measurement of risk

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Risk and Return

Sep 26, 2012

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Learning Objectives

Define risk, risk aversion, and risk-return tradeoff.

Measure risk. Identify different types of risk. Explain methods of risk reduction. Describe how firms compensate for

risk. Discuss the CAPM.

Financial CrisisFinancial Crisis▪ The failure of one company The failure of one company can lead to the failure of otherscan lead to the failure of others▪If AIG had been allowed to fail If AIG had been allowed to fail it likely would have taken many it likely would have taken many other companies with itother companies with it

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Financial CrisisFinancial Crisis This risk is sometimes referred to as This risk is sometimes referred to as

“systematic risk”, or Market Risk“systematic risk”, or Market Risk Systematic risk cannot be diversified Systematic risk cannot be diversified

away (because it affects everyone)away (because it affects everyone) Sometimes different groups of assets Sometimes different groups of assets

go up and down together in value, go up and down together in value, (i.e., all software companies)(i.e., all software companies)

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Risk and Rates of Return Risk is the potential for unexpected

events to occur or a desired outcome not to occur.

If two financial alternatives are similar except for their degree of risk, most people will choose the less risky alternative because they are risk averse, i.e. they don’t like risk.

Risk and Rates of Return

Risk averse investors will require higher expected rates of return as compensation for taking on higher levels of risk than someone who is risk tolerant (more willing to take on risk.) Axiom 1

Measuring Risk We can never avoid risk entirely, i.e.,

getting out of bed or staying Measuring risk is difficult; it depends

on the degree of uncertainty in a situation

The greater the probability of an uncertain outcome, the greater the degree of risk (i.e., drilling for oil)

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Expected Return & Standard Deviation

Most decisions have a number of different possible outcomes or returns

Expected return is the mean, the average of a set of values, of the probability distribution of possible outcomes. i.e., sales projections

Future returns are not known with certainty. The standard deviation is a measure of this uncertainty.

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Expected ReturnExpected Return

To calculate expected return, compute To calculate expected return, compute the weighted average of possible returnsthe weighted average of possible returns

where= Expected return Vi = Possible value of return during period i Pi = Probability of V occurring during period i

Vi x Pi)

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Expected Return Expected Return CalculationCalculationExample:Example:

You are evaluating Zumwalt Corporation’s common stock. You estimate the following returns given different states of the economy

State of Economy Probability Return

Economic Downturn .10 –5%Zero Growth .20 5%Moderate Growth .40 10%High Growth .30 20%

N

iii kPkk

1

)(

= – 0.5%= 1.0%= 4.0%= 6.0%

k = 10.5%

Expected rate of return on Expected rate of return on the stock is 10.5%the stock is 10.5%

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Measurement of Measurement of Investment RiskInvestment Risk

Example:Example:You evaluate two investments: Zumwalt Corporation’s common stock and a one year Gov't Bond paying a guaranteed 6%.

Link to Society for Risk Analysis

100%

Return

Probability of Return

T-BillT-Bill

6%Return

10%

Probability of Return

Zumwalt CorpZumwalt Corp

5%

20%30%40%

10% 20%–5%

There is risk in owning Zumwalt There is risk in owning Zumwalt stock, no risk in owning the T-billsstock, no risk in owning the T-bills

http://www.sra.org/

Standard Deviation A numerical indicator of how widely

dispersed the possible values are around a mean (Fig. 7-1) p. 164

The more widely dispersed (Bold), the larger the standard deviation, and the greater the risk of unexpected values

The closer dispersed (Calm), the lower the standard deviation, and the lesser the risk of unexpected values.

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Measurement of Investment Measurement of Investment RiskRisk

Standard Deviation (Standard Deviation (measures the dispersion of measures the dispersion of returns. It is the square root of the variance.returns. It is the square root of the variance.

