Downside Risk in Practice

Although investors associate risk with negative outcomes and downside fluctuations, modern portfolio theory does not. For investors, volatility per se is not necessarily bad; volatility below a benchmark is. A stock that magnifies the market's fluctuations is not necessarily bad; one that magnifies the market's downside swings is. Even Harry Mar‐kowitz, the father of modern portfolio theory, viewed downside risk as a better way to assess risk than the “mean‐variance” framework that he ultimately proposed and that has since become the standard. This article highlights the shortcomings of traditional measures of risk (the standard deviation and beta), introduces the concept of downside risk, and discusses two measures of it—the “semideviation” and “downside beta.” It also discusses the use of such measures in asset pricing models to estimate required returns on equity. Data from a few well‐known companies are used to illustrate that the cost of equity based on downside risk can be substantially different from that based on the CAPM. The article concludes with a brief discussion of risk‐adjusted returns and a comparison of the traditional method of calculating such returns with both the Sharpe ratio and its counterpart in a downside risk framework, the Sortino ratio. The appendix demonstrates how to calculate these risk measures in Excel.     

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.     

The effect of growth opportunities on the market reaction to dividend cuts: evidence from the 2008 financial crisis

We consider returns from rebalanced and buy and hold portfolios consisting of the same stocks. Theoretical properties are derived using Jensen’s inequality and the Hölder’s Defect Formula. Simulations are used to confirm theory and to investigate ambiguous cases where theory is silent. Rebalancing decreases total return volatility, while buy and hold produces greater expected return. Results are more opaque with respect to Sharpe Ratios and expected geometric means. Our empirical tests are based on portfolios composed of the risk-free asset, CRSP market value returns and returns from five Fama–French industries. While rebalancing reduces volatility and momentum effect, our tests largely favor the buy and hold strategy due to the high relative returns enjoyed by stocks vis-a-vis the risk-free asset. Transactions cost for rebalancing the portfolio are economically negligible.     

Portfolio performance of linear SDF models: an out-of-sample assessment

We evaluate linear stochastic discount factor models using an ex-post portfolio metric: the realized out-of-sample Sharpe ratio of mean–variance portfolios backed by alternative linear factor models. Using a sample of monthly US portfolio returns spanning the period 1968–2016, we find evidence that multifactor linear models have better empirical properties than the CAPM, not only when the cross-section of expected returns is evaluated in-sample, but also when they are used to inform one-month ahead portfolio selection. When we compare portfolios associated to multifactor models with mean–variance decisions implied by the single-factor CAPM, we document statistically significant differences in Sharpe ratios of up to 10 percent. Linear multifactor models that provide the best in-sample fit also yield the highest realized Sharpe ratios.     

Using industry momentum to improve portfolio performance

Minimum-variance portfolios, which ignore the mean and focus on the (co)variances of asset returns, outperform mean–variance approaches in out-of-sample tests. Despite these promising results, minimum-variance policies fail to deliver a superior performance compared with the simple 1/N rule. In this paper, we propose a parametric portfolio policy that uses industry return momentum to improve portfolio performance. Our portfolio policies outperform a broad selection of established portfolio strategies in terms of Sharpe ratio and certainty equivalent returns. The proposed policies are particularly suitable for investors because portfolio turnover is only moderately increased compared to standard minimum-variance portfolios.     

Liquidity risk,leverage and long-run IPO returns

We examine the risk-return characteristics of a rolling portfolio investment strategy where more than 6000 Nasdaq initial public offering (IPO) stocks are bought and held for up to 5 years. The average long-run portfolio return is low, but IPO stocks appear as “longshots”, as 5-year buy-and-hold returns of 1000% or more are somewhat more frequent than for non-issuing Nasdaq firms matched on size and book-to-market ratio. The typical IPO firm is of average Nasdaq market capitalization but has relatively low book-to-market ratio. We also show that IPO firms exhibit relatively high stock turnover and low leverage, which may lower systematic risk exposures. To examine this possibility, we launch an easily constructed “low-minus-high” (LMH) stock turnover portfolio as a liquidity risk factor. The LMH factor produces significant betas for broad-based stock portfolios, as well as for our IPO portfolio and a comparison portfolio of seasoned equity offerings. The factor-model estimation also includes standard characteristic-based risk factors, and we explore mimicking portfolios for leverage-related macroeconomic risks. Because they track macroeconomic aggregates, these mimicking portfolios are relatively immune to market sentiment effects. Overall, we cannot reject the hypothesis that the realized return on the IPO portfolio is commensurable with the portfolio's risk exposures, as defined here.     

