CiteULike: pdlug's portfolio

Feasibility of Portfolio Optimization under Coherent Risk Measures

Imre Kondor — 2008-06-28T12:18:14-00:00

(3 Apr 2008)

It is shown that the axioms for coherent risk measures imply that whenever there is an asset in a portfolio that dominates the others in a given sample (which happens with finite probability even for large samples), then this portfolio cannot be optimized under any coherent measure on that sample, and the risk measure diverges to minus infinity. This instability was first discovered on the special example of Expected Shortfall which is used here both as an illustration and as a prompt for generalization.

Asset Allocation: Management Style and Performance Measurement

William Sharpe — 2008-04-25T04:08:31-00:00

Journal of Portfolio Management, (1992), pp. 7-19.

It is widely agreed that asset allocation accounts for a large part of the variability in the return on a typical investor's portfolio. This is especially true if the overall portfolio is invested in multiple funds, each including a number of securities. Asset allocation is generally defined as the allocation of an investor's portfolio among a number of "major" asset classes. Clearly such a generalization cannot be made operational without defining such classes. Once a set of asset classes has been defined, it is important to determine the exposures of each component of an investor's overall portfolio to movements in their returns. Such information can be aggregated to determine the investor's overall effective asset mix. If it does not conform to the desired mix, appropriate alterations can then be made. Once a procedure for measuring exposures to variations in returns of major asset classes is in place, it is possible to determine how effectively individual fund managers have performed their functions and the extent (if any) to which value has been added through active management. Finally, the effectiveness of the investor's overall asset allocation can be compared with that of one or more benchmark asset mixes. An effective way to accomplish all these tasks is to use an asset class factor model. After describing the characteristics of such a model, we illustrate applications of a model with twelve asset classes to analyze the performance of a set of open-end mutual funds between 1985 and 1989.

Portfolio Optimization with Linear and Fixed Transaction Costs

M Lobo — 2008-04-25T04:06:02-00:00

Annals of Operations Research, Vol. 152, No. 1. (July 2007), pp. 376-394.

We consider the problem of portfolio selection, with transaction costs and constraints on exposure to risk. Linear transaction costs, bounds on the variance of the return, and bounds on different shortfall probabilities are efficiently handled by convex optimization methods. For such problems, the globally optimal portfolio can be computed very rapidly. Portfolio optimization problems with transaction costs that include a fixed fee, or discount breakpoints, cannot be directly solved by convex optimization. We describe a relaxation method which yields an easily computable upper bound via convex optimization. We also describe a heuristic method for finding a suboptimal portfolio, which is based on solving a small number of convex optimization problems (and hence can be done efficiently). Thus, we produce a suboptimal solution, and also an upper bound on the optimal solution. Numerical experiments suggest that for practical problems the gap between the two is small, even for large problems involving hundreds of assets. The same approach can be used for related problems, such as that of tracking an index with a portfolio consisting of a small number of assets.

Optimal Execution of Portfolio Transactions

R Almgren — 2007-08-29T15:23:06-00:00

(2001)

We consider the execution of portfolio transactions with the aim of minimizing a combination of volatility risk and transaction costs arising from permanent and temporary market impact. For a simple linear cost model, we explicitly construct the efficient frontier in the space of time-dependent liquidation strategies, which have minimum expected cost for a given level of uncertainty. This analysis yields a number we call the "half-life" of a trade, the natural time for execution in the absence...

Analysis of Kelly-optimal portfolios

Paolo Laureti — 2007-12-18T20:34:40-00:00

(17 Dec 2007)

We investigate the use of Kelly's strategy in the construction of an optimal portfolio of assets. With asset prices undergoing a multiplicative random process, we derive approximate analytical results for the optimal investment fractions under various constraints. We show that, when returns and volatilities of the assets are small and borrowing is forbidden, the Kelly-optimal portfolio lies on Markowitz Efficient Frontier. When short positions are also forbidden, only a small fraction of the available assets is included in the Kelly-optimal portfolio. This phenomenon, that we call condensation, is explored in detail.

