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Tail Risk Hedging: A Roadmap for Asset Owners
Tail Risk Hedging: A Roadmap for Asset Owners

Linear Factor Models and the Estimation of Expected Returns
Linear Factor Models and the Estimation of Expected Returns

Managing biodiversity correctly – Efficient portfolio - Bio
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Credit Loss Distribution and Copula in Risk Management
Credit Loss Distribution and Copula in Risk Management

... closed analytic form. This results has been extensively used in deriving approximations for more complex portfolios and instruments like derivatives such as collateralized debt obligations (CDO), as well as in regulatory capital estimates and portfolio risk management. Importantly, Vasicek’s result ...
Over/Under-Reaction of Stock Markets
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...  If these pension fund assets are primarily invested by portfolio managers who follow relative strength rules, then the winners portfolio may benefit from additional price pressure in this month.  Similarly, the larger than average returns in November and December may in part be due to price press ...
The n-period Binomial Model
The n-period Binomial Model

... This section shows an important difference between the arithmetic and the geometric mean rate of return. It is shown that the geometric mean is always less than the arithmetic mean and that the difference between the two is approximately half the variance of the return. This is an important distinct ...
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here
here

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... The SDF approach to asset pricing indicates that the price of a security is obtained by "discounting" its future payoff by a valid SDF so that the expected present value of the payoff is equal to the current price. In practice, finding a valid SDF, i.e., an SDF that prices each asset correctly, is i ...
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... Muchinsky, 1985; Harrison, Newman, & Roth, 2006). We will understand the impact of job satisfaction in organisational performance, specifically, in firm value. This variable will be measured by future stock returns. Generally, the variable job satisfaction is measured by surveys (Ostroff, 1992; Tala ...
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download

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NBER WORKING PAPER SERIES FINANCIAL INNOVATION, MARKET PARTICIPATION AND ASSET PRICES Laurent Calvet

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Fat Tails and their (Un)happy Endings
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Modern portfolio theory

Modern portfolio theory (MPT) is a theory of finance that attempts to maximize portfolio expected return for a given amount of portfolio risk, or equivalently minimize risk for a given level of expected return, by carefully choosing the proportions of various assets. Although MPT is widely used in practice in the financial industry and several of its creators won a Nobel memorial prize for the theory, in recent years the basic assumptions of MPT have been widely challenged by fields such as behavioral economics.MPT is a mathematical formulation of the concept of diversification in investing, with the aim of selecting a collection of investment assets that has lower overall risk than any other combination of assets with the same expected return. This is possible, intuitively speaking, because different types of assets sometimes change in value in opposite directions. For example, to the extent prices in the stock market move differently from prices in the bond market, a combination of both types of assets can in theory generate lower overall risk than either individually. Diversification can lower risk even if assets' returns are positively correlated.More technically, MPT models an asset's return as a normally or elliptically distributed random variable, defines risk as the standard deviation of return, and models a portfolio as a weighted combination of assets, so that the return of a portfolio is the weighted combination of the assets' returns. By combining different assets whose returns are not perfectly positively correlated, MPT seeks to reduce the total variance of the portfolio return. MPT also assumes that investors are rational and markets are efficient.MPT was developed in the 1950s through the early 1970s and was considered an important advance in the mathematical modeling of finance. Since then, some theoretical and practical criticisms have been leveled against it. These include evidence that financial returns do not follow a normal distribution or indeed any symmetric distribution, and that correlations between asset classes are not fixed but can vary depending on external events (especially in crises). Further, there remains evidence that investors are not rational and markets may not be efficient. Finally, the low volatility anomaly conflicts with CAPM's trade-off assumption of higher risk for higher return. It states that a portfolio consisting of low volatility equities (like blue chip stocks) reaps higher risk-adjusted returns than a portfolio with high volatility equities (like illiquid penny stocks). A study conducted by Myron Scholes, Michael Jensen, and Fischer Black in 1972 suggests that the relationship between return and beta might be flat or even negatively correlated.
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