Risk and Return Chapter 7

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Risk and Return

Oct 7, 2009

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Learning Objectives

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

How to measure risk. Identify different types of risk. Explain methods of risk reduction. Describe how firms compensate for risk. Discuss the Capital Asset Pricing Model

(CAPM) – how risk impacts rate of return

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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.

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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

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Measuring Risk

We can never avoid risk entirely, i.e., getting out of bed or stayingMeasuring risk is difficult; it depends on the degree of uncertainty in a situationThe greater the probability of an uncertain outcome, the greater the degree of risk (drilling for oil)

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Expected Return & Standard Deviation

Most decisions have a number of different possible outcomes or returnsExpected return is the mean, the average of a set of values, of the probability distribution of possible returns. i.e., sales projectionsFuture returns are not known with certainty. The standard deviation is a measure of this uncertainty.

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Standard Deviation

A numerical indicator of how widely dispersed the possible values are around a mean (Fig. 7-1) p. 119 (164)The more widely dispersed (Bold), the larger the standard deviation, and the greater the risk of unexpected valuesThe closer dispersed (Calm), the lower the standard deviation, and the lesser the risk of unexpected values.

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Expected Return

Expected return is the mean, or average, of the probability distribution of possible future returns.To calculate expected return, compute the 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 CalculationExample: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% 1.00

= – 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 Investment RiskExample:Example:You evaluate two investments: Zumwalt (10.5%) Corporation’s common stock and a one year Government Note paying a guaranteed 6%.

Link to Society for Risk Analysis

100%

Return

Probability of Return

T-T-NoteNote

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/

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Measurement of Investment RiskStandard Deviation (measures the dispersion of returns. It is the square root (SQRT) 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 Return

Economic 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% = .5725%

( - 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%

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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 = 18.06610.5 – 7.566 = 2.934And this holds true for one standard deviation, or only 2/3 of the timeThe other 1/3 of the time it could be above or below the standard deviation!

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Measuring Risk

Review standard deviations, Calm vs Bold on page 121 (166)See Fig 7-3, page 123 (168) for comparison of Calm vs Bold for one and two standard deviationsCalculate coefficient of variation, page 123(168), (Standard Deviation / Mean)

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

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Market related Risk - Risk due to overall market conditions

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

Risk and Rates of Return (Use slides, not book; skip Business & Financial risk)

Firm Specific Risk - Risk due to factors within the firm

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

Example: Stock price will most likely fall if a major government contract is discontinued unexpectedly.Diversification: If investors hold stock in

many companies, the firm specific risk will be cancelled out. Why?Even if investors hold many stocks, cannot eliminate the market related risk. Why?

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Diversifiable vs Non-diversifiable

Diversifiable risk, affects only one company, - give examplesNon-diversifiable risk, affects all companies, - give examples – credit/liquidity crisisHow many stocks in the DJIA?Discuss recent changes in the DOWSee fig 7-4, page 129 (174); demonstrates how diversification cancels out risk

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Risk and Diversification Total risk includes both company specific

and market related risk As you diversify, and cancel out company

specific risk, total risk approximates market related risk


# of stocks in Portfolio

Variability of Returns Total RiskTotal Risk

17# of stocks in Portfolio

Variability of Returns

Risk and Diversification If an investor holds enough stocks in

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


Firm Specific RiskFirm Specific Risk

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Risk and Diversification If an investor holds enough stocks in

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

However, Market related risk remains

# of stocks in Portfolio

Variability of Returns


Market Related Market Related RiskRisk

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Market risk is the risk that affects the overall market. How does your company react to market fluctuations? The same? More? Less?To measure how an individual company’s stock reacts to overall market fluctuations, we need to compare individual stock returns to the overall market returns.


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A proxy for the market return is usually used: An index of stocks such as the S&P 500, or Dow Jones Industrial AverageA regression analysis of the individual stock returns to the returns of the market index measures the degree that stocks are impacted by the marketLet’s compare PepsiCo to the S & P 500

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Risk and Rates of ReturnRegress individual stock (PepsiCo) returns on Market (S & P 500) index

S&PS&PReturnReturn

PepsiCoPepsiCoReturnReturn

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

5%

10%

15%

-5%

-10%

-15%

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S&PS&PReturnReturn


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

5%

10%

15%

-5%

-10%

-15%

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

Risk and Rates of ReturnRegress 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 ReturnRegress individual stock returns on Market index for 22 months

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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 ReturnRegress individual stock returns on Market index returns – draw a best fit line

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Risk and Rates of ReturnRegress individual stock returns on Market index returns – calculate the slope of the line

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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Market Risk is measured by Beta


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 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 Beta


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

Beta < 1Low Risk Company (examples?)Return on stock will be less affected by the

market than average Beta > 1

High Market Risk Company (examples?)Stock return will be more affected by the

market than average

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kj = kRF + j ( kM – kRF )

Security Market LineSecurity Market Line

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

The Capital Asset Pricing ModelInvestors adjust their required

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

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CAPM Example

Suppose that the required return on the 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

CAPM Example


kj = 5% + j (12% – 5% )

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Beta1.51.0.50

15%

10%

5%

Risk & Risk & Return on Return on marketmarket

CAPM Example


kj = 5% + j (12% – 5% )

Risk Free RateRisk Free Rate

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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 ExampleSuppose that the required return on the market is 12% and the risk free rate is 5%.If Beta is 1.2, then Kj = 13.4

kj = 5% + j (12% – 5% )

Market

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CAPM Example

See Table 7-4, p. 137 (182), and Figure 7-7, p. 138 (183)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

Risk and Return Chapter 7

Economy & Finance

Transcript of Risk and Return Chapter 7