Example:Example:Compute the standard deviation on Zumwalt common stock. the mean () was previously computed as 10.5%

SQRT(P(V - )2)

State of Economy Probability ReturnEconomic Downturn .10 5%Zero Growth .20 5%Moderate Growth .40 10%High Growth .30 20%

(- - 10.5%)2 = .24025%

( - 10.5%)2 = .001%( - 10.5%)2 = .27075%

( - 10.5%)2 = .0605%

= variancevariance

2 2 = .005725 = = .005725 = 0.5725% 0.5725% = SQRT of 0.005725= SQRT of 0.005725 = .07566 = 7.566%= .07566 = 7.566%

Measurement of Investment Risk

The standard deviation of 7.566% means that Zumwalt’s return would be in the 10.5% range (the mean), plus or minus 7.566%!

That ‘s a very wide range! High Risk! 10.5 + 7.566 = 18.066 10.5 – 7.566 = 2.934 And this holds true for one standard

deviation, or only 2/3 of the time The other 1/3 of the time it could be above

or below the standard deviation!

Measuring Risk Review standard deviations, Calm vs

Bold on page 166 See Fig 7-3, page 168 for comparison

of Calm vs Bold for one and two standard deviations

Calculate coefficient of variation, page168, (Standard Deviation / Mean)

Calm 15.5% (low risk <20%) vs Bold 38.5% (high risk >30%). Zumwalt 7.566/10.5 = 72.1%!

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― Market related Risk - Risk due to overall market Market related Risk - Risk due to overall market conditionsconditions

Stock price is likely to rise if overall stock market is doing well.

Risk and Rates of Risk and Rates of ReturnReturn

– Firm Specific Risk - Risk due to factors within the firmFirm Specific Risk - Risk due to factors within the firm

Risk of a company's stock can be separated into two parts:

Stock price will most likely fall if a major government contract is discontinued unexpectedly.

Diversification: If investors hold stock in many companies, Diversification: If investors hold stock in many companies, the firm specific risk will be cancelled out.the firm specific risk will be cancelled out.

Even if investors hold many stocks, cannot eliminate the market related risk

Diversifiable vs Non-diversifiable Diversifiable risk (company specific)

affects only one company, - give examples

Non-diversifiable risk (market risk), affects all companies, - give examples – credit/liquidity crisis

How many stocks in the DJIA? Discuss recent changes in the DOW See fig 7-4, page 174; demonstrates

how diversification cancels out risk

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Risk and DiversificationRisk and Diversification– Total investment risk is composed of two Total investment risk is composed of two

types, firm specific risk (top) and market types, firm specific risk (top) and market related risk (bottom). Both affect stock price.related risk (bottom). Both affect stock price.


# of stocks in Portfolio

Variability of Returns

Total RiskTotal Risk

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Risk and DiversificationRisk and Diversification– If an investor holds enough stocks in If an investor holds enough stocks in

portfolio (about 20) company specific portfolio (about 20) company specific (diversifiable) risk is virtually eliminated(diversifiable) risk is virtually eliminated

# of stocks in Portfolio



Market Related Market Related RiskRisk

2020# of stocks in Portfolio


Risk and DiversificationRisk and Diversification– When company specific risk is eliminated, When company specific risk is eliminated,

then all you have left is market related (non then all you have left is market related (non diversifiable) risk that applies to all diversifiable) risk that applies to all investmentsinvestments


Firm Specific RiskFirm Specific Risk

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Market risk is the risk of the overall market, Market risk is the risk of the overall market, so to measure we need to compare so to measure we need to compare individual stock returns to the overall individual stock returns to the overall market returns.market returns.

A proxy for the market is usually used: An A proxy for the market is usually used: An index of stocks such as the S&P 500index of stocks such as the S&P 500

Market risk measures how individual stock Market risk measures how individual stock returns are affected by total market returnsreturns are affected by total market returns

So let’s compare the returns of PepsiCo to So let’s compare the returns of PepsiCo to the S & P 500the S & P 500

Measuring & Measuring & Understanding Market Understanding Market RiskRisk

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S&PS&PReturnReturn

PepsiCoPepsiCoReturnReturn

-15% 15%-10% -5% 10%5%

5%

10%

15%

-5%

-10%

-15%

Jan 1999PepsiCo-0.37%S&P -1.99%

Risk and Rates of Risk and Rates of ReturnReturn Regress individual stock returns on Market indexRegress individual stock returns on Market index

