Lecture FourLecture Four

RISK RISK

& &

RETURNRETURN

Formal Definition- Formal Definition- RISKRISK

# The variability of returns from # The variability of returns from those that are expected. Or,those that are expected. Or,

# The chance that some # The chance that some unfavorable event will occur. Or,unfavorable event will occur. Or,

# The chance of financial loss, or # The chance of financial loss, or the variability of returns the variability of returns associated with a given asset.associated with a given asset.

Formal Definition- Formal Definition- ReturnReturn

# The total gain or loss experienced on an # The total gain or loss experienced on an investment over a given period of time; investment over a given period of time; calculated by dividing the asset’s cash calculated by dividing the asset’s cash distributions during the period, plus change in distributions during the period, plus change in value, and divide by its beginning-of-period value, and divide by its beginning-of-period investment value.investment value.

Formula:Formula:

KKtt = actual, expected or required rate of = actual, expected or required rate of return during period treturn during period tCCtt = cash flow received from the asset investment = cash flow received from the asset investment

in the time period t-1 to t.in the time period t-1 to t.PPtt = Price (value) of asset at time t = Price (value) of asset at time t

PPt-1t-1 = price (value) of asset at time t-1 = price (value) of asset at time t-1

1-t

1-ttt

P

P-PC

tk

ExampleExample

Example1: Kohinur Co. a high-tech DVD renter Example1: Kohinur Co. a high-tech DVD renter wishes to determine the rate of return on two of wishes to determine the rate of return on two of its DVD, model A and model B. Model A was its DVD, model A and model B. Model A was purchased 1 year ago for Tk. 20000 and currently purchased 1 year ago for Tk. 20000 and currently has a market value of Tk. 21500. During the year, has a market value of Tk. 21500. During the year, it generated Tk. 800 of after tax cash receipts. it generated Tk. 800 of after tax cash receipts. Model B was purchased 4 years ago; its value in Model B was purchased 4 years ago; its value in the year just completed declined from Tk. 12000 the year just completed declined from Tk. 12000 to Tk. 11800. It generated Tk. 1700 cash receipts. to Tk. 11800. It generated Tk. 1700 cash receipts. Calculate the annual rate of return.Calculate the annual rate of return.

Example2: Exercise 5.2Example2: Exercise 5.2

Risk PreferenceRisk Preference

Risk Indifferent:Risk Indifferent: The attitude toward The attitude toward risk in which no change in return would risk in which no change in return would be required for an increase in risk.be required for an increase in risk.

Risk-averse:Risk-averse: The attitude toward risk in The attitude toward risk in which an increased return would be which an increased return would be required for an increase in risk.required for an increase in risk.

Risk-seeking:Risk-seeking: The attitude toward risk The attitude toward risk in which a decreased return would be in which a decreased return would be accepted for an increase in risk. accepted for an increase in risk.

Sources of RiskSources of Risk Firm-Specific Risks:Firm-Specific Risks:

– Business Risk: the chances that the firm will not Business Risk: the chances that the firm will not be able to cover its operating costs.be able to cover its operating costs.

– Financial Risk: the chance that the firm will be Financial Risk: the chance that the firm will be unable to cover its financial obligations as they unable to cover its financial obligations as they come due.come due.

Shareholders-Specific Risks:Shareholders-Specific Risks:– Interest rate risk: affects of change in interest Interest rate risk: affects of change in interest

rate.rate.– Liquidity Risk: the chance that investment cannot Liquidity Risk: the chance that investment cannot

be liquidated at reasonable pricebe liquidated at reasonable price– Market Risk: the chance that the value of Market Risk: the chance that the value of

investment will decline because of market factorsinvestment will decline because of market factors

Sources of RiskSources of Risk

Firm and Shareholder Risk:Firm and Shareholder Risk:– Event Risk: impacts of unexpected eventEvent Risk: impacts of unexpected event– Exchange Rate Risk: impacts of fluctuation Exchange Rate Risk: impacts of fluctuation

in the currency exchange rate.in the currency exchange rate.– Purchasing Power Risk: impact of inflation Purchasing Power Risk: impact of inflation

or deflation on the consumers’ purchasing or deflation on the consumers’ purchasing power.power.

– Tax Risk: the chance that unfavorable tax Tax Risk: the chance that unfavorable tax law will occur.law will occur.

Measuring RiskMeasuring Risk

Probability Distribution:Probability Distribution:

A listing of all possible outcomes or A listing of all possible outcomes or events with a probability (chance of events with a probability (chance of occurrence) assigned to each occurrence) assigned to each outcome.outcome.

