Ch08-ppt-risk And Rates Of Return-1

Risk and Rates of Return

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Essentials of Chapter 8 What does it mean to take risk when investing? How are risk and return of an investment measured? For what type of risk is an average investor rewarded? How can investors reduce risk? What actions do investors take when the return they require to purchase an investment is different from the return the investment is expected to produce?

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Defining and Measuring Risk Risk is the chance that an unexpected outcome will occur A probability distribution is a listing of all possible outcomes with a probability assigned to each

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Example

Example Q:If you toss a coin four times what is the chance of getting x heads? The mean of this X P(X) distribution is 2, 0 0.0625 since it is a 1 0.2500 symmetrical 2 0.3750 distribution. 3

0.2500

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0.0625 1.0000

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Calculate the Mean

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Discrete Probability Distribution

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Variance and Standard Deviation

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Probability Distributions It either will rain, or it will not. Only two possible outcomes. Outcome (1)

Probability (2)

Rain

0.40 = 40%

No Rain

0.60 = 60% 1.00 100%

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Probability Distributions

Martin Products and U. S. Electric State of the Probability of This Economy State Occurring Boom Normal Recession

0.2 0.5 0.3 1.0

Rate of Return on Stock if This State Occurs Martin Products U.S. Electric 110% 22% -60%

20% 16% 10%

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Expected Rate of Return Rate of return expected to be realized from an investment during its life Mean value of the probability distribution of possible returns Weighted average of the outcomes, where the weights are the probabilities

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Expected Rate of Return

Probability of This State State of the Economy Occurring P ( r i) (1) Boom Normal Recession

(2) 0.2 0.5 0.3 1.0

Martin Products Return if This State Product: Occurs (ri) (2) x (3) (3) 110% 22% -60%

^ = rm

= (4) 22% 11% -18% 15%

U. S. Electric Return if This Product: State Occurs (ri) (2) x (5) (5) 20% 16% 10%

^ = rm

= (6) 4% 8% 3% 15%

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Expected Rate of Return

rˆ =Pr1r1 +Pr2 r2 +L +Prnrn n

=∑Priri i=1

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Continuous versus Discrete Probability Distributions Discrete Probability Distribution: number of possible outcomes is limited, or finite.

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Discrete Probability Distributions a. Martin Products Probability of Occurrence

b. U. S. Electric Probability of Occurrence

0.5 -

0.5 -

0.4 -

0.4 -

0.3 -

0.3 -

0.2 -

0.2 -

0.1 -

0.1 -

-60 -45 -30 -15 0 15 22 30 45 60 75 90 110 Rate of Expected Rate Return (%) of Return (15%)

-10 -5

0 5 10

16 20 25

Expected Rate of Return (15%)

Rate of Return (%) 14

Continuous Versus Discrete Probability Distributions Continuous Probability Distribution: number of possible outcomes is unlimited, or infinite.

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Continuous Probability Distributions Probability Density U. S. Electric

Martin Products -60

0

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110 Rate of Return (%) Expected Rate of Return 16

Measuring Risk: The Standard Deviation Calculating Martin Products’ Standard Deviation Expected Payoff Return ri r^ (1) (2) 110% 15% 22% 15% -60% 15%

ri - r^

(r i - ^r)

(1) - (2) = (3) 95 7 -75

(4) 9,025 49 5,625

2

^

Probability

^ Pr (r i - r) i

(5) 0.2 0.5 0.3

(4) x (5) = (6) 1,805.0 24.5 1,687.5

2

Variance = σ 2 = 3,517.0

Standard Deviation = σ m = σ m2 = 3,517 = 59.3% 17

Measuring Risk: The Standard Deviation n

Expected rate of return =rˆ=∑ ri (ri −rˆ)P 2

i= 1

n

Variance = σ =∑ ri (ri - rˆ)P 2

2

i=1

Standard deviation =σ=

n

r (r - rˆ)P ∑ 2

i

i

i=1

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Measuring Risk: Coefficient of Variation Calculated as the standard deviation divided by the expected return Useful where investments differ in risk and expected returns Risk σ Coefficient of variation = CV = = ˆ Return r

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Risk Aversion and Required Returns Risk-averse investors require higher rates of return to invest in higher-risk securities Risk Premium (RP): The portion of the expected return that can be attributed to an investment’s risk beyond a riskless investment The difference between the expected rate of return on a given risky asset and that on a less risky asset

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Expected Rate of Return Expected ending value - Beginning value Expected rate = of return Beginning value

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Portfolio Returns

rˆ p Expected return on a portfolio, The weighted average expected return on the stocks held in the portfolio

rˆp =w1rˆ1 +w2rˆ2 +L +wNrˆN N

=∑w jrˆj j=1

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Portfolio Returns Realized rate of return, r The return that is actually earned Actual return usually different from expected return

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Returns Distribution for Two Perfectly Negatively Correlated Stocks (ρ = -1.0) and for Portfolio WM: Stock W

