Is S&P100 Index a Mean-Variance Efficient Portfolio?

A novel portfolio selection model in a hybrid uncertain environment

The advent of futures contracts on residential housing indices has enabled the creation of synthetic investment positions in residential property, an asset class previously unattainable for institutional investors. To determine whether institutional investors have an incentive to utilize this method to invest in residential real estate, I examine the investment characteristics of the S&P/Case-Shiller Composite Home Price Index over the period 1987-2006. These investment characteristics will determine whether the futures contracts gain usage amongst investors and therefore, at least in part, whether these derivative contracts are successful in the long term. The results show that residential real estate is a low risk/low return type of investment, with risk adjusted performance lower than that of commercial real estate, but higher than most other asset classes. Residential real estate exhibits negative correlations with all other asset classes, making it excellent for diversification purposes. Within mean-variance efficient portfolios, residential property has large weightings in conservative up to mid-risk tolerance portfolios. More aggressive investors would not optimally invest in residential, although they would have a significant weighting on commercial property. However, if considered within an Asset Liability Management framework for a defined benefit pension plan, residential real estate plays little role in the optimal portfolio for any risk tolerance, although commercial real estate does. Overall, residential real estate has investment characteristics quite distinct from the commercial real estate in which institutions have traditionally invested, although the final weight in an optimal portfolio depends upon the objective and risk tolerance of the investor.

In 1992, John Mulvey co-edited a Special Issue, entitled Financial Engineering , in the Annals of Operations Research. In that issue, Guerard, Takano, and Yamane (1992) reported mean-variance efficient portfolios for the Japanese and U.S. equity markets and showed that the use of a regression-weighted composite model of earnings, book value, cash flow, sales, and their relative variables and forecasted earnings, outperformed their respective equity benchmarks by approximately 400 basis points annually. William T. (Bill) Ziemba was the referee of the Guerard et al. (1992) paper. Markowitz and Xu (1994) tested the composite model strategy and found that its excess returns were statistically significant from a variety of models tested, and the composite model strategy was not the result of data mining. We updated our US research in Wilmott (2020) and expended the model to five non-US stock universes. Thirty years after the ANOR issue, we report factor backtesting results and robust regression modeling in creating optimized US and Japanese portfolio results for the 1980-2022 period, a combination of methods and the latest commercially available multi-factor models for portfolio selection. The weighted latent root regression modeling is still relevant. Our results suggest that stock selection models can be effectively employed to deliver excess returns, although the excess returns have fallen. The authors believe that financial anomalies exist, persist, and most likely will exist and can be profitably exploited. Quantitative investing requires constant implementation and discipline to maximize client wealth.

Implied Expected Returns and the Choice of a Mean-Variance Efficient Portfolio Proxy

This paper addresses the problem of approximating random variables in terms of sums consisting of a real constant and of a stochastic integral with respect to a given semimartingale $X$. The criterion is minimization of $\\mathbf{L}^2$–distance, or "least-squares". This problem has a straightforward and well-known solution when $X$ is a Brownian motion or, more generally, a square-integrable martingale, with respect to the underlying probability measure $P$. We address the general, semimartingale case by means of a duality approach; the adjoint variables in this duality are signed measures, absolutely continuous with respect to $P$, under which $X$ behaves like a martingale. It is shown that this duality is useful, in that the value of an appropriately formulated dual problem can be computed fairly easily; that it "has no gap" (i.e., the values of the primal and dual problems coincide); that the signed measure which is optimal for the dual problem can be easily identified whenever it exists; and that the duality is also "strong", in the sense that one can then identify the optimal stochastic integral for the primal problem. In so doing, the theory presented here both simplifies and extends the extant work on the subject. It has also natural connections and interpretations in terms of the theory of "variance-optimal" and "mean-variance efficient" portfolios in Mathematical Finance, pioneered by H. Markowitz and then greatly extended by H. Föllmer, D. Sondermann and most notably M. Schweizer.

Any given set of asset parameters yields a specific mean–variance optimal tangency portfolio. Yet, when the number of assets is large, there are some general characteristics of optimal portfolios that hold ‘almost surely’. This paper investigates these characteristics. We analytically show that the proportion of assets held short converges to 50% as the number of assets grows. This is a fundamental and robust property of mean–variance optimal portfolios, and it does not depend on the parameter estimation method, the investment horizon, or on a special covariance structure. While it is known that optimal portfolios may all have positive weights in some special situations (e.g. uncorrelated assets), the analysis shows that these cases occupy a zero measure in the parameter space, and therefore should not be expected to be observed empirically. Thus, our analysis offers a general explanation for the empirical finding of many short positions in optimal portfolios.

