The Portable Financial Analyst: What Practitioners Need to Know / Edition 2 available in Hardcover
The Portable Financial Analyst: What Practitioners Need to Know / Edition 2
- ISBN-10:
- 0471267600
- ISBN-13:
- 9780471267607
- Pub. Date:
- 09/29/2003
- Publisher:
- Wiley
The Portable Financial Analyst: What Practitioners Need to Know / Edition 2
Hardcover
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Product Details
| ISBN-13: | 9780471267607 |
|---|---|
| Publisher: | Wiley |
| Publication date: | 09/29/2003 |
| Series: | Wiley Finance , #151 |
| Edition description: | REV |
| Pages: | 272 |
| Product dimensions: | 4.65(w) x 10.43(h) x 0.94(d) |
About the Author
Read an Excerpt
The Portable Financial Analyst
What Practitioners Need to Know
By Mark P. Kritzman
John Wiley & Sons
Copyright © 2003
Mark P. Kritzman
All right reserved.
ISBN: 0-471-26760-0
Chapter One
The Nobel Prize
On October 16, 1990, the Royal Swedish Academy of Sciences announced
its selection for the Nobel Memorial Prize in Economic Science. For the
first time since the prize for economics was established in 1968, the Royal
Academy chose three individuals whose primary contributions were in finance
and whose affiliations were not with arts and science schools, but
rather with schools of business. Harry Markowitz was cited for his pioneering
research in portfolio selection, while William Sharpe shared the
award for developing an equilibrium theory of asset pricing. Merton Miller
was a co-winner for his contributions in corporate finance, in which he
showed, along with Franco Modigliani, that the value of a firm should be
invariant to its capital structure and dividend policy.
The pioneering research of these individuals revolutionized finance and
accelerated the application of quantitative methods to financial analysis.
PORTFOLIO SELECTION
In his classic article, "Portfolio Selection," Markowitz submitted that investors
should notchoose portfolios that maximize expected return, because
this criterion by itself ignores the principle of diversification. He
proposed that investors should instead consider variances of return, along
with expected returns, and choose portfolios that offer the highest expected
return for a given level of variance. He called this rule the E-V maxim.
Markowitz showed that a portfolio's expected return is simply the
weighted average of the expected returns of its component securities. A
portfolio's variance is a more complicated concept, however. It depends on
more than just the variances of the component securities.
The variance of an individual security is a measure of the dispersion of
its returns. It is calculated by squaring the difference between each return in
a series and the mean return for the series, then averaging these squared differences.
The square root of the variance (the standard deviation) is often
used in practice because it measures dispersion in the same units in which
the underlying return is measured.
Variance provides a reasonable gauge of a security's risk, but the average
of the variances of two securities will not necessarily give a good indication
of the risk of a portfolio comprising these two securities. The
portfolio's risk depends also on the extent to which the two securities move
together-that is, the extent to which their prices react in like fashion to a
particular event.
To quantify co-movement among security returns, Markowitz introduced
the statistical concept of covariance. The covariance between two
securities equals the standard deviation of the first times the standard deviation
of the second times the correlation between the two.
The correlation, in this context, measures the association between
the returns of two securities. It ranges in value from 1 to -1. If one security's
returns are higher than its average return when another security's
returns are higher than its average return, for example, the correlation
coefficient will be positive, somewhere between 0 and 1. Alternatively, if
one security's returns are lower than its average return when another security's
returns are higher than its average return, then the correlation
will be negative.
The correlation, by itself, is an inadequate measure of covariance because
it measures only the direction and degree of association between securities'
returns. It does not account for the magnitude of variability in
each security's returns. Covariance captures magnitude by multiplying the
correlation by the standard deviations of the securities' returns.
Consider, for example, the covariance of a security with itself. Obviously,
the correlation in this case equals 1. A security's covariance with itself
thus equals the standard deviation of its returns squared, which, of
course, is its variance.
Finally, portfolio variance depends also on the weightings of its
constituent securities-the proportion of a portfolio's market value invested
in each. The variance of a portfolio consisting of two securities
equals the variance of the first security times its weighting squared
plus the variance of the second security times its weighting squared plus
twice the covariance between the securities times each security's weighting.
The standard deviation of this portfolio equals the square root of
the variance.
From this formulation of portfolio risk, Markowitz was able to offer
two key insights. First, unless the securities in a portfolio are perfectly inversely
correlated (that is, have a correlation of -1), it is not possible to
eliminate portfolio risk entirely through diversification. If we divide a
portfolio equally among its component securities, for example, as the
number of securities in the portfolio increases, the portfolio's risk will
tend not toward zero but, rather, toward the average covariance of the
component securities.
