The mean-variance formulation by Markowitz in 1956 and its efficient solution by Wolfe in 1959 paved a foundation for modern portfolio selection. In this work we start reviewing basic concepts about portfolio selection, showing one starting solution and then the mean-variance analysis proposed by Markowitz. We show an algorithm for efficient frontier derivation, proposed by Wolfe, and analyze t...

Using daily returns of the S&P500 stocks from 2001 to 2011, we perform a backtesting study of the portfolio optimization strategy based on the extreme risk index (ERI). This method uses multivariate extreme value theory to minimize the probability of large portfolio losses. With more than 400 stocks to choose from, our study applies extreme value techniques in portfolio management on a large sc...

Portfolio theory assumes that investors accept risk. This means thatin the equal rate of return on the two assets, the assets were chosenthat have a lower risk level. Modern portfolio theory is accepted byinvestors who believe that they are not cope with the market. Sothey keep many different types of securities in order to access theoptimum efficiency rate that is close to the rate of return o...

A key result of the Capital Asset Pricing Model (CAPM) is that the market portfolio— the portfolio of all assets in which each asset’s weight is proportional to its total market capitalization—lies on the mean-variance-efficient frontier, the set of portfolios having mean-variance characteristics that cannot be improved upon. Therefore, the CAPM cannot be consistent with efficient frontiers for...

The methods by which fuels can be converted into electricity all belong to different “technology families”: the “gas-fired-turbine-family”, the “coal-fired-turbine-family”, etc. Each family consists of different generations of similar technologies, as in a vintage model. Within a family, the latest generation embodies the most recent level and type of knowledge, becoming more and more outdated ...

This research shows that a portfolio of wheat varieties could enhance profitability and reduce risk over the selection of a single variety for Kansas wheat producers. Many Kansas wheat farmers select varieties solely based on published average yields. This study uses portfolio theory from business investment analysis to find the optimal, yield-maximizing and riskminimizing combination of wheat ...

The problem of modeling claims occurring in periodic random environments is discussed in this paper. In the classical approach of risk theory, the occurrence of claims is modeled by counting processes that do not account for claims following a periodic pattern. The author discusses how the use of the classical approach to model a periodic portfolio might lead to the miscalculation of important ...

Two related and under-studied components of modeling are: a) the process by which simplifying assumptions are derived; and b) the process by which tests of model validity are designed. This case study illustrates these processes for two simple investment models: a) a version of the model supporting classical portfolio theory; and b) a version of a mean-reverting model consistent with some of th...