In the formation of an efficient portfolio, many methods can be used. Of course with its own assumptions and advantages. In the process, reasonable investor assumptions tend to be risk averse. Investors who are risk averse are investors who, when faced with two investments with the same expected return, will choose an investment with a lower risk level. If an investor has several efficient portfolio choices, then the most optimal portfolio will be chosen. Optimal portfolio with mean-variance efficient portfolio criteria, investors only invest in risky assets. Investors do not include risk free assets in their portfolios. Mean-variance efficient portfolio is defined as a portfolio that has a minimum variance among all possible portfolio that can be formed, at the mean level of the same expected return. The mean variant method of the two constraints can be used as a basis in determining the optimal portfolio weight by minimizing the risk of portfolio return with two constraints. In this article the problem referred to is symbolized by lamda and beta. With this two-constraint method, the results obtained are more detailed so that they can describe the results of a sharper analysis for an investor.

Stochastic Orderings represent a relevant approach in portfolio selection for various reasons. Firstly, Stochastic Ordering are theoretically justified by Expected Utility theory. Typically, investors are classified according to their attitude toward risk. For each class of investors then, it is possible to define stochastic orderings coherent with investors' preference. Secondly, Stochastic Orderings are flexible enough to allow different definitions of efficiency suitable for each category of investors. This Thesis proposes several applications of Stochastic Orderings to portfolio selection problems. In the first chapter, an analysis of the relationship between Second order of Stochastic Dominance efficient set and Mean Variance Efficient Frontier is proposed. Not only the two sets differ under many aspects, but the Global Minimum Variance portfolio and other Mean Variance Efficient portfolios are dominated in the sense of Second order of Stochastic Dominance. Based on this fact, the chapter concludes proposing dominating strategies able to outperform the Global Minimum Variance portfolio. In the second chapter, starting from recent findings in the literature, that address the behavior of investors as non satiable, nor risk averting nor risk seeking, an extension of classic definition of Stochastic Dominance efficiency, linked to behavioral finance is given. In particular, investors' behavior changes according to market conditions. The last part of the chapter presents a methodology, based on estimation function theory, to test for portfolio efficiency with respect a general stochastic ordering. Both the analysis of efficiency for Second order of Stochastic Dominance and behavioral finance, questioned the validity of highly diversified choices. For this reason, this thesis concludes introducing Risk Diversification measures, a new class of functional quantifying the amount of idiosyncratic risk diversified among the assets in a portfolio. The Mean Risk Diversification Efficient Frontier is introduced, along with the concept of Mean Risk Diversification efficiency. The empirical analysis describes the relationship between risk aversion, Risk Diversification and classic diversification, and show how Risk Diversification based strategies perform under periods of financial distress.

In this study, we produce mean-variance efficient portfolios for various universes in the U.S. equity market, and show that the use of a composite of analyst earnings forecast, revisions, and breadth variable as a portfolio tilt variable and an R&D quadratic term enhances stockholder wealth. The use of the R&D screen creates portfolios in which total active return generally rise relative to the use of the analyst variable. Stock selection may not necessarily rise as risk index and sector index returns are affected by the use of the R&D quadratic term. R&D expenditures of corporations may be integrated into a mean-variance efficient portfolio creation system to enhance stockholder returns and wealth. The use of an R&D variable enhances stockholder wealth relative to the use of capital expenditures or dividends as the quadratic term. The stockholder return implications of the R&D quadratic variable are particularly interesting given that most corporations allocate more of their resources to capital expenditures than R&D.

Deals with a continuous-time version of the Markowitz mean-variance portfolio selection problem. The proposed model is concerned with a basket of securities consisting of one bank account and multiple stocks. One distinct feature of the model is that the market parameters, including the bank interest rate and the appreciation and volatility rates of the stocks, depend on the market mode that switches between a finite number of states. It is assumed that the random regime switching is independent of the random sources that drive the stock prices. Although the model is more realistic and takes into account possible random volatility, it essentially renders the underlying market incomplete. We use a Markov-chain modulated diffusion formulation to model the problem. By using techniques of stochastic linear-quadratic control, we obtain mean-variance efficient portfolios and efficient frontiers in explicitly closed forms, based on solutions of two systems of linear ordinary differential equations. We also address related issues such as minimum variance portfolio and mutual fund theorem. The results are notably different from those for the case when there is no regime switching. Nonetheless, if the interest rate is independent of the Markov chain and is deterministic, then the results exhibit (rather unexpected) similarity to their no-regime-switching counterparts, even if the stocks appreciation and volatility rates are Markov-modulated.

