Linear programing models for portfolio optimization using a benchmark

We consider the problem of constructing a perturbed portfolio by utilizing a benchmark portfolio. We propose two computationally efficient portfolio optimization models, the mean-absolute deviation risk and the Dantzig-type, which can be solved using linear programing. These portfolio models push the existing benchmark toward the efficient frontier through sparse and stable asset selection. We implement these models on two benchmarks, a market index and the equally-weighted portfolio. We carry out an extensive out-of-sample analysis with 11 empirical datasets and simulated data. The proposed portfolios outperform the benchmark portfolio in various performance measures, including the mean return and Sharpe ratio.     

Private equity benchmarks and portfolio optimization

Portfolio optimization using private equity is typically based on one of three indices: listed private equity, transaction-based private equity, or appraisal value-based private equity indices. However, we show that none of these indices is fully suitable for portfolio optimization. We introduce here a new benchmark index for venture capital and buyouts, which is updated monthly, adjusted for autocorrelation (de-smoothing), and available contemporaneously. We illustrate how our benchmark enables superior quantitative portfolio optimization.     

Risk-sensitive benchmarked asset management

This paper extends the risk-sensitive asset management theory developed by Bielecki and Pliska and by Kuroda and Nagai to the case where the investor's objective is to outperform an investment benchmark. The main result is a mutual fund theorem. Every investor following the same benchmark will take positions, in proportions dependent on his/her risk sensitivity coefficient, in two funds: the log-optimal portfolio and a second fund which adjusts for the correlation between the traded assets, the benchmark and the underlying valuation factors.     

Benchmark-based evaluation of portfolio performance: a characterization

Benchmarking is a universal practice in portfolio management and is well-studied in the optimal portfolio selection literature. This paper derives axiomatic foundations of the relative return, which underlies a benchmark-based evaluation of portfolio performance. We show that the existence of a benchmark naturally arises from a few basic axioms and is tightly linked to the economic theory. Our method relies on the use of both axiomatic and economic approaches to index number theory. We also analyze the problem of optimal portfolio selection under complete uncertainty about a future price system, where the objective function is the relative return.     

A note on the returns from minimum variance investing

Disappointed with the performance of market weighted benchmark portfolios yet skeptical about the merits of active portfolio management, investors in recent years turned to alternative index definitions. Minimum variance investing is one of these popular concepts. I show in this paper that the portfolio construction process behind minimum variance investing implicitly picks up risk-based pricing anomalies. In other words the minimum variance tends to hold low beta and low residual risk stocks. Long/short portfolios based on these characteristics have been associated in the empirical literature with risk adjusted outperformance. This paper shows that 83% of the variation of the minimum variance portfolio excess returns (relative to a capitalization weighted alternative) can be attributed to the FAMA/FRENCH factors as well as to the returns on two characteristic anomaly portfolios. All regression coefficients (factor exposures) are highly significant, stable over the estimation period and correspond remarkably well with our economic intuition. The paper also shows that a direct combination of market weighted benchmark portfolio and risk based characteristic portfolios will provide a statistically significant improvement over the indirect pickup via the minimum variance portfolio.     

Modern portfolio management with conditioning information

This paper studies models in which active portfolio managers utilize conditioning information unavailable to their clients to optimize performance relative to a benchmark. We derive explicit solutions for the optimal strategies with multiple risky assets, with or without a risk-free asset, and consider various constraints on portfolio risks or weights. The optimal strategies feature a mean–variance efficient component (to minimize portfolio variance), and a hedging demand for the benchmark portfolio (to maximize correlation with the benchmark). A currency portfolio example shows that the optimal strategies improve the measured performance by 53% out of sample, compared with portfolios ignoring conditioning information.     

Long-Term Synthetic Puts

We present the possibility of replicating the performance of a long-term put, which is not available in the financial markets, by a set of other traded financial assets. First, a benchmark portfolio is formed out of one share of stock and one put on the stock with a certain exercise price and a long time until maturity. The general form of a portfolio, consisting of shares of stock, bonds, and options on the stock, is discussed, which is expected to perform like the benchmark portfolio. Then a class of these synthetic puts is examined to determine which type of synthetic put may dominate the others.     

Efficient fund of hedge funds construction under downside risk measures

We consider portfolio allocation in which the underlying investment instruments are hedge funds. We consider a family of utility functions involving the probability of outperforming a benchmark and expected regret relative to another benchmark. Non-normal return vectors with prescribed marginal distributions and correlation structure are modeled and simulated using the normal-to-anything method. A Monte Carlo procedure is used to obtain, and establish the quality of, a solution to the associated portfolio optimization model. Computational results are presented on a problem in which we construct a fund of 13 CSFB/Tremont hedge-fund indices.     