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S&PS&PReturnReturn


-15% 15%-10% -5% 10%5%

5%

10%

15%

-5%

-10%

-15%

Plot Plot Remaining Remaining PointsPoints

Risk and Rates of ReturnRisk and Rates of Return Regress individual stock returns on Market indexRegress individual stock returns on Market index

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S&PS&PReturnReturn


-15% 15%-10% -5% 10%5%

5%

10%

15%

-5%

-10%

-15%

Best Fit Best Fit Regression Regression LineLine

Risk and Rates of Risk and Rates of ReturnReturnRegress individual stock returns on

Market index returns

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Risk and Rates of ReturnRisk and Rates of ReturnRegress individual stock returns on Market index returns

S&PS&PReturnReturn


-15% 15%-10% -5% 10%5%

5%

10%

15%

-5%

-10%

-15%

Slope =Slope = riseriserunrun

5.5%5.5%5%5%== = 1.1= 1.1

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S&PS&PReturnReturn


-15% 15%-10% -5% 10%5%

5%

10%

15%

-5%

-10%

-15%

Slope = 1.1 = Beta (Slope = 1.1 = Beta (

Risk and Rates of Risk and Rates of ReturnReturn Market Risk is measured by BetaMarket Risk is measured by Beta

– Beta is the slope of the regression Beta is the slope of the regression (characteristic) line(characteristic) line

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Market Risk is measured by Beta

Risk and Rates of Return

Beta is the slope of the regression (characteristic) line, i.e., 1.1 for PepsiCo

Beta measures the relationship between the company returns and the market returns; measures non-diversifiable risk

PepsiCo has 1.1 times (10%) more volatility than the average stock in the S & P 500, which has a slope of 1.0.(by definition)

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Interpreting BetaInterpreting Beta


Beta = 1Market Beta = 1Company with a beta of 1 has average risk

Beta < 1Low Risk CompanyReturn on stock will be less affected by the market

than average Beta > 1

High Market Risk CompanyStock return will be more affected by the market

than average• Beta of T-Bill? = 0

The Capital Asset Pricing Model Investors adjust their required Investors adjust their required

rates of return to compensate for rates of return to compensate for risk.risk.The CAPM measures required rate of return for investments, given the degree of market risk measured by beta.

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kj = kRF + j ( kM – kRF )

Security Market Security Market LineLine

where:where:Kj = required rate of return on the jth securityKRF = risk free rate of return (T-Bill)KM = required rate of return on the marketBj = Beta for the jth security

Km – Krf = Risk!

The Capital Asset Pricing Model

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CAPM ExampleCAPM Example Suppose that the required return on the Suppose that the required return on the

market is 12% and the risk free rate is 5%.market is 12% and the risk free rate is 5%.

kj = kRF + j ( kM – kRF )

Security Market LineSecurity Market Line

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Beta1.51.0.50

15%

10%

5%Risk Free RateRisk Free Rate



kj = 5% + j (12% – 5% )

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Beta1.51.0.50

15%

10%

5%

Risk & Risk & Return on Return on marketmarket



kj = 5% + j (12% – 5% )

Risk Free RateRisk Free Rate

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Beta1.51.0.50

15%

10%

5%



SML

Connect Points forConnect Points forSecurity Market LineSecurity Market Line

Market

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Beta1.5.50

15%

10%

5%

SML13.4%

1.0 1.2

If beta = 1.2If beta = 1.2 kkjj = 13.4 = 13.4

CAPM ExampleCAPM ExampleSuppose that the required return on the market is 12% and the risk free rate is 5%.

kj = 5% + j (12% – 5% )

Market

CAPM Example See Table 7-4, 180, and Figure 7-7,

p. 181 Project low risk – example? Project average risk – example? Project high risk – example? Note: Market risk premium = Km –

Krfi.e., 12%(Km) – 4%(Krf) = 8% market risk premium

measurement of risk

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