QuantPapers

A little article about fat tails.

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Abstract

The purpose of this paper is to present a simple quantitative method that improves the risk-adjusted returns across various asset classes. The approach is examined since 1972 in an allocation framework utilizing a combination of publicly traded indices including the Standard and Poor’s 500 Index (S&P 500), Morgan Stanley Capital International Developed Markets Index (MSCI EAFE), Goldman Sachs Commodity Index (GSCI), National Association of Real Estate Investment Trusts Index (NAREIT), and United States Government 10-Year Treasury Bonds. The empirical results are equity-like returns with bond-like volatility and drawdown, and over thirty consecutive years of positive returns.

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Quasi-Monte Carlo (QMC) methods have been playing an important role for high-dimensional problems
in computational finance. Several techniques, such as the Brownian bridge (BB) and the principal component
analysis, are often used in QMC as possible ways to improve the performance of QMC. This paper proposes
a new BB construction, which enjoys some interesting properties that appear useful in QMC methods. The
basic idea is to choose the new step of a Brownian path in a certain criterion such that it maximizes the
variance explained by the new variable while holding all previously chosen steps fixed. It turns out that
using this new construction, the first few variables are more “important” (in the sense of explained variance)
than those in the ordinary BB construction, while the cost of the generation is still linear in dimension.
We present empirical studies of the proposed algorithm for pricing high-dimensional Asian options and
American options, and demonstrate the usefulness of the new BB.

LinWang.pdf

Abstract

Any admissible portfolio performance measure should satisfy four minimal conditions: it assigns zero performance to each reference portfolio and it is linear, continuous, and nontrivial. Such an admissible measure exists if and only if the securities market obeys the law of one price. A positive admissible measure exists if and only if there is no arbitrage. This article characterizes the (infinite) set of admissible performance measures. It is shown that performance evaluation is generally quite arbitrary. A mutual fund
data set is also used to demonstrate how the measurement method developed here can be applied.

The paper

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Abstract

We study time variation in expected excess bond returns. We run regressions of one-year excess returns on initial forward rates. We find that a single factor, a single tent-shaped linear combination of forward rates, predicts excess returns on one- to five-year maturity bonds with R2 up to 0.44. The return-forecasting factor is countercyclical and forecasts stock returns. An important component of the returnforecasting factor is unrelated to the level, slope, and curvature movements described by most term structure models. We document that measurement errors do not affect our central results. (JEL G0, G1, E0, E4)

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Alternative

The 20th anniversary of what came to be known as “Black Monday”—19 October 1987—provides a platform for considering, yet again, the role of risk in the financial markets. On that single day, the Dow Jones Industrial Average dropped from 2,246 to 1,738, an astonishing decline of almost 25 percent that is nearly twice the largest previous daily decline of 13 percent (24 October 1929). Black Monday was a black swan.

In his book The Black Swan: The Impact of the Highly Improbable, Nassim Nicholas Taleb lists three characteristics of a black swan: rarity (it is an outlier), extremeness (it carries an extreme impact), and retrospective predictability (after it happens, human nature enables us to accept it by concocting explanations that make it seem predictable). Black Monday demonstrates that not only can anything happen in the stock market; anything does happen.

In this article, I take advantage of the anniversary of Black Monday to explore risk as a measurable aspect of investing and as an uncertainty that is always with us. We speak of “forecasts” and “probabilities,” but the application of the laws of probability to our financial markets is badly misguided. Black swans do occur.

Black swans remind us of uncertainty. What other black swans are lurking beyond the horizon, waiting to become part of financial market history? The fact is that the movements of the stock market exhibit a lot of randomness. So, the knowledge that black swans can and do occur holds important lessons for how we think about risk.

Black swans are one reason that many theorists warn us to beware of using past Gaussian stock market return patterns and thinking we have defined the bounds by which we can predict the future. Furthermore, changes in the nature and structure of our equity markets—and a radical shift in the participants—are making shocking and unexpected market aberrations ever more probable. Over the past two centuries, the United States has moved from an agricultural economy to a manufacturing economy, to a service economy, and to a financial economy—and a global one at that. The nation is becoming a country where no business actually makes anything. Our financial intermediaries merely trade pieces of paper, swap stocks and bonds back and forth with one another, and pay the financial croupiers a veritable fortune.

Moreover, long before the recent wave of complex financial products, observers noted that the financial system is particularly prone to innovation. Indeed, the value of these financial “products”—stock market futures and options—has overwhelmed the total value of the stock market itself. Now, one of the riskiest of derivatives, credit-default swaps, alone totals $45 trillion, an amazing ninefold increase over the last three years. These swaps are five times the size of the U.S. national debt and three times U.S. GDP. We have become increasingly vulnerable to black swans because our financial economy has swamped our productive economy.

Direct link to Black Monday and Black Swans

This is from the CFA publications site, you should definitely check it out!!
http://www.cfapubs.org/doi/sum/10.2469/faj.v64.n2.9