The diversification effects of volatility-related assets

We examine whether investors can improve their investment opportunity sets through the addition of volatility-related assets into various groupings of benchmark portfolios. By first analyzing the weekly returns of three VIX-related assets over the period 1996-2008 and then applying mean-variance spanning tests, we find that adding VIX-related assets does lead to a statistically significant enlargement of the investment opportunity set for investors. Our empirical findings are robust and have two implications. First, there is scope for the further development of financial products relating to volatility indexes. Second, hedge fund managers can utilize VIX futures contracts or VIX-squared portfolios to enhance their equity portfolio performance, as measured by the Sharpe ratio.     

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.     

Normative portfolio theory

In this paper, we correct the adverse impact of estimation risk on both portfolio weights and performance with two new equity allocation methods we implement with estimation-free and estimated ex-ante returns. Portfolios with estimation-free ex-ante returns and systematic-to-unsystematic risk weights have statistically higher Sharpe ratios than both similar portfolios with estimated ex-ante returns and 1/N′th portfolios. Optimal portfolio methods with well-behaved weights guide investors in a way not hitherto possible (normative portfolio theory).     

Measuring Mutual Fund Performance with Characteristic-Based Benchmarks

This article develops and applies new measures of portfolio performance which use benchmarks based on the characteristics of stocks held by the portfolios that are evaluated. Specifically, the benchmarks are constructed from the returns of 125 passive portfolios that are matched with stocks held in the evaluated portfolio on the basis of the market capitalization, book-to-market, and prior-year return characteristics of those stocks. Based on these benchmarks, “Characteristic Timing” and “Characteristic Selectivity” measures are developed that detect, respectively, whether portfolio managers successfully time their portfolio weightings on these characteristics and whether managers can select stocks that outperform the average stock having the same characteristics. We apply these measures to a new database of mutual fund holdings covering over 2500 equity funds from 1975 to 1994. Our results show that mutual funds, particularly aggressive-growth funds, exhibit some selectivity ability, but that funds exhibit no characteristic timing ability.     

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.     

REGULAR(IZED) HEDGE FUND CLONES

This article addresses the problem of portfolio construction in the context of efficient hedge fund investments replication. We propose a modification to the standard Sharpe “style analysis” by introducing a constraint on the asset weights 1‐norm and 2‐norm. This constraint regularizes the optimization problem, allows efficient selection of relevant factor's and has significant effects on the stability of the resulting asset mix and the risk–return characteristics of the replicating portfolio. The empirical results suggest that the norm‐constrained replicating portfolios exhibit significant correlations with their benchmarks, often higher than 0.9; have a fraction, which is about half to two‐thirds, of active positions relative to those determined through the standard method; and are obtained with turnover, which is in some instances about one‐fourth of that for the standard method.     

Portfolio selection with a drawdown constraint

When identifying optimal portfolios, practitioners often impose a drawdown constraint. This constraint is even explicit in some money management contracts such as the one recently involving Merrill Lynch’ management of Unilever’s pension fund. In this setting, we provide a characterization of optimal portfolios using mean–variance analysis. In the absence of a benchmark, we find that while the constraint typically decreases the optimal portfolio’s standard deviation, the constrained optimal portfolio can be notably mean–variance inefficient. In the presence of a benchmark such as in the Merrill Lynch–Unilever contract, we find that the constraint increases the optimal portfolio’s standard deviation and tracking error volatility. Thus, the constraint negatively affects a portfolio manager’s ability to track a benchmark.     

Relative Performance Evaluation of Mutual Funds: A Non-Parametric Approach

We propose an alternative mutual fund performance index which addresses the benchmark problem and controls for economies of scale in managing mutual funds. We advance a new concept of 'return-cost' efficiency as another important element in evaluating portfolio management, in addition to the mean-variance efficiency concept. Our index based on a non-parametric estimation is shown to be similar to the Sharpe index with multiple slopes (or factors). We have shown that all fund categories, except income funds, have similar average efficiency scores after controlling for economies of scale. Most funds operate in increasing returns to scale and seem to be successful in holding mean-variance efficient portfolios, but unsuccessful in allocating transaction costs efficiently, evidenced by excessive turnovers and loads.     