A dynamic model of active portfolio management with benchmark orientation

This paper studies optimal dynamic portfolios for investors concerned with the performance of their portfolios relative to a benchmark. Assuming that asset returns follow a multi-linear factor model similar to the structure of Ross (1976) [Ross, S., 1976. The arbitrage theory of the capital asset pricing model. Journal of Economic Theory, 13, 342–360] and that portfolio managers adopt a mean tracking error analysis similar to that of Roll (1992) [Roll, R., 1992. A mean/variance analysis of tracking error. Journal of Portfolio Management, 18, 13–22], we develop a dynamic model of active portfolio management maximizing risk adjusted excess return over a selected benchmark. Unlike the case of constant proportional portfolios for standard utility maximization, our optimal portfolio policy is state dependent, being a function of time to investment horizon, the return on the benchmark portfolio, and the return on the investment portfolio. We define a dynamic performance measure which relates portfolio’s return to its risk sensitivity. Abnormal returns at each point in time are quantified as the difference between the realized and the model-fitted returns. Risk sensitivity is estimated through a dynamic matching that minimizes the total fitted error of portfolio returns. For illustration, we analyze eight representative mutual funds in the U.S. market and show how this model can be used in practice.     

Robust and adaptive algorithms for online portfolio selection

We present an online approach to portfolio selection. The motivation is within the context of algorithmic trading, which demands fast and recursive updates of portfolio allocations as new data arrives. In particular, we look at two online algorithms: Robust-Exponentially Weighted Least Squares (R-EWRLS) and a regularized Online minimum Variance algorithm (O-VAR). Our methods use simple ideas from signal processing and statistics, which are sometimes overlooked in the empirical financial literature. The two approaches are evaluated against benchmark allocation techniques using four real data sets. Our methods outperform the benchmark allocation techniques in these data sets in terms of both computational demand and financial performance.     

The Impact of Downward Rating Momentum

Rating downgrades are known to make subsequent downgrades more likely. We analyze the impact of this “downward momentum” on credit portfolio risk and bond portfolio management. Using Standard&Poor’s ratings from 1996 to 2005, we apply a novel approach to estimate a transition matrix that is sensitive to previous downgrades and contrast it with an insensitive benchmark matrix. First, we find that, under representative economic conditions, investors who rely on insensitive transition matrices underestimate the momentum-sensitive Value-at-Risk (VaR), on average, by 107 basis points. Second, we show that bond portfolio managers should use our downgrade-sensitive probabilities of default as they seem to be better calibrated than momentum-insensitive estimates.     

Measuring investment performance with a stochastic parameter regression model

This paper develops a generalization of the Hildreth and Houck (1968) random coefficient model for use in evaluating the macroforecasting ability of portfolio managers. Most studies have assumed that astute managers ignore the strength of the market trend and create a binary portfolio beta with one value during up markets and a lower value during down markets. In contrast, this paper examines a model in which the superior manager adjusts beta period by period according to changing market conditions. The findings indicate that portfolio managers are not superior macroforecasters.     

Predicting systematic risk: Implications from growth options

In accordance with the well-known financial leverage effect, decreases in stock prices cause an increase in the levered equity beta for a given unlevered beta. However, as growth options are more volatile and have higher risk than assets in place, a price decrease may decrease the unlevered equity beta via an operating leverage effect. This is because price decreases are associated with a proportionately higher loss in growth options than in assets in place. Most of the existing literature focuses on the financial leverage effect: This paper examines both effects. We show, with a simple option pricing model, the opposing effects at work when the firm is a portfolio of assets in place and growth options. Our empirical results show that, contrary to common belief, the operating leverage effect largely dominates the financial leverage effect, even for initially highly levered firms with presumably few growth options. We then link variations in betas to measurable firm characteristics that proxy for the fraction of the firm invested in growth options. We show that these proxies jointly predict a large fraction of future cross-sectional differences in betas. These results have important implications on the predictability of equity betas, hence on empirical asset pricing and on portfolio optimization that controls for systematic risk.     

The diversification cost of large,concentrated equity stakes. How big is it? Is it justified?

