1. Agenda for 29 July (Chapter 13)
Expected Returns, Variances, and Standard Deviations for individual securities
Expected Returns, Variances, and Standard Deviations for portfolios
Announcements, Surprises, and Expected Returns
Risk: Systematic and Unsystematic
Capital Asset Pricing Model
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2. Expected Returns
Expected returns are based on the probabilities of possible outcomes
In this context, “expected” means average if the process is repeated many times
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3. Variance and Standard Deviation
Variance and standard deviation measure the volatility of returns
Weighted average of squared deviations
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4. Example: Expected Returns
Suppose you have predicted the following returns for stocks C and T in three possible states of the economy. What are the expected returns?
State Probability C T___
Boom
Normal
Recession
E(RC) = .3(15) + .5(10) + .2(2) = 9.9%
E(RT) = .3(25) + .5(20) + .2(1) = 17.7%
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5. Example: Variance & Standard Deviation
What are the variance and standard deviation for each stock?
Stock C
2 = .3( )2 + .5( ) ( )2 =
 = 4.50%
Stock T
2 = .3( )2 + .5( ) ( )2 =
 = 8.63%
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6. Portfolios A portfolio is a collection of assets
An asset’s risk and return are important in how they affect the risk and return of the portfolio
The risk-return trade-off for a portfolio is measured by the portfolio expected return and standard deviation, just as with individual assets
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7. Portfolio Expected Return
The expected return of a portfolio is the weighted average of the expected returns of the respective assets in the portfolio
You can also find the expected return by finding the portfolio return in each possible state and computing the expected value as we did with individual securities
Here, w(j) is the % of the portfolio invested in security j.
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8. Portfolio Variance
Compute the portfolio return for each state: RP = w1R1 + w2R2 + … + wmRm
Compute the expected portfolio return using the same formula as for an individual asset
Compute the portfolio variance and standard deviation using the same formulas as for an individual asset
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9. Example: Portfolio Expected Return and Standard Deviation
Consider the following information on returns and probabilities:
Invest 50% of your money in Asset A and 50% in B
State Probability A B Portfolio
Boom % -5% 12.5%
Bust % 25% 7.5%
What are the expected return and standard deviation for each asset?
What are the expected return and standard deviation for the portfolio?
Download the portfolio problem spreadsheet.
Note – the returns on these two securities are perfectly negatively correlated:
Calculate covariance
Correlation = covariance/product of standard deviations.
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10. Expected vs. Unexpected Returns
Realized returns are generally not equal to expected returns
There is the expected component and the unexpected component
At any point in time, the unexpected return can be either positive or negative
Over time, the average of the unexpected component is zero; by definition, something that is unexpected is purely random!
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11. Announcements and News
Announcements and news contain both an expected component and a surprise component
It is the surprise component that affects a stock’s price and therefore its return (positively or negatively)
This is apparent when we watch how stock prices move in response to news about the firm that is not anticipated; e.g., a better or worse than expected earnings announcement
Lecture Tip: It is easy to see the effect of unexpected news on stock prices and returns. Consider the following two cases: (1) On November 17, 2004 it was announced that K-Mart would acquire Sears in an $11 billion deal. Sears’ stock price jumped from a closing price of $45.20 on November 16 to a closing price of $52.99 (a 7.79% increase) and K-Mart’s stock price jumped from $ on November 16 to a closing price of $ on November 17 (a 7.69% increase). Both stocks traded even higher during the day. Why the jump in price? Unexpected news, of course. (2) On November 18, 2004, Williams-Sonoma cut its sales and earnings estimates for the fourth quarter of 2004 and its share price dropped by 6%. There are plenty of other examples where unexpected news causes a change in price and expected returns.
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12. Systematic Risk Also known as non-diversifiable risk or market risk
Includes risk factors that affect firms generally; e.g., macroeconomic factors such as GDP, inflation, interest rates, demographic change, changes in consumer preferences, and so forth.
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13. Unsystematic Risk Also known as diversifiable or unique risk
Includes risk factors that are firm-specific; e.g., property damage, lawsuits, product recalls, labor strikes, theft of intellectual property by hackers, and so forth.