Cross-Asset Skew

The dissertation explores the effect of different constrained portfolio strategies on investors' welfare. A constrained portfolio strategy gives investors a sub-optimal asset allocation that results in investors' welfare losses. To measure those welfare losses I compare constrained portfolios with optimal portfolios by using the concept of the proportionate opportunity cost along with various CRRA utility functions.;Chapter 1 discusses reasons the investors use constrained portfolio strategies, describes the different constrained portfolio strategies that are used in the dissertation, derives the proportionate opportunity cost, describes the derivation of the joint probability distribution functions for asset returns, and describes the way the historical extreme asset returns values are exaggerated to check the robustness of the estimates of the proportionate opportunity cost.;The first essay, in Chapter 2, analyzes investors' welfare losses from being constrained to choose a mean-variance efficient portfolio. I show that the mean-variance strategy shows a moderately good approximation to the optimal portfolio strategy. When extreme values of returns are not exaggerated in the returns distribution, investors' welfare losses do not exceed 5.6% of initial wealth. With extreme returns values exaggerated in the returns distribution, investors' welfare losses do not exceed 11% of initial wealth.;The second essay, in Chapter 3, analyzes investors' welfare losses from investing in a non-well-diversified number of assets. The analysis is performed with and without a short-selling constraint. I show that without the short-selling constraint and with no exaggeration of extreme values of asset returns the lowest well-diversified number of assets for an investor with low risk aversion is 24. The number decreases as the level of risk aversion increases, and when the short-selling constraint is introduced.;The second part of the chapter explores investors' welfare losses when they restrict themselves to either stocks or bonds but not both. I show that for investors with low levels of risk aversion welfare losses do not exceed 1.5% of initial wealth when they invest in only one type of assets. For investors with medium and high levels of relative risk aversion, constrained portfolios that include only one type of assets, stocks only or bonds only, along with Treasury bills, give expected utility about as high as unconstrained portfolios that include both types of assets, stocks and bonds.;The third essay, in Chapter 4, analyzes investors' welfare losses from being restricted from short selling. I show that with a nominally risk-free asset the optimal portfolio strategy with the short-selling constraint performs almost as

Valuing Fuel Diversification in Optimal Investment Policies for Electricity Generation Portfolios

Mean-variance portfolio optimization is widely used by financial professionals as a fundamental strategy for constructing portfolios that achieve the highest returns for a given degree of risk tolerance. This traditional approach suffers from computational instability issues, which are often solved by integrating regularization-based methods. However, regularized mean-variance models overlook sector considerations, emphasizing a need for market-informed portfolio optimization. In this paper, we propose an extended mean-variance portfolio selection framework that incorporates a new adaptive sparse-group least absolute shrinkage and selection operator (LASSO) regularization as a penalty parameter. In the proposed model, the sparse optimal portfolio is selected considering both sectors and assets simultaneously. Moreover, the inclusion of adaptive weights in the regularization, estimated based on chosen criteria, enables the use of more market data in a Markowitz portfolio model. We also develop an efficient alternating direction method of multipliers (ADMM) algorithm that guarantees convergence, for finding the optimal sparse portfolio. The effectiveness of the suggested portfolio selection model is validated by numerical results derived from the constituents of the Standard and Poor’s 500. These results demonstrate superior performance over our selected benchmark models across various evaluation measurements.

We introduce a novel framework for the portfolio selection problem in which investors aim to target a return distribution, and the optimal portfolio has a return distribution as close as possible to the targeted one. The proposed framework can be applied to a variety of investment objectives. In this paper, we focus on improving the higher moments of mean-variance-efficient portfolios by designing the target so that its first two moments match those of the chosen efficient portfolio but has more desirable higher moments. We show theoretically that the optimal portfolio is in general different from the mean-variance portfolio, but remains mean-variance efficient when asset returns are Gaussian. Otherwise, it can move away from the efficient frontier to better match the higher moments of the target distribution. An extensive empirical analysis using three characteristic-sorted datasets and a dataset of 100 individual stocks indicates that the proposed framework delivers a satisfying compromise between mean-variance efficiency and improved higher moments.