Robust Portfolio Management

E Erdogan — 2007-12-10T21:35:04-00:00

In this paper we present robust models for index tracking and active portfolio management. The goal of these models is to control the e#ect of statistical errors in estimating market parameters on the performance of the portfolio. The proposed models allow one to impose additional side constraints such as bounds on the portfolio holdings, constraints on the portfolio beta, limits on cash exposure, etc. The optimal portfolios are computed by solving second-order cone programs. Since the...

Robust portfolio selection problems

G Iyengar — 2006-05-13T09:26:08-00:00

In this paper we show how to formulate and solve robust portfolio selection problems. The objective of these robust formulations is to systematically combat the sensitivity of the optimal portfolio to statistical and modeling errors in the estimates of the relevant market parameters. We introduce "uncertainty structures" for the market parameters and show that the robust portfolio selection problems corresponding to these uncertainty structures can be reformulated as second-order cone programs...

Reaching Goals by a Deadline: Digital Options and Continuous-Time Active Portfolio Management

Sid Browne — 2007-05-29T16:04:39-00:00

(February 1996)

We study a variety of optimal investment problems for objectives related to attaining goals by a fixed terminal time. We start by finding the policy that maximizes the probability of reaching a given wealth level by a given fixed terminal time, for the case where an investor can allocate his wealth at any time between n+1 investment opportunities: n risky stocks, as well as a risk-free asset that has a positive return. This generalizes results recently obtained by Kulldorff and Heath for the case of a single investment opportunity. We then use this to solve related problems for the following cases: (i) when the investor has an external source of income; (ii) when the investor faces external liabilities, as arises in pension fund management; and (iii) when the investor is interested solely in beating the return of a given stochastic benchmark, as is sometimes the case in institutional money management and certain risk management applications. One of the benchmarks we consider for this last problem is that of the return of the optimal growth policy, for which the resulting controlled process is always a supermartingale. For the general case, we provide a thorough and complete analysis of the optimal strategy. For one special case, namely that of a single stock with constant coefficients, the optimal policy is independent of the underlying drift. We explain this by exhibiting a remarkable correspondence between the probability maximizing results and the pricing and hedging of a particular derivative security, known as a digital or binary option. In fact, we show that for this case, the optimal policy to maximize the probability of reaching a given value of wealth by a predetermined time is equivalent to simply buying a European digital option with a particular strike price and payoff. A similar result holds for the general case, but with the stock replaced by a particular (index) portfolio, namely the optimal growth or log-optimal portfolio.

Portfolio Selection

Harry Markowitz — 2006-03-31T18:40:42-00:00

The Journal of Finance, Vol. 7, No. 1. (1952), pp. 77-91.

Portfolios from Sorts

Neil Chriss — 2007-03-19T21:39:57-00:00

(27 April 2005)

Modern portfolio theory produces an optimal portfolio from estimates of expected returns and a covariance matrix. We present a method for portfolio optimization based on replacing expected returns with ordering information, that is, with information about the order of the expected returns. We give a simple and economically rational definition of optimal portfolios that extends Markowitz' meanvariance optimality condition in a natural way; in particular, our construction allows full use of covariance information. We also provide efficient numerical algorithms. The formulation we develop is very general and is easily extended to a variety of cases, for example, where assets are divided into multiple sectors or there are multiple sorting criteria available.

Optimal Portfolios from Ordering Information

Robert Almgren — 2006-12-06T14:53:00-00:00

Journal of Risk (December 2004)

Modern portfolio theory produces an optimal portfolio from estimates of expected returns and a covariance matrix. We present a method for portfolio optimization based on replacing expected returns with ordering information, that is, with information about the order of the expected returns. We give a simple and economically rational definition of optimal portfolios that extends Markowitz' meanvariance optimality condition in a natural way; in particular, our construction allows full use of covariance information. We also provide efficient numerical algorithms. The formulation we develop is very general and is easily extended to a variety of cases, for example, where assets are divided into multiple sectors or there are multiple sorting criteria available.