Risk Return Risk and Return Both are positively

Risk& Return

Risk and Return • Both are positively related • Investors purchase financial assets such as shares of stock because they desire to increase their wealth, i. e. , earn a positive rate of return on their investments. The future, however, is uncertain; investors do not know what rate of return their investments will realize.

Assume positive rate of return of 3 company: Risk Return X=10% Y= 12% Z=20% X= 9% Y=9. 5% Z= 30%

• In finance, we assume that individuals base their decisions on what they expect to happen and their assessment of how likely it is that what actually occurs will be close to what they expected to happen. When evaluating potential investments in financial assets, these two dimensions of the decision making process are called return and risk. • The concepts presented in this section include the development of measures of expected return and risk on an individual financial asset and on a portfolio of financial assets, the principle of diversification, and the Capital Asset Pricing Model (CAPM).

Return % (high return) Expected Return, E(R)= ∑PR Required rate of return, R(R)= Rf + [Rm – Rf] Risk % (less risk) SD=√∑ [R- E(R)]2*P CV=SD/E(R)

Expected Return • The future is uncertain. Investors do not know with certainty whether the economy will be growing rapidly or be in recession. As such, they do not know what rate of return their investments will yield. Therefore, they base their decisions on their expectations concerning the future. • E(R)= ∑PR

The expected rate of return on a stock represents the mean of a probability distribution of possible future returns on the stock. The table below provides a probability distribution for the returns on stocks A and B. Question: Which stock between A and B you will prefer? State Probability (P) Return on Stock A Return on Stock B a 20% 5% 50% b 30% 10% 30% c 30% 15% 10% d 20% -10%

Expected Return on Stock A Probability Return P*R 20%=. 20 5%=. 05 . 20*. 05=. 01 30%=. 30 10%=. 10 . 03 30%=. 30 15%=. 15 . 045 20%=. 20 . 04 ∑PR=. 125=12. 5%

Expected Return on Stock B Probability Return PR 20%=. 20 50%=. 50 . 20*. 50=. 10 30%=. 30 . 09 30%=. 30 10%=. 10 . 03 20%=. 20 -10%=-. 10 -. 02 ∑PR=. 20=20%

Standard Deviation (SD) • a statistical measure of the variability of a distribution around its mean. It is the square root of variance. Note, this is for a discrete distribution. Where expected return of alternative securities are equal. SD=√∑ [R- E(R)]2*P

SD of Stock A Given that, E(R)=12. 5%=. 125 Probability Return (P) (R) P*R [R- E(R)]2*P 20%=. 20 5%=. 05 . 01 . 005*. 20=. 001 30%=. 30 10%=. 10 . 03 30%=. 30 15%=. 15 . 045 (. 05 -. 125) 2=. 005 (. 10 -. 125) 2=. 001 (. 15 -. 125) 2=. 001 20%=. 20 . 04 (. 20 -. 125) 2=. 005*. 20=. 001 ∑PR=. 125 . 001*. 30=. 001 ∑ [R- E(R)]2*P=. 004 SD=√∑ [R- E(R)]2*P =√. 004 =. 063 = 33. 015 %

Coefficient of Variation (CV) is the ratio of the standard deviation of a distribution to the mean of that distribution. It is a measure of relative risk, where expected return of alternative securities are unequal. CV= SD/E(R) Given that, SD: 33. 015% E(R): 12. 5% CV= SD/E(R) = 33. 015/12. 5 =2. 64%

Capital Asset Pricing Model (CAPM) Because investors are risk averse, they will choose to hold a portfolio of securities to take advantage of the benefits of Diversification. Therefore, when they are deciding whether or not to invest in a particular stock, they want to know how the stock will contribute to the risk and expected return of their portfolios. The standard deviation of an individual stock does not indicate how that stock will contribute to the risk and return of a diversified portfolio. Thus, another measure of risk is needed; a measure of a security's sytematic risk. This measure is provided by the Capital Asset Pricing Model (CAPM). CAPM is a model that describes the relationship between risk and expected (required) return; in this model, a security’s expected (required) return is the risk-free rate plus a premium based on the systematic risk of the security.