Outcome Probability Outcome Probability

Rain 0.4 = 40%Rain 0.4 = 40%

No Rain No Rain 0.60.6 = = 60 60

1.0 = 100%1.0 = 100%

Measuring RiskMeasuring Risk

Expected Return:Expected Return:

The weighted average of possible returns, with The weighted average of possible returns, with the weights being the probabilities of occurrence.the weights being the probabilities of occurrence.

Formula:Formula:

Where,Where,KKjj = return for the = return for the JJth outcometh outcome

PrPrjj = probability of occurrence of = probability of occurrence of j jth th outcomeoutcome

n = number of outcomes consideredn = number of outcomes considered

jj Pr X k n

1j

k

Measuring RiskMeasuring Risk There are three statistical tools used to measure the risk- There are three statistical tools used to measure the risk-

Range, Standard Deviation, and Coefficient of Variation Range, Standard Deviation, and Coefficient of Variation (CV):(CV):

RangeRange: Measures the difference between the highest value : Measures the difference between the highest value of the return and its lowest value. Higher the range, of the return and its lowest value. Higher the range, higher will be the risk of an asset.higher will be the risk of an asset.

Standard Deviation:Standard Deviation: The most common statistical indicator The most common statistical indicator of an asset’s risk; it measures the dispersion around the of an asset’s risk; it measures the dispersion around the expected value or the average value of squared expected value or the average value of squared deviations from mean. It is a measure of volatility.deviations from mean. It is a measure of volatility.

Formula:Formula: σσk k = =

Higher the standard deviation greater the riskHigher the standard deviation greater the risk

n

1j

jj Pr x)k'(k 2

Measuring RiskMeasuring Risk Coefficient of Variation (CV):Coefficient of Variation (CV):

The ratio of the standard deviation of a The ratio of the standard deviation of a distributing to the mean (expected distributing to the mean (expected return) of that distribution. It measures return) of that distribution. It measures the risk per unit of return.the risk per unit of return.

Formula: CV = Formula: CV = σσ/k/k

The higher the coefficient of variation, the The higher the coefficient of variation, the greater will be risk.greater will be risk.

Example: 5-7, 5-10Example: 5-7, 5-10

ExampleExample

The market and stock j have the following The market and stock j have the following probability distribution:probability distribution:

Probability Km KjProbability Km Kj 0.3 15% 20%0.3 15% 20% 0.4 09 050.4 09 05 0.3 18 120.3 18 12a. Calculate the expected rates of return for the a. Calculate the expected rates of return for the

market and stock j.market and stock j.b. Calculate the standard deviation for market b. Calculate the standard deviation for market

and stock j.and stock j.c. Calculate the coefficient of variation for the c. Calculate the coefficient of variation for the

market and stock j.market and stock j.

Portfolio Risk and Portfolio Risk and ReturnsReturns

PortfolioPortfolio: A portfolio consists of : A portfolio consists of individual stocks where the objective is individual stocks where the objective is to maximize the returns it generates.to maximize the returns it generates.

Portfolio ReturnPortfolio Return: Is the weighted : Is the weighted average of the expected returns on the average of the expected returns on the individual stocks in the portfolio, with individual stocks in the portfolio, with the weights being the fraction of the the weights being the fraction of the total portfolio invested in each stock.total portfolio invested in each stock.

Formula KFormula Kpp = sum W = sum WjjKKjj, j=1 to n , j=1 to n

Portfolio Risk and Portfolio Risk and ReturnsReturns

Portfolio RiskPortfolio Risk: It is calculated by using : It is calculated by using correlation coefficient, r. The relationship correlation coefficient, r. The relationship between two variables is called between two variables is called correlation, and the coefficient which correlation, and the coefficient which measures the degree of the relationship measures the degree of the relationship between the variables is called the between the variables is called the correlation coefficient. Its value moves correlation coefficient. Its value moves from -1 to +1, where, -1 denotes perfectly from -1 to +1, where, -1 denotes perfectly negative correlation and +1 measures negative correlation and +1 measures perfectly positive correlation.perfectly positive correlation.

Use of Correlation Use of Correlation Coefficient: Coefficient:

DiversificationDiversification Diversification refers to use of multiple stocks Diversification refers to use of multiple stocks

which are negatively (or lower positively) which are negatively (or lower positively) correlated to reduce the risk to near zero or as correlated to reduce the risk to near zero or as low as possible.low as possible. DO NOT PUT ALL OF YOUR EGGS IN THE SAME DO NOT PUT ALL OF YOUR EGGS IN THE SAME

BASKETBASKET– Uncorrelated stocks are those which has near zero Uncorrelated stocks are those which has near zero

correlation coefficient.correlation coefficient.– Use of perfectly negative correlated stock will result in Use of perfectly negative correlated stock will result in

zero risk. It is impossible to have perfectly negative zero risk. It is impossible to have perfectly negative correlation.correlation.