Stock M

Portfolio WM

25

25

25

15

15

15

0

0

0

-10

-10

-10

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Returns Distributions for Two Perfectly Positively Correlated Stocks (ρ = +1.0) and for Portfolio MM’: Stock M

Stock MM’

Stock M’

25

25

25

15

15

15

0

0

0

-10

-10

-10

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Portfolio Risk Correlation Coefficient, ρ Measures the degree of relationship between two variables. Perfectly correlated stocks have rates of return that move in the same direction. Negatively correlated stocks have rates of return that move in opposite directions. ρ = ν (∑xy) – (∑x)(∑y) / √ {n(∑x2) – (∑x)2} {n(∑y2) – (∑y)2}

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Portfolio Risk Risk Reduction Combining stocks that are not perfectly correlated will reduce the portfolio risk through diversification. The riskiness of a portfolio is reduced as the number of stocks in the portfolio increases. The smaller the positive correlation, the lower the risk.

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Firm-Specific Risk versus Market Risk Firm-Specific Risk: That part of a security’s risk associated with random outcomes generated by events, or behaviors, specific to the firm. Firm-specific risk can be eliminated through proper diversification.

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Firm-Specific Risk versus Market Risk Market Risk: That part of a security’s risk that cannot be eliminated through diversification because it is associated with economic, or market factors that systematically affect all firms.

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Firm-Specific Risk versus Market Risk Relevant Risk: The risk of a security that cannot be diversified away, or its market risk. This reflects a security’s contribution to a portfolio’s total risk.

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The Concept of Beta Beta Coefficient, β : A measure of the extent to which the returns on a given stock move with the stock market. β = 0.5: Stock is only half as volatile, or risky, as the average stock. β = 1.0: Stock has the same risk as the average risk. β = 2.0: Stock is twice as risky as the average stock.

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Portfolio Beta Coefficients The beta of any set of securities is the weighted average of the individual securities’ betas

β p = w 1 β1 + w 2 β 2 +  + w n β n N

= ∑ w jβ j j=1

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The Relationship Between Risk and Rates of Return ˆrj = expected rate of return on the jth stock rj = required rate of return on the j stock th

rRF = risk − free rate of return RPM = (rM - rRF ) = market risk premium RPj = (rM - rRF )βj = risk premium on the j stock th

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Market Risk Premium RPM is the additional return over the risk-free rate needed to compensate investors for assuming an average amount of risk. Assuming: Treasury bonds yield = 6%, Average stock required return = 14%, Then the market risk premium is 8 percent:

RPM = rM - rRF = 14% - 6% = 8%.

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Risk Premium for a Stock Risk Premium for Stock j = RPM x β

j

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The Required Rate of Return for a Stock Security Market Line (SML): The line that shows the relationship between risk as measured by beta and the required rate of return for individual securities.

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Security Market Line

rhigh

SML :rj =rRF + rM − rRF ) β ( j

Required Rate of Return (%) = 22

rM = rA = 14 rLOW = 10 rRF = 6

0 2.0

Safe Stock Risk Premium: 4%

Market (Average Stock) Risk Premium: 8%

Relatively Risky Stock’s Risk Premium: 16%

Risk-Free Rate: 6%

0.5

1.0

1.5

Risk, β 37

The Impact of Inflation rRF is the price of money to a riskless borrower. The nominal rate consists of: a real (inflation-free) rate of return, and an inflation premium (IP).

An increase in expected inflation would increase the risk-free rate.

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Changes in Risk Aversion The slope of the SML reflects the extent to which investors are averse to risk. An increase in risk aversion increases the risk premium and increases the slope.

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Changes in a Stock’s Beta Coefficient The Beta risk of a stock is affected by: composition of its assets, use of debt financing, increased competition, and expiration of patents.

Any change in the required return (from change in beta or in expected inflation) affects the stock price.

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Stock Market Equilibrium The condition under which the expected return on a security is just equal to its required return Actual market price equals its intrinsic value as estimated by the marginal investor, leading to price stability

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Changes in Equilibrium Stock Prices Stock prices are not constant due to changes in: Risk-free rate, rRF, Market risk premium, rM – rRF, Stock X’s beta coefficient, β

x,

Stock X’s expected growth rate, gX, and Changes in expected dividends, D0.

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Physical Assets Versus Securities Riskiness of corporate assets is only relevant in terms of its effect on the stock’s risk.

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Word of Caution CAPM (Capital Asset Price Model) Based on expected conditions Only have historical data As conditions change, future volatility may differ from past volatility Estimates are subject to error

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Chapter 8 Essentials What does it mean to take risk when investing?  An investment is risky if more than one outcome is possible

How are risk and return of an investment measured?  By the variability of its possible outcomes - greater variability = greater risk

How can investors reduce risk?  Risk can be reduced through diversification

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Chapter 8 Essentials For what type of risk is an average investor rewarded?  Investors should only be rewarded for risks they must take

What actions do investors take when the return they require to purchase an investment is different from the return the investment is expected to produce?  Investors will purchase a security only when its expected return is greater than its required return

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