CAPM Assumptions 1. Capital markets are efficient. 2. Homogeneous investor expectations over a given period. 3. Risk-free asset return is certain 4. Market portfolio contains only systematic risk

Required rate of return, R(R) = Rf + [Rm – Rf] A B Pharmaceutical industry has a beta of Banking industry has a beta of 1. 45. The 2. 15. The risk-free rate is 5% and the risk-free rate is 3% and the expected return on market portfolio is 9%. return on market portfolio is 10%. You are interested to invest in the stock of B bank A. Calculate the Required rate of return limited. Calculate the Required rate of return R(R) = Rf + [Rm – Rf] = 5% + [ 9 %- 5 %]* 2. 15 =13. 6% R(R) = Rf + [Rm – Rf] =3% + [10%-3%]* 1. 45 =13. 15%

Decision making: between A & B Stock Expected Required return rate of return SD CV A 12. 5% 13. 6% 33. 015% 2. 64% B 20% 13. 15% ? ? ? ?

Risk Attitudes Certainty Equivalent (CE) is the amount of cash someone would require with certainty at a point in time to make the individual indifferent between that certain amount and an amount expected to be received with risk at the same point in time. Certainty equivalent > Expected value : Risk Preference Certainty equivalent = Expected value : Risk Indifference Certainty equivalent < Expected value : Risk Aversion

Portfolio Risk and Return Most investors do not hold stocks in isolation. Instead, they choose to hold a portfolio of several stocks. When this is the case, a portion of an individual stock's risk can be eliminated, i. e. , diversified away. Why Diversification? • Minimization of risk • Best return On this page we shall explore this concept further to demonstrate that the benefits of diversification, i. e. , the reduction in risk, depend upon the correlation coefficient (or covariance) between the returns on the securities comprising the portfolio.

Total Risk = Systematic Risk + Unsystematic Risk Systematic Risk is the variability of return on stocks or portfolios associated with changes in return on the market as a whole. Unsystematic Risk is the variability of return on stocks or portfolios not explained by general market movements. It is avoidable through diversification.

Characteristic Line A straight line on a graph that shows the relationship over time between returns on a stock and returns on the market. The line is used to illustrate a stock's alpha (the vertical intercept) and beta (the line's slope) and to show the difference between systematic and unsystematic risk. The characteristic line is used to measure statistically the undiversifiable risk and diversifiable risk of individual assets and portfolios How Characteristic Line leads to CAPM? The characteristic regression line of an asset explains the asset’s systematic variability of returns in terms of market forces that affect all assets simultaneously The portion of total risk not explained by characteristic line is called unsystematic risk Assets with high degrees systematic risk must be priced to yield high returns in order to induce investors to accept high degrees of risk that are undivesifiable in the market CAPM illustrates positive relationship between systematic risk and return on an asset

Beta An index of systematic risk. It measures the sensitivity of a stock’s returns to changes in returns on the market portfolio. The beta for a portfolio is simply a weighted average of the individual stock betas in the portfolio. It measures the volatility of a stock (or portfolio) relative to the market. Beta Coefficients Combine the correlation between the stock's return and the market return. • Interpretation of the Numerical Value of Beta • Beta = 1. 0 Stock's return has same volatility as the market return • Beta > 1. 0 Stock's return is more volatile than the market return • Beta < 1. 0 Stock's return is less volatile than the market return

Security Market Line (SML) The Security Market Line, or SML, is a line on a chart derived from the Markowitz Portfolio Theory. The Security Market Line is a graphical representation of the Capital Asset Pricing Model and it plots levels of risk against the expected return of the entire market at a given point in time. Going by values of beta, the security market line shows that the relationship between risk and return is linear for individual securities (i. e. increased risk = increased return). Essentially it shows what return you need to earn on an investment in order for it to be worth taking, and this increases with the riskiness of the investment.