An analysis of the importance of S&;P 500 discretionary constituent changes

The main purpose of this paper is to investigate the impact of the S&P 500 index committee’s decisions to change the constituent firms in the index on benchmark risk measures. The index is managed and changed discretionally by the index committee to make it as representative of the market condition as possible. In addition, the index constantly changes due to important corporate events such as bankruptcies, mergers and acquisitions, and spin-offs. We reconstruct market portfolios by retaining all discretionally deleted firms in a 3 and 5 year periods. We estimate betas at every deletion date in terms of reconstructed market portfolios; we found that these estimate betas are significantly different from the betas obtained from the constantly updated S&P 500 portfolio. We also found that such portfolios are less representative of the business cycle than the actual S&P 500 portfolio. Finally, we found that the portfolio returns obtained by retaining all discretionally deleted firms deviate significantly from the returns of the actual S&P 500 index over the studied period, October 1989 to December 2007.     

Equilibrium prices in the presence of delegated portfolio management

This paper analyzes the asset pricing implications of commonly used portfolio management contracts linking the compensation of fund managers to the excess return of the managed portfolio over a benchmark portfolio. The contract parameters, the extent of delegation, and equilibrium prices are all determined endogenously within the model we consider. Symmetric (fulcrum) performance fees distort the allocation of managed portfolios in a way that induces a significant and unambiguous positive effect on the prices of the assets included in the benchmark and a negative effect on the Sharpe ratios. Asymmetric performance fees have more complex effects on equilibrium prices and Sharpe ratios, with the signs of these effects fluctuating stochastically over time in response to variations in the funds' excess performance.     

“好”的不确定性、“坏”的不确定性与股票市场定价——基于中国股市高频数据分析

不确定性并不是都是“坏”的,“好”的不确定性也同样存在。本文采用Barndorff-Nielsen et al.(2010)提出的已实现半方差作为股票市场“好”的不确定性和“坏”的不确定性的代理指标,并在此基础上构建了相对符号变差(RSV),分析RSV对中国股市定价的影响。基于2007-2017年中国A股5分钟高频数据的实证研究发现:(1)与理论解释相一致,RSV与股票收益之间呈现负相关关系。无论是基于单变量分组、双变量分组还是公司层面的截面回归,这种影响在经济上和统计上都显著。(2)RSV是独立于已实现偏度的一个重要定价因子,且RSV对股票的定价能力强于已实现偏度的定价能力。(3)RSV对中国股市的影响是状态依存的,相对于经济景气程度高的状态,在经济景气程度低的状态下RSV定价影响更大。(4)基于RSV构建的投资组合的表现明显优于市场超额收益率组合、SMB组合和HML组合的表现。     

Surprises,sentiments, and the expectations hypothesis of the term structure of interest rates

Between 2005 and 2009, we document evident time-varying credit risk price discovery between the equity and credit default swap (CDS) markets for 174 US non-financial investment-grade firms. We test the economic significance of a simple portfolio strategy that utilizes fluctuation in CDS spreads as a trading signal to set stock positions, conditional on the CDS price discovery status of the reference entities. We show that a conditional portfolio strategy which updates the list of CDS-influenced firms over time, yields a substantively larger realized return net of transaction cost over the unconditional strategy. Furthermore, the conditional strategy’s Sharpe ratio outperforms a series of benchmark portfolios over the same trading period, including buy-and-hold, momentum and dividend yield strategies.     

International asset allocation using the market implied cost of capital

The Black and Litterman (Financ Anal J 48(5):28–43, 1992) (BL) approach to portfolio optimization requires investor views on expected asset returns as an input. I demonstrate that the market implied cost of capital (ICC) is ideal for quantifying those views on a country level. I benchmark this approach against a BL optimization using time-series models as investor views, the equally weighted portfolio, and allocation methods based on stock market capitalization and GDP. I find that the ICC portfolio offers an increase in average return of 2.1 percentage points (yearly) as compared to the value-weighted portfolio, while having a similar standard deviation. The resulting difference in Sharpe ratios is statistically significant and robust to the inclusion of transaction costs, varying BL parameters, and a less strictly defined investment universe.     

INTERNATIONAL DIVERSIFICATION OF EQUITIES AND FIXED-INCOME SECURITIES

Portfolio selection models have been applied principally to common stocks traded in the United States and in foreign stock markets. This study examines the efficient set of portfolios selected from a choice set that includes returns derived from domestic and international corporate bond and government bond indices as well as domestic and international stock indices. To assess the benefits of international multi-asset diversification, the authors examine the following issues: (1) the extent to which international and domestic fixed-income securities are included in efficient portfolios; (2) the effect on efficient set composition of using the Sharpe portfolio selection model as compared to the Markowitz portfolio selection model; (3) the sensitivity of efficient set characteristics produced from a single-index based portfolio selection model to alternative world market indices; and (4) the correspondence between expected and realized portfolio risk and return for the different portfolio selection models.