolio Risk & Return: Mean-variance Model Finding the Efficient portfolio Risk averse investors in the capital market look for efficient portfolio that would provide the highest expected return for any degree of risk The lowest degree of risk for any expected return.