risk and return chapter 7
TRANSCRIPT
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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 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
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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
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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
Risk and Rates of Return
# 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
Risk and Rates of Return
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
Risk and Rates of Return
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.
Risk and Rates of Return
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Risk and Rates of Return
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
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 ReturnRegress individual stock returns on Market index
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S&PS&PReturnReturn
PepsiCoPepsiCoReturnReturn
-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
PepsiCoPepsiCoReturnReturn
-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
PepsiCoPepsiCoReturnReturn
-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
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 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
Risk and Rates of Return
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
Suppose that the required return on the market is 12% and the risk free rate is 5%.
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
Suppose that the required return on the market is 12% and the risk free rate is 5%.
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