– Most of the assets are less than perfectly correlated Most of the assets are less than perfectly correlated and addition of assets to a portfolio will lower and lower and addition of assets to a portfolio will lower and lower the risk.the risk.

Types of RiskTypes of Risk

Total Security Risk =Total Security Risk =

Nondiversifiable risk + Diversifiable Nondiversifiable risk + Diversifiable riskrisk

# Diversifiable Risk:# Diversifiable Risk:

The portion of an asset’s risk that is The portion of an asset’s risk that is attributable to firm-specific, random attributable to firm-specific, random causes; can be eliminated through causes; can be eliminated through diversification. Also called diversification. Also called unsystematic risk or company-specific unsystematic risk or company-specific risk.risk.

Types of RiskTypes of Risk

# Nondiversifiable Risk:# Nondiversifiable Risk: The relevant portion of an asset’s risk The relevant portion of an asset’s risk

attributable to market factors that effect attributable to market factors that effect all firms; cannot be eliminated through all firms; cannot be eliminated through diversification. Also called systematic diversification. Also called systematic risk or market risk.risk or market risk.

Diversification:Diversification: Spread your risk across a number of Spread your risk across a number of

assets or investments in order to assets or investments in order to reducing total risk of investments.reducing total risk of investments.

DiversificationDiversification

05 10 15

Number of Securities

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Relationship between Relationship between Risk and Returns Risk and Returns

(CAPM)(CAPM) The Capital asset Pricing Model (CAPM)The Capital asset Pricing Model (CAPM)

measures the link between the non-measures the link between the non-diversifiable risk and return for all assets.diversifiable risk and return for all assets.

BetaBeta measures the extent to which the measures the extent to which the return on a given stock move with the return on a given stock move with the stock market. If the historical returns on stock market. If the historical returns on the market are plotted on the X axis and the market are plotted on the X axis and the similar returns of the individual stocks the similar returns of the individual stocks are plotted on the Y axis, the slope of the are plotted on the Y axis, the slope of the line is called the beta coefficient or beta line is called the beta coefficient or beta in short.in short.

Relationship between Relationship between Risk and Returns Risk and Returns

(CAPM)(CAPM) Beta can also be calculated using the Beta can also be calculated using the

following formula following formula

BBjj = The ratio between Cov (return on asset j = The ratio between Cov (return on asset j and the return on the market) and the and the return on the market) and the variance of the return on the market variance of the return on the market

portfolio.portfolio. If the value of beta is greater than 1, it If the value of beta is greater than 1, it

shows above average market risk, if equal to shows above average market risk, if equal to 1, average market risk and, if less than 1, it 1, average market risk and, if less than 1, it shows below average market risk.shows below average market risk.

Relationship between Relationship between Risk and Returns Risk and Returns (CAPM)(CAPM)

Portfolio Beta:Portfolio Beta: Mutual fund managers use Mutual fund managers use portfolio beta to determine the risky ness portfolio beta to determine the risky ness of their portfolio. It shows the weighted of their portfolio. It shows the weighted average of the individual stock beta.average of the individual stock beta.

(Formula P.236)(Formula P.236) The Security Market Line (SML):The Security Market Line (SML): The line The line

that shows the relationship between the that shows the relationship between the risk measured by the beta and the risk measured by the beta and the required rate of return for individual required rate of return for individual securities.securities.

Relationship between Relationship between Risk and Returns Risk and Returns (CAPM)(CAPM)

SML: kSML: kjj = K = KRFRF + (K + (KMM – K – KRFRF)b)bjj

Where, Kj is the required return on stock jWhere, Kj is the required return on stock j

Krf is risk free rate of return govt Krf is risk free rate of return govt treasury bond.treasury bond.

Km is the rerun on the market portfolioKm is the rerun on the market portfolio

bj is the beta coefficient of stock j.bj is the beta coefficient of stock j.

Figure of SML P.240Figure of SML P.240

CAPMCAPM

Write a critique of CAPMWrite a critique of CAPM

QuestionsQuestions Define risk. According to the preference of risk Define risk. According to the preference of risk

investors are divided into three types explain.investors are divided into three types explain. Identify and explain the sources of risks affecting the Identify and explain the sources of risks affecting the

managers and investors.managers and investors. Compare between standard deviation and coefficient Compare between standard deviation and coefficient

of variation as measurement of risk.of variation as measurement of risk. What is a port folio? How portfolio risk and returns What is a port folio? How portfolio risk and returns

are calculated?are calculated? Define correlation coefficient. What does it’s value Define correlation coefficient. What does it’s value

mean?mean? Explain the types of risk. What type of risk CAPM try Explain the types of risk. What type of risk CAPM try

to explain?to explain? Define the following terms: CAPM, beta and SML. Use Define the following terms: CAPM, beta and SML. Use

graph to explain.graph to explain.