Portfolio managers make decisions about investment mix and policy, matching investments to objectives, asset allocation for individuals and institutions, and balancing risk against performance. Portfolio management is about strengths, weaknesses, opportunities, and threats in the choice of debt vs. equity, domestic vs. international, growth vs. safety, and other trade-offs encountered in the attempt to maximize return at a given appetite for risk.
Portfolio managers are presented with investment ideas by internal buy-side analysts and sell-side analysts from investment banks. It is their job to sift through the relevant information and use their judgment to buy and sell securities. Throughout the day they read reports, talk to company managers, and monitor industry and economic trends, looking for the right company and time to invest the portfolio’s capital.
A team of analysts and researchers are ultimately responsible for establishing an investment strategy, selecting appropriate investments, and allocating each investment properly for a fund or asset management vehicle. In the case of mutual and exchange-traded funds (ETFs), there are two forms of portfolio management: passive and active. Passive management simply tracks a market index, commonly referred to as indexing or index investing.
Active management involves a single manager, co-managers, or a team of managers who attempt to beat the market return by actively managing a fund’s portfolio through investment decisions based on research and decisions on individual holdings. Closed-end funds are generally actively managed.
Modern portfolio theory was introduced in a 1952 doctoral thesis by Harry Markowitz; see Markowitz model. It assumes that an investor wants to maximize a portfolio’s expected return contingent on any given amount of risk. For portfolios that meet this criterion, known as efficient portfolios, achieving a higher expected return requires taking on more risk, so investors are faced with a trade-off between risk and expected return. This risk-expected return relationship of efficient portfolios is graphically represented by a curve known as the efficient frontier.
All efficient portfolios, each represented by a point on the efficient frontier, are well-diversified. While ignoring higher moments can lead to significant over-investment in risky securities, especially when volatility is high,the optimization of portfolios when return distributions are non-Gaussian is mathematically challenging.
Portfolio optimization often takes place in two stages: optimizing weights of asset classes to hold, and optimizing weights of assets within the same asset class. An example of the former would be choosing the proportions placed in equities versus bonds, while an example of the latter would be choosing the proportions of the stock sub-portfolio placed in stocks X, Y, and Z. Equities and bonds have fundamentally different financial characteristics and have different systematic risk .
Hence can be viewed as separate asset classes; holding some of the portfolio in each class provides some diversification, and holding various specific assets within each class affords further diversification. By using such a two-step procedure one eliminates non-systematic risks both on the individual asset and the asset class level. For the specific formulas for efficient portfolios, see Portfolio separation in mean-variance analysis.
One approach to portfolio optimization is to specify a von Neumann–Morgenstern utility function defined over final portfolio wealth; the expected value of utility is to be maximized. To reflect a preference for higher rather than lower returns, this objective function is increasing in wealth, and to reflect risk aversion it is concave. For realistic utility functions in the presence of many assets that can be held, this approach, while theoretically the most defensible, can be computationally intensive.
Harry Markowitz developed the “critical line method”, a general procedure for quadratic programming that can handle additional linear constraints and upper and lower bounds on holdings. Moreover, in this context, the approach provides a method for determining the entire set of efficient portfolios. Its application here was later explicated by William Sharpe.
Portfolio optimization is usually done subject to constraints, such as regulatory constraints, or illiquidity. These constraints can lead to portfolio weights that focus on a small sub-sample of assets within the portfolio. When the portfolio optimization process is subject to other constraints such as taxes, transaction costs, and management fees, the optimization process may result in an under-diversified portfolio.
Investors may be forbidden by law to hold some assets. In some cases, unconstrained portfolio optimization would lead to short-selling of some assets. However short-selling can be forbidden. Sometimes it is impractical to hold an asset because the associated tax cost is too high. In such cases appropriate constraints must be imposed on the optimization process.
Transaction costs are the costs of trading in order to change the portfolio weights. Since the optimal portfolio changes with time, there is an incentive to re-optimize frequently. However, too frequent trading would incur too-frequent transactions costs; so the optimal strategy is to find the frequency of re-optimization and trading that appropriately trades off the avoidance of transaction costs with the avoidance of sticking with an out-of-date set of portfolio proportions.
This is related to the topic of tracking error, by which stock proportions deviate over time from some benchmark in the absence of re-balancing.Different approaches to portfolio optimization measure risk differently. In addition to the traditional measure, standard deviation, or its square (variance), which are not robust risk measures, other measures include the Sortino ratio, CVaR (Conditional Value at Risk), and statistical dispersion.
Investment is a forward-looking activity, and thus the covariances of returns must be forecast rather than observed. Portfolio optimization assumes the investor may have some risk aversion and the stock prices may exhibit significant differences between their historical or forecast values and what is experienced. In particular, financial crises are characterized by a significant increase in correlation of stock price movements which may seriously degrade the benefits of diversification.
In a mean-variance optimization framework, accurate estimation of the variance-covariance matrix is paramount. Quantitative techniques that use Monte-Carlo simulation with the Gaussian copula and well-specified marginal distributions are effective. Allowing the modeling process to allow for empirical characteristics in stock returns such as autoregression, asymmetric volatility, skewness, and kurtosis is important. Not accounting for these attributes can lead to severe estimation error in the correlations, variances and covariances that have negative biases (as much as 70% of the true values).
Other optimization strategies that focus on minimizing tail-risk (e.g., value at risk, conditional value at risk) in investment portfolios are popular amongst risk averse investors. To minimize exposure to tail risk, forecasts of asset returns using Monte-Carlo simulation with vine copulas to allow for lower (left) tail dependence (e.g., Clayton, Rotated Gumbel) across large portfolios of assets are most suitable. (Tail) risk parity focuses on allocation of risk, rather than allocation of capital.
- “Portfolio Selection”.
- Portfolio Selection: Efficient Diversification of Investments.
- Measuring financial risk and portfolio optimization with a non-Gaussian multivariate model”.
- Journal of Financial and Quantitative Analysis
- Naval Research Logistics Quarterly.
- The Critical Line Method
- Optimization of conditional value-at-risk”
- Optimizing the Omega Ratio using Linear Programming”
- Lectures on stochastic programming: Modeling and theory
- Robust dependence modeling for high-dimensional covariance matrices with financial applications”.
- Portfolio Selection Using Genetic Algorithm
- Is diversification always optimal?”
- The Myth of Diversification”.
- Enhancing mean–variance portfolio selection by modeling distributional asymmetries”
- Canonical vine copulas in the context of modern portfolio management: Are they worth it?”
- Cooperative games with general deviation measures”,
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