Lecture Tip: You can expand the discussion of the difference between systematic and unsystematic risk by using the example of a strike by employees. Students will generally agree that this is unique or unsystematic risk for one company. However, what if the UAW stages the strike against the entire auto industry. Will this action impact other industries or the entire economy? If the answer to this question is yes, then this becomes a systematic risk factor. The important point is that it is not the event that determines whether it is systematic or unsystematic risk; it is the impact of the event.
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14. Returns Total Return = expected return + unexpected return
Unexpected return = systematic portion + unsystematic portion
Therefore, total return can be expressed as follows:
Total Return = expected return + systematic portion unsystematic portion
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15. Systematic and Unsystematic Risk
Non-zero correlation occurs naturally since stocks tend to be positively correlated with each other
Note that according to the combinatorial equation, the number of unique pairs in a group of n securities is equal (n-1)/n.
In the portfolio variance formula shown here, we have the (quite familiar) expression which decomposes risk into its unique and systematic components.
Changing the composition of the risk pool (by varying n) does not affect expected return, but it does affect variance!

16. Systematic and Unsystematic Risk
Draw the familiar diagram which decomposes risk into its systematic and unsystematic components.

17. Systematic Risk Principle
There is a reward for bearing risk
There is not a reward for bearing risk unnecessarily
The expected return on a risky asset depends only on that asset’s systematic risk since unsystematic risk can be diversified away
A discussion of diversification via mutual funds and ETFs may add to the students’ understanding.
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18. Measuring Systematic Risk
How do we measure systematic risk?
We use the beta coefficient
What does beta tell us?
A beta of 1 implies the asset has the same systematic risk as the overall market
A beta < 1 implies the asset has less systematic risk than the overall market
A beta > 1 implies the asset has more systematic risk than the overall market
Note that Beta is a standardized covariance – it is equal to the ratio of the covariance between an individual security and the overall market divided by the variance of the overall market; it indicates how much systematic risk a security has compared with the overall market.
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19. Total vs. Systematic Risk
Consider the following information:
Standard Deviation Beta
Security C 20% 1.25
Security K 30% 0.95
Which security has more total risk?
Which security has more systematic risk?
Which security should have the higher expected return?
Security K has the higher total risk
Security C has the higher systematic risk
Security C should have the higher expected return
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20. The Risk Reward Ratio for the Overall Market A Graphical Illustration
Note: the equation for the line in this graph is E(RM) = Rf + M[E(RM) – Rf]; the slope of the line is (E(RM) – Rf)/M
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21. The Capital Asset Pricing Model (CAPM)
In equilibrium, all assets and portfolios must have the same reward-to-risk ratio, and they all must equal the reward-to-risk ratio for the market; i.e.,
Since the beta of the market is (by definition) equal to 1, this implies that
Discuss the economics of this – if you receive a higher reward-to-risk ratio with A than with the market, this means that A is undervalued, so people bid the price of A up, which reduces its reward-to-risk ratio. If A gets too expensive relative to the overall market, then it’s reward-to-risk ratio is too low relative to the market. This encourages investors to sell A until it’s reward-to-risk ratio is on par with the overall market.
The
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22. Factors Affecting Expected Return
Pure time value of money: measured by the risk-free rate
Reward for bearing systematic risk: measured by the market risk premium
Amount of systematic risk: measured by beta
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23. The Capital Asset Pricing Model (CAPM)
The capital asset pricing model defines the relationship between risk and return
If we know an asset’s systematic risk, we can use the CAPM to determine its expected return
This is true whether we are talking about financial assets or physical assets
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24. Field Research – look up betas for publicly traded companies
Apple
Google
JP Morgan Chase
Ford
Walmart
Amazon
Facebook
Assuming that the MRP is 8% and Rf is 2%, what is the expected return for each of these companies?
Calculate the beta of an equally weighted portfolio consisting of these companies. What is the expected return on this portfolio?\
Syntax for finding beta is symbol>
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