Second, unless all the securities in a portfolio are perfectly positively
correlated with each other (a correlation of 1), a portfolio's standard deviation
will always be less than the weighted average standard deviation of
its component securities. Consider, for example, a portfolio consisting of
two securities, both of which have expected returns of 10 percent and standard
deviations of 20 percent and which are uncorrelated with each other.
If we allocate portfolio assets equally between these two securities, the
portfolio's expected return will equal 10 percent, while its standard deviation
will equal 14.14 percent. The portfolio offers a reduction in risk of
nearly 30 percent relative to investment in either of the two securities separately.
Moreover, this risk reduction is achieved without any sacrifice of expected
return.
Markowitz also demonstrated that, for given levels of risk, we can
identify particular combinations of securities that maximize expected return.
He deemed these portfolios "efficient" and referred to a continuum
of such portfolios in dimensions of expected return and standard deviation
as the efficient frontier. According to Markowitz's E-V maxim, investors
should choose portfolios located along the efficient frontier. It is
almost always the case that there exists some portfolio on the efficient
frontier that offers a higher expected return and less risk than the least
risky of its component securities (assuming the least risky security is not
completely riskless).
The financial community was slow to implement Markowitz's theory,
in large part because of a practical constraint. In order to estimate the risk
of a portfolio of securities, one must estimate the variances of every security,
along with the covariances between every pair of securities. For a portfolio
of 100 securities, this means calculating 100 variances and 4,950
covariances-5,050 risk estimates! In general, the number of required risk
estimates (variances and covariances) equals n(n + 1)/ 2, where n equals the
number of securities in the portfolio. In 1952, when Markowitz published
"Portfolio Selection," the sheer number of calculations formed an obstacle
in the way of acceptance. It was in part the challenge of this obstacle that
motivated William Sharpe to develop a single index measure of a security's
risk.
THE CAPITAL ASSET PRICING MODEL
James Tobin, the 1981 winner of the Nobel Prize in economics, showed
that the investment process can be separated into two distinct steps: (1) the
construction of an efficient portfolio, as described by Markowitz, and (2)
the decision to combine this efficient portfolio with a riskless investment.
This two-step process is the famed separation theorem.
Sharpe extended Markowitz's and Tobin's insights to develop a theory
of market equilibrium under conditions of risk. First, Sharpe showed that
there is along the efficient frontier a unique portfolio that, when combined
with lending or borrowing at the riskless interest rate, dominates all other
combinations of efficient portfolios and lending or borrowing.
Figure 1.1 shows a two-dimensional graph, with risk represented by
the horizontal axis and expected return represented by the vertical axis.
The efficient frontier appears as the positively sloped concave curve. The
straight line emanating from the vertical axis at the riskless rate illustrates
the efficient frontier with borrowing and lending. The segment of the line
between the vertical axis and the efficient portfolio curve represents some
combination of the efficient portfolio M and lending at the riskless rate,
while points along the straight line to the right represent some combination
of the efficient portfolio and borrowing at the riskless rate. Combinations
of portfolio M and lending or borrowing at the riskless rate will always offer
the highest expected rate of return for a given level of risk.
With two assumptions, Sharpe demonstrated that in equilibrium investors
will prefer points along the line emanating from the riskless rate
that is tangent to M. The requisite assumptions are (1) there exists a single
riskless rate at which investors can lend and borrow in unlimited amounts,
and (2) investors have homogeneous expectations regarding expected returns,
variances, and covariances. Under these assumptions, Sharpe showed
that portfolio M is the market portfolio, which represents the maximum
achievable diversification.
Within this model, Sharpe proceeded to demonstrate that risk can be
partitioned into two sources-that caused by changes in the value of the
market portfolio, which cannot be diversified away, and that caused by
nonmarket factors, which is diversified away in the market portfolio. He
labeled the nondiversifiable risk systematic risk and the diversifiable risk
unsystematic risk.
Sharpe also showed that a security's systematic risk can be estimated
by regressing its returns (less the riskless rate) against the market portfolio's
returns (less riskless rate). The slope from this regression equation,
which Sharpe called beta, quantifies the security's systematic risk when
multiplied by the market risk. The unexplained variation in the security's
return (the residuals from the regression equation) represents the security's
unsystematic risk. He then asserted that, in an efficient market, investors
are only compensated for bearing systematic risk, because it cannot be diversified
away, and the expected return of a security is, through beta, linearly
related to the market's expected return.
