1. Risk and Return
To risk or not to risk, that is the question…

2. Standard deviation and normal distribution
normal distribution is completely defined by
its mean and standard deviation
the probability of abnormally high or low returns
depends on the standard deviation
Std Devs Cumulative
from mean probability %

3. Markowitz Portfolio Theory
Price changes vs. Normal distribution
IBM - Daily % change
Proportion of Days
Daily % Change

4. Calculating mean (or expected) return
Probability
Probability Return x return
% %
Total %
Mean or
expected
return

5. Calculating variance and standard deviation
Deviation Probability
from mean x squared
Probability Return return deviation
% %
Total
Variance
Standard deviation = square root of variance = 14%

6. Calculating variance and standard deviation of Merck returns from past monthly data
from mean Squared
Month Return return deviation
% %
Total
Mean: /6 = 2.8%
Variance: /6 =
Std dev: Sq root of = % per month
Annualised std dev: x square root (12) = 20.3%

7. Mean and standard deviation
mean measures average (or expected return)
standard deviation (or variance) measures the
spread or variability of returns
risk averse investors prefer high mean & low
standard deviation 20 15
better
expected 10
return 5 5 10 15 20
standard deviation

8. Expected portfolio return
Portfolio Expected Proportion x
proportion (x) return (r) return (xr)
Merck % %
McDonald
Total %
Expected
portfolio
return

9. Calculating covariance and correlation
Deviation from Probability
Return on: mean return: x product of
Prob A B A B deviations
% % % %
Mean Total
Std dev
Covariance
Correlation = = =
coefficient (sd A) x (sd B) x 14
covariance
136

10. Calculating covariance and correlation between Merck and McDonald from past monthly data
Deviation Product
Return: from mean: of
Month Merck McD Merck McD deviations
% % % %
Total
Mean
Covariance: /6 = 17.7
Std dev Merck: %
Std dev McD: %
Corr. co-effic: Cov/(sdMe . sdMcD )
= 17.7/(5.9 x 7.7) = .39

11. Effect of changing correlations: Portfolio of Merck & McDonald

12. Mean & standard deviation: Portfolio of Merck & McDonald

13. The set of portfolios between A and B are efficient portfolios
Expected return B x x x x x x x x x x x x x x x x A x x x x x x
Standard deviation
The set of portfolios between A and B
are efficient portfolios

14. Adding a riskless asset to the efficient frontier
tangency portfolio
riskless rate

15. Portfolio composition with a riskless asset
Regardless of the investor's attitude to
risk, he should split his portfolio between
the tangency portfolio and the riskless asset.
- the tangency portfolio provides the
maximum reward per unit of risk
- the riskless asset adjusts the level of risk

16. Two basic ideas about risk and return
1. Investors require compensation
for risk
2. They care only about a stock's
contribution to portfolio risk

17. Capital asset pricing model
Expected
return
Expected
market
return
Risk
free
rate .5
1.0
Beta
r = rf +
(rm - rf )

18. Capital asset pricing model - example
If Treasury bill rate = %
Bristol Myers Squibb beta =
Expected market risk premium = %
r = rf + beta (rm - rf )
= (8.4) = 12.4%

19. Testing the CAPM Beta vs. Average Risk Premium
Avg Risk Premium 30 20 10
SML
Investors
Market Portfolio
Portfolio Beta
1.0

20. Testing the CAPM Return vs. Book-to-Market Dollars (log scale)
High-minus low book-to-market
Small minus big

21. Validity of capital asset pricing model
EVIDENCE IS MIXED:
1. Long-run average returns are significantly related
to beta.
2. But beta is not a complete explanation. Low beta
stocks have earned higher rates of return than
predicted by the model. So have small company stocks
and stocks with low price to book value ratios.

22. Capital asset pricing model is attractive
Because:
1. It is simple and usually gives sensible
answers.
2. It distinguishes between diversifiable
and non-diversifiable risk.

23. CAPM is controversial BECAUSE:
1. No one knows for sure how to define and
measure the market portfolio -- and using
the wrong market index could lead to the
wrong answers.
2. The model is hard to prove -- or disprove.
3. The model has competitors.

24. The Consumption CAPM
In standard CAPM, investors are concerned with the level and uncertainty of their wealth. (Consumption is outside the model)
In the Consumption CAPM, investors are concerned with the level and uncertainty of their consumption. Stocks that provide low consumption (those with low consumption betas) should have low expected returns.
Is the Consumption CAPM useful?
It has the advantage that you don’t have to identify the market portfolio.
Unfortunately consumption is difficult to measure (especially total consumption for everyone).
Consumption CAPM is difficult to apply for practical use.

25. Arbitrage Pricing Theory (APT)
APT assumes that
r = a + b1 (rfactor 1 ) + b2 (rfactor 2 ) noise
Suppose that a diversified portfolio has no exposure to any
factor. It is essentially risk-free and should offer a return of rf.
So a = rf.
The expected risk premium on a portfolio that is exposed only
to factor 1 (say) should vary in proportion to its exposure to
that factor. If a portfolio is exposed to several factors then its risk will
vary in proportion to those factors. So
r - rf = b1 (rfactor 1 - rf ) + b2 (rfactor 2 - rf )

26. Arbitrage pricing theory (APT)
Preserves distinction between diversifiable and non-diversifiable risk
CAPM and APT can both hold - e.g. CAPM implies one factor APT, with r = r
But APT is more general - e.g. unlike CAPM, market portfolio doesn't have to be efficient
But usefulness of APT requires heavy-duty statistics to
identify factors
measure factor returns
factor1 m