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Risk and Return ... 1 (perfect negative correlation and

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Title: Risk and Return ... 1 (perfect negative correlation and


1
Return and Risk for Capital Market Securities
2
Rate of Return Concepts
  • Dollar return
  • Number of received over a period (one year,
    say)
  • Sum of cash distributed plus capital gain (loss)
  • Percentage return
  • Dollar return/(beginning-of-period value)
  • cash distribution capital gain
  • Real vs. Nominal return
  • Real return, r, related to nominal return, R,
    by 1R (1r)(1h)

3
Standard Deviation as a Measure of Risk
  • Variance and standard deviation give equal weight
    to observations above below mean
  • These make sense as risk measures if the return
    distribution is symmetrical

4
Investor Portfolio Choices Risk and Return
  • How does holding securities in portfolios affect
    the risk-return combinations available to
    investors?
  • When and why does it pay to diversify across
    securities?

5
Return Distributions
  • Expected Return and Standard Deviation for stocks
    and portfolios with S possible scenarios

6
Portfolio Return and Variance
  • Whats the relationship between portfolio
    variance and variances of individual securities?

7
Covariance
  • Covariance measures the extent to which two
    securities returns tend to vary together

8
Correlation
  • Correlation is a standardized measure of
    covariance
  • ?AB varies between -1 (perfect negative
    correlation and 1 (perfect positive correlation)

9
Portfolio Variance and Correlation (2 Securities)
10
When Does Diversification Pay?
  • Combine two securities with the lowest possible
    return correlation
  • Combine large numbers of identical securities
    whose returns are less than perfectly correlated

11
a) Diversifying with 2 Securities
  • With perfect positive correlation, combining
    securities does not improve the risk-return
    possibilities (opportunity set)
  • The lower the correlation, the more the
    opportunity set improves
  • With perfect negative correlation, we can
    eliminate risk altogether

12
b) Diversifying Across Many, Identical
Securities
  • Diversification can eliminate unsystematic risk
  • Systematic risk stems from the common thread
    running through all securities returns and
    cannot be diversified away

13
Diversification and the Reward for Risk
  • Total Risk Systematic Risk Unsystematic Risk
  • Well diversified portfolios should contain almost
    entirely systematic risk
  • Investors shouldnt expect a reward for bearing
    unsystematic risk, since that can be eliminated
    (fairly cheaply) through diversification

14
Measuring Systematic Risk
  • Suppose the return on Security i at time t takes
    the form

Expected Return Surprise
Return
15
Measuring Systematic Risk Using Regression
  • Suppose we regress returns on Security i against
    the returns on the market portfolio
  • The regression error term represents ?it, the
    surprise return component
  • The slope coefficient, ?it, represents the extent
    to which i moves with the market
  • R2 total risk that is systematic
    (1-R2 unsystematic)

16
Properties of Beta
  • From the properties of linear regression, we can
    say about beta

17
Beta Estimates (Table 11.5)(updated from
finance.yahoo.com)
18
Portfolio Beta
  • Portfolio beta is the weighted average of the
    individual security betas
  • Since ?M 1, the average beta of all securities
    is equal to 1

19
The Security Market Line
  • All securities should plot along the same
    security market line
  • If they didnt, investors would shun one security
    in favor of another

20
Capital Asset Pricing Model (CAPM)
  • Since the market portfolio should also plot along
    the security market line, for any security i

21
Interpreting CAPM
Pure time value
Reward for bearing systematic risk
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