It is important to distinguish between a single index model and the
Capital Asset Pricing Model (CAPM). A single index model does not require
the intercept of the regression equation (alpha) to equal 0 percent. It
simply posits a single source of systematic, or common, risk. Stated differently,
the residuals from the regression equation are uncorrelated with each
other. The important practical implication is that it is not necessary to estimate
covariances between securities. Each security's contribution to portfolio
risk is captured through its beta coefficient. The CAPM, by contrast,
does require the intercept of the regression equation to equal 0 percent in
an efficient market. The CAPM itself does not necessarily assume a single
source of systematic risk. This is tantamount to allowing for some correlation
among the residuals.
INVARIANCE PROPOSITIONS
Between the publication of Markowitz's theory of portfolio selection and
Sharpe's equilibrium theory of asset pricing, Franco Modigliani (the 1985
Nobel Prize winner in economics) and Merton Miller published two related
articles in which they expounded their now famous invariance
propositions. The first, "The Cost of Capital, Corporation Finance, and
the Theory of Investment," appeared in 1958. It challenged the then
conventional wisdom that a firm's value depends on its capital structure
(i.e., its debt/equity mix).
In challenging this traditional view, Modigliani and Miller invoked the
notion of arbitrage. They argued that if a leveraged firm is undervalued, investors
can purchase its debt and its shares. The interest paid by the firm is
offset by the interest received by the investors, so the investors end up holding
a pure equity stream. Alternatively, if an unleveraged firm is undervalued,
investors can borrow funds to purchase its shares. The substitutability
of individual debt for corporate debt guarantees that firms in the same risk
class will be valued the same, regardless of their respective capital structures.
In essence, Modigliani and Miller argued in favor of the law of one price.
In a subsequent article, "Dividend Policy, Growth, and the Valuation
of Shares," Modigliani and Miller proposed that a firm's value is invariant,
not only to its capital structure, but also to its dividend policy (assuming
the firm's investment decision is set independently). Again, they invoked
the notion of substitutability, arguing that repurchasing shares has the
same effect as paying dividends; thus issuing shares and paying dividends is
a wash. Although the cash component of an investor's return may differ as
a function of dividend policy, the investor's total return, including price
change, should not change with dividend policy.
Modigliani and Miller's invariance propositions provoked an enormous
amount of debate and research. Much of the sometimes spirited debate centered
on the assumption of perfect capital markets. In the real world, where
investors cannot borrow and lend at the riskless rate of interest, where both
corporations and individuals pay taxes, and where investors do not share
equal access with management to relevant information, there is only spotty
evidence to support Modigliani and Miller's invariance propositions.
But the value of the contributions of these Nobel laureates does not depend
on the degree to which their theories hold in an imperfect market environment.
It depends, rather, on the degree to which they changed the
financial community's understanding of the capital markets. Markowitz
taught us how to evaluate investment opportunities probabilistically, while
Sharpe provided us with an equilibrium theory of asset pricing, enabling us
to distinguish between risk that is rewarded and risk that is not rewarded.
Miller, in collaboration with Modigliani, demonstrated how the simple notion
of arbitrage can be applied to determine value, which subsequently
was extended to option valuation-yet another innovation that proved
worthy of the Nobel Prize.
(Continues...)
Excerpted from The Portable Financial Analyst
by Mark P. Kritzman
Copyright © 2003 by Mark P. Kritzman.
Excerpted by permission.
All rights reserved. No part of this excerpt may be reproduced or reprinted without permission in writing from the publisher.
Excerpts are provided by Dial-A-Book Inc. solely for the personal use of visitors to this web site.
Table of Contents
Foreword: Time and Magic: What This Book Is About.Preface.
Chapter 1. The Noble Prize.
Chapter 2. Uncertainty.
Chapter 3. Utility.
Chapter 4. Lognormality.
Chapter 5. Return and Risk.
Chapter 6. Higher Moments.
Chapter 7. Duration and Convexity.
Chapter 8. The Term Structure of Interest Rates.
Chapter 9. Serial Dependence.
Chapter 10. Time Diversification.
Chapter 11. Regressions.
Chapter 12. Factor Methods.
Chapter 13. Estimating Volatility: Part I.
Chapter 14. Estimating Volatility: Part II.
Chapter 15. Hypothesis Testing.
Chapter 16. Future Value and Risk of Loss.
Chapter 17. Event Studies.
Chapter 18. Simulation.
Chapter 19. Value at Risk.
Chapter 20. Optimization.
Chapter 21. Risk Budgets.
Chapter 22. Hedging.
Chapter 23. Opton Valuation and Replication.
Chapter 24. Commodity Futures Conracts.
Chapter 25. Currencies.
Glossary.
Notes.
Index.