Title: Risk and Return ... 1 (perfect negative correlation and
1Return and Risk for Capital Market Securities
2Rate 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)
3Standard 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
4Investor 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?
5Return Distributions
- Expected Return and Standard Deviation for stocks
and portfolios with S possible scenarios
6Portfolio Return and Variance
- Whats the relationship between portfolio
variance and variances of individual securities?
7Covariance
- Covariance measures the extent to which two
securities returns tend to vary together
8Correlation
- Correlation is a standardized measure of
covariance - ?AB varies between -1 (perfect negative
correlation and 1 (perfect positive correlation)
9Portfolio Variance and Correlation (2 Securities)
10When 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
11a) 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
12b) 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
13Diversification 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
14Measuring Systematic Risk
- Suppose the return on Security i at time t takes
the form
Expected Return Surprise
Return
15Measuring 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)
16Properties of Beta
- From the properties of linear regression, we can
say about beta
17Beta Estimates (Table 11.5)(updated from
finance.yahoo.com)
18Portfolio 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
19The 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
20Capital Asset Pricing Model (CAPM)
- Since the market portfolio should also plot along
the security market line, for any security i
21Interpreting CAPM
Pure time value
Reward for bearing systematic risk