While the hypothesis that ownership concentration can affect the value of a company has seen a lot of empirical study, little light has been shed on a complementary problem, that these concentrated owners have a cost of their position due to an undiversified portfolio. Using a unique data set of the actual diversification of all Norwegian equity owners, we show that the largest owners of a corporation in fact have very undiversified equity portfolios, and that such owners have significant costs to their concentrated portfolios. At the level of risk of a benchmark portfolio, if they were to move from their present portfolio composition in risky assets to a well diversified portfolio, their returns would have increased by about 13 percentage points in annual terms. We ask whether this cost can be explained by estimated benefits of ownership concentration (private benefits), and show that extant estimates of private benefits are too low to offset our cost estimates.     

On the price of risk in a mean-risk optimization model

We investigate a mean-risk model for portfolio optimization where the risk quantifier is selected as a semi-deviation or as a standard deviation of the portfolio return. We analyse the existence of solutions to the problem under general assumptions. When the short positions are not constrained, we establish a lower bound on the cost of risk associated with optimizing the mean–standard deviation model and show that optimal solutions do not exist for any positive price of risk which is smaller than that bound. If the investment allocations are constrained, then we obtain a lower bound on the price of risk in terms of the shadow prices of said constraints and the data of the problem. A Value-at-Risk constraint in the model implies an upper bound on the price of risk for all feasible portfolios. Furthermore, we provide conditions under which using this upper bound as the cost of risk parameter in the model provides a non-dominated optimal portfolio with respect to the second-order stochastic dominance. Additionally, we study the relationship between minimizing the mean–standard deviation objective and maximizing the coefficient of variation and show that both problems are equivalent when the upper bound is used as the cost of risk. Additional relations between the Value-at-Risk constraint and the coefficient of variation are discussed as well. We illustrate the results numerically.     

Benchmarking the performance of recommended allocations to equities,bonds, and cash by international investment houses

We conduct performance tests of the recommended asset allocations made by a panel of international investment houses (the “Houses”) from 1982 through 2005. We compare the returns and Sharpe Ratios from the recommended-weight portfolio against those of several benchmark portfolios and to a set of 10,000 returns and Sharpe Ratios from randomly shuffled-weight and shuffled-weight change portfolios. We find that the Houses generally fail to outperform the benchmarks. The shuffled-weight change benchmark exhibits a robust “style-preserving” property in that the average portfolio standard deviation is nearly equal to the portfolio standard deviation from the actual recommended weights.     

The Diversification Effects of Initial Public Offerings

Abstract:  A firm's stock becomes publicly tradable through an initial public offering (IPO). This study suggests a portfolio diversification perspective to explore IPOs. We examine whether investors can gain diversification benefits by adding an IPO portfolio to a set of benchmark portfolios sorted by firm size and book-to-market ratio. Using US IPOs from 1980-2002, we find that adding a value-weighted IPO portfolio does lead to a statistically and economically significant enlargement of the investment opportunity set for investors relative to investing solely in a set of benchmark portfolios. Specifically, the Sharpe ratio of the tangency portfolio increases by 5.50% on average after including IPO stocks. Furthermore, IPOs associated with prestigious lead underwriters are the main source of this augmentation of the mean-variance investment opportunity set. Finally, our study implies that issuing IPO exchange traded funds or similar products can provide diversification gains to investors.     

Mean-variance versus utility maximization revisited: The case of constant relative risk aversion

We examine if mean-variance (M-V) is a good proxy for portfolios based on the Constant Relative Risk Aversion (CRRA) utility function. M-V portfolios are considered good proxies for portfolios from several utility functions which is why they are routinely used in the portfolio theory literature as the benchmark. Our results clearly show this is not the case. Low risk CRRA portfolios are in many cases very different to M-V portfolios, especially with respect to downside risk. If a risk-free asset is available, in many cases, no M-V portfolio is an adequate proxy for CRRA portfolios. The implications of our findings are that: i) M-V portfolios are a poor proxy for investors with CRRA preferences, ii) CRRA portfolios are more suited to investors who care about downside risk than M-V portfolios, and iii) the efficacy of M-V to proxy for utility maximization should be examined more thoroughly.     

Market conditions,risk, and real estate portfolio returns: Some empirical evidence

This research examined the return behavior of a portfolio of American and New York Stock Exchange real estate firms. A dummy variable procedure was used to test for excess return and/or change in risk behavior across market conditions. The findings were as follows. First, no excess return was found for any model specification. Second, no changes in beta were found using the benchmark approach. The beta shifted when an up market was defined as a nonrecessionary period; the beta behaved procyclically. However, the subperiod tests indicated that effect was transitory and period specific.