30,086 research outputs found
When do improved covariance matrix estimators enhance portfolio optimization? An empirical comparative study of nine estimators
The use of improved covariance matrix estimators as an alternative to the
sample estimator is considered an important approach for enhancing portfolio
optimization. Here we empirically compare the performance of 9 improved
covariance estimation procedures by using daily returns of 90 highly
capitalized US stocks for the period 1997-2007. We find that the usefulness of
covariance matrix estimators strongly depends on the ratio between estimation
period T and number of stocks N, on the presence or absence of short selling,
and on the performance metric considered. When short selling is allowed,
several estimation methods achieve a realized risk that is significantly
smaller than the one obtained with the sample covariance method. This is
particularly true when T/N is close to one. Moreover many estimators reduce the
fraction of negative portfolio weights, while little improvement is achieved in
the degree of diversification. On the contrary when short selling is not
allowed and T>N, the considered methods are unable to outperform the sample
covariance in terms of realized risk but can give much more diversified
portfolios than the one obtained with the sample covariance. When T<N the use
of the sample covariance matrix and of the pseudoinverse gives portfolios with
very poor performance.Comment: 30 page
Regularizing Portfolio Optimization
The optimization of large portfolios displays an inherent instability to
estimation error. This poses a fundamental problem, because solutions that are
not stable under sample fluctuations may look optimal for a given sample, but
are, in effect, very far from optimal with respect to the average risk. In this
paper, we approach the problem from the point of view of statistical learning
theory. The occurrence of the instability is intimately related to over-fitting
which can be avoided using known regularization methods. We show how
regularized portfolio optimization with the expected shortfall as a risk
measure is related to support vector regression. The budget constraint dictates
a modification. We present the resulting optimization problem and discuss the
solution. The L2 norm of the weight vector is used as a regularizer, which
corresponds to a diversification "pressure". This means that diversification,
besides counteracting downward fluctuations in some assets by upward
fluctuations in others, is also crucial because it improves the stability of
the solution. The approach we provide here allows for the simultaneous
treatment of optimization and diversification in one framework that enables the
investor to trade-off between the two, depending on the size of the available
data set
Diversification Across Mining Pools: Optimal Mining Strategies under PoW
Mining is a central operation of all proof-of-work (PoW) based
cryptocurrencies. The vast majority of miners today participate in "mining
pools" instead of "solo mining" in order to lower risk and achieve a more
steady income. However, this rise of participation in mining pools negatively
affects the decentralization levels of most cryptocurrencies. In this work, we
look into mining pools from the point of view of a miner: We present an
analytical model and implement a computational tool that allows miners to
optimally distribute their computational power over multiple pools and PoW
cryptocurrencies (i.e. build a mining portfolio), taking into account their
risk aversion levels. Our tool allows miners to maximize their risk-adjusted
earnings by diversifying across multiple mining pools which enhances PoW
decentralization. Finally, we run an experiment in Bitcoin historical data and
demonstrate that a miner diversifying over multiple pools, as instructed by our
model/tool, receives a higher overall Sharpe ratio (i.e. average excess reward
over its standard deviation/volatility).Comment: 13 pages, 16 figures. Presented at WEIS 201
Risk minimization and portfolio diversification
We consider the problem of minimizing capital at risk in the Black-Scholes
setting. The portfolio problem is studied given the possibility that a
correlation constraint between the portfolio and a financial index is imposed.
The optimal portfolio is obtained in closed form. The effects of the
correlation constraint are explored; it turns out that this portfolio
constraint leads to a more diversified portfolio
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