Financial Management I
Module 2 Notes
William N. Goetzmann
Class II
The Geography of the Efficient Frontier
In the previous class, we saw how the risk and the return for investments may be
characterized by measures of central tendency and measures of variation, i.e. mean and standard
deviaiton. In fact, statistics are the foundations of modern finance, and virtually all the
innovations of the past thirty years, called "Modern Portfolio Theory," have been based upon
statistical models. Because of this, it is useful to review what a statistic is, and how it relates to
theinvestment problem. In general, a statistic is a function that reduces a large amount of
information to a small amount. For instance, the average is a single number that summarizes the
typical "location" of a set of numbers. Statistics boil down a lot of information to a few useful
numbers -- as such, they ignore a great deal. Before modern portfolio theory, the decision about
whether to include a security in a portfolio was based principally upon fundamental analysis of
the firm, its financial statements and its dividend policy. Finance professor Harry Markowitz
began a revolution by suggesting that the value of a security to an investor might best be evaluated
by its mean, its standard deviation, and its correlation to other securities in the portfolio. This
audacious suggestion amounted to ignoring a lot of information about the firm -- its earnings, its
dividend policy, its captial structure, its market, its competitors -- and calculating a few simple
statistics. In this class, we will follow Markowitz' lead and see where the technology of modern
portfolio theory will take us.
I. The Risk and return of securities
- historical estimates of risk and return
- variation across industry
- reduction of relevant information to two dimensions
I. Two dimensions of investor choice
Some investors prefer D, some prefer E, some prefer A. No songle asset dominates.
In fact, using historical risk and return data, we can look at investor choices over major U.S. asset
classes. The axes plot monthly stadard deviation of total returns, and average monthly returns over
the period 1926 through 1995. Notice that small stocks, provide the highest return, but with the
highest risk. Which asset class would you choose it invest your money? Is there any single asset
class that dominates the rest?
(Courtesy Ibbotson Associates)
II. Portfolios of Assets
The dynamics of stocks
Correlation, Covariance and Boom and Bust cycles
The standard deviation of any portfolio of A and B Can be expressed
as:
What if the correlation of A&B = 0 ?
What if the correlation of A&B = 1 ?
What if the correlation of A&B = -1 ?
Negative Weights, and shorting stock
III. More Securities and More Diversification
III. The Effects of Diversification
- As the number of assets increases, the risk of the portfolio
decreases
- There are limits to the extent that the risk can decrease
- This limit identifies the level of systematic risk
IV. Features of the Efficient Frontier
The Efficient Set:
minimum level of risk for each level of return
maximum level of return for each level of risk
Minimum Variance Portfolio
Maximum Return Portfolio
The Inefficient Frontier
V. Markowitz and the First Efficient Frontier
- upside down
- needed lots of correlation estimates
VI. The Efficient Frontier with the Riskless Asset
- Frontier becomes a line
- Lies everywhere above curve
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