CHAPTER 8 Risk and Rates of Return

Kamrul Huda Talukdar CHAPTER 8Risk and Rates of Return Lecturer North South University

CHAPTER 8Risk and Rates of Return Stand-alone risk Portfolio risk Risk & return: CAPM / SML

Investment returns The rate of return on an investment can be calculated as follows: (Amount received – Amount invested) Return =________________________ Amount invested For example, if $1,000 is invested and $1,100 is returned after one year, the rate of return for this investment is: ($1,100 - $1,000) / $1,000 = 10%.

Investment risk • The chance that some unfavorable event will occur. • Investment risk is related to the probability of earning a low or negative actual return. • The greater the chance of lower than expected or negative returns, the riskier the investment. • Two types of investment risk • Stand-alone risk • Portfolio risk

Stand Alone Risk • The risk an investor would face if he or she held only one asset • This risk is due to the special characteristic of the particular asset. • Can be measured using statistical tools

Statistical and Financial Terms • Probability Distribution • Expected Rates of return r^ (r-hat) • Historical, or past realized, rates of return, r (r-bar) • Standard Deviation, σ (sigma) • Coefficient of Variation (CV)

Probability Distribution • A listing of all possible outcomes, and the probability (chance of occurrence out of 1) of each occurrence. • The rate of return expected to be realized from an investment. • The weighted average of probability distribution of possible results. Expected Return

Standard Deviation • Standard deviation is a statistical measure of the variability of a set of observation. • The tighter the probability distribution the lower the risk, since the range of possible returns become smaller. • Using sigma we can see how much the return can deviate away from the expected or weighted average. This is the measure of stand alone risk. • The smaller the standard deviation the tighter the deviating range of returns are and thus the lower the risk.

Standard Deviation • Pi = Probability of outcome • ri = Rate of return • r^ = Expected rate of return • N = number of observations • ∑ = Summation • √ = Square root rt = Rate of return rAvg = Average rate of return N = number of observations ∑ = Summation √ = Square root

Coefficient of Variation • Lets compare two stocks • Stock A: • Expected Return = 8% • Standard Deviation = 15% • Stock B: • Expected Return = 15% • Standard Deviation = 29% • Which stock to invest in?

Coefficient of Variation • Coefficient of Variation is the ratio of stand alone risk and expected return. • CV = σ/r^ • Stock A (CV) = 15/8 = 1.875 • Stock B (CV) = 29/15 = 1.933 • So it is better to invest in Stock A since it has lower risk per unit of return compared to Stock B

Risk Aversion and Premiums • It is assumed that a rational investor is risk-averse • Risk-averse investors dislike risk and will not purchase risky asset unless compensated with higher rate of return • The extra amount of return expected from a riskier asset compared to a less risky asset is called risk premium

Portfolio Risk • In cases of stocks or shares investors rarely invest in only one. They invest their money in a group of shares to create a portfolio. • So instead of stand alone risks of each of the stocks what becomes important is the entire portfolio’s risk. • Risk and return of an individual stock should be analyzed in terms of how the security affects the risk and return of the portfolio in which it is held.

Expected Portfolio Return • The weighted average of the expected returns on the individual assets held in the portfolio

Diversification • Securities held in portfolio reduces the overall risk an investor is exposed to. • This is due to the effect of Diversification. One stock can earn extra return to cover up the loss of another stock’s negative return. • Since it is assumed that rational investors are risk averse thus most investments are done in portfolio of stocks

Graphical Presentation of Diversification

Correlation Coefficient (ρ) • Unlike expected portfolio return, portfolio risk is not the weighted average of individual stock’s standard deviation (stand alone risk). • Portfolio risk depends on correlation between the stocks i.e. the tendency of two variables to move together. • Correlation coefficient (ρ) is a standardized measure, in between -1 and 1, for the degree of relationship between two variables.

Diversifiable Risk & Market Risk • Diversification is completely useless for reducing risk if stocks in the portfolio are perfectly positively correlated. • The more stocks are added in a portfolio the more diversified it becomes and the less riskier. • The risk reduces at a decreasing rate. • Risk never becomes completely zero. There are still some risk left even if a portfolio is fully diversified.

Diversifiable Risk & Market Risk • Diversifiable risk is that part of a security’s risk associated with random events, or news. • It can be completely eliminated by proper diversification. • Also known as company specific risk, unsystematic risk. • Market risk is the risk associated with the entire market and cannot be diversified away. • It is the risk that remains after diversification and thus known as nondiversifiable, or systematic or beta risk. Caused by political and macroeconomic factors.

Market Portfolio • A portfolio containing all the stocks in the market is a market portfolio. • Since most investors are considered rationally risk-averse and so it is expected for them to invest in a market portfolio. However: • High administrative costs and commissions to brokers more than offsets the benefits • Some investors believe they can correctly identify undervalued stocks and can beat the market often.

Stock Market Index • All stock market in the world create indices to proxy for either the entire market portfolio or the portfolio of the top performers of the market. • An index is an imaginary portfolio of securities representing a particular market or a portion of it. • Each index has its own calculation methodology and is usually expressed in terms of a change from a base value. Thus, the percentage change is more important than the actual numeric value. • Examples: DSE General Index, DSE All Share Index, DSE-20, S&P 500, Dow Jones Industrial Average, NASDAQ Composite.

Relevant Risk & Beta Coefficient • Relevant risk the portion of an individual stock’s risk that contributes to the market risk of it’s portfolio. • It is the extent to which a given stock’s returns move up and down with the market, measured by Beta Coefficient (ϐ). • It is considered that all other risks are diversified away in a portfolio except the relevant risks of the individual stocks.

Finding Beta Coefficient • Covariance is a measure of the degree to which returns on two risky assets move in tandem. A positive covariance means that asset returns move together. A negative covariance means returns move inversely. Similar to Correlation Coefficient. • Variance is the square of standard deviation • Beta of Market = 1.0

Portfolio Beta • Beta of a portfolio of securities is the weighted average of the individual securities’ beta.

Capital Asset Pricing Model (CAPM) • A model based on the proposition that any stock’s required rate of return is equal to the risk-free rate plus a risk premium that reflects only the risk remaining after diversification. • Required rate of return on a stock = Risk-free rate of return + Risk premium of that stock. • ri = rRF + (rM – rRF)bi

Security Market Line (SML) • A graph of CAPM equation. It shows the relationship between risk as measured by beta and required rates of return on individual securities.

CHAPTER 8 Risk and Rates of Return