Constructing Asset Pricing Models With Specific Factor Loadings

We demonstrate how one can build pricing formulae in which factors other than beta may be viewed as determinants of asset returns. This is important conceptually as it demonstrates how the additional factors can compensate for a market portfolio proxy that is mis‐specified, and also shows how such a pricing model can be specified ex ante. The procedure is implemented by first selecting an ‘orthogonal’ portfolio which falls on the mean‐variance efficient frontier computed from the empirical average returns, variances and covariances on the equity securities of a large sample of firms. One then determines the inefficient index portfolio which leads to a vector of betas that when multiplied by the average return on the orthogonal portfolio, and which when subtracted from the vector of average returns for the firms comprising the sample, yields an error vector that is equal to the vector of numerical values for the variables that are to form the basis of the asset pricing formula. There will then be a perfect linear relationship between the vector of average returns for the firms comprising the sample, the vector of betas based on the inefficient index portfolio and such other factors that are deemed to be important in the asset pricing process. We illustrate computational procedures using a numerical example based on the quality of information contained in published corporate financial statements.     

Robust portfolio estimation under skew-normal return processes

In this paper, we study issues related to the optimal portfolio estimators and the local asymptotic normality (LAN) of the return process under the assumption that the return process has an infinite moving average (MA) (∞) representation with skew-normal innovations. The paper consists of two parts. In the first part, we discuss the influence of the skewness parameter δ of the skew-normal distribution on the optimal portfolio estimators. Based on the asymptotic distribution of the portfolio estimator ? for a non-Gaussian dependent return process, we evaluate the influence of δ on the asymptotic variance V(δ) of ?. We also investigate the robustness of the estimators of a standard optimal portfolio via numerical computations. In the second part of the paper, we assume that the MA coefficients and the mean vector of the return process depend on a lower-dimensional set of parameters. Based on this assumption, we discuss the LAN property of the return's distribution when the innovations follow a skew-normal law. The influence of δ on the central sequence of LAN is evaluated both theoretically and numerically.     

Computing optimal rebalance frequency for log-optimal portfolios

Log-optimal investment portfolio is deemed to be impractical and cost-prohibitive due to inherent need for continuous rebalancing and significant overhead of trading cost. We study the question of how often a log-optimal portfolio should be rebalanced for any given finite investment horizon. We develop an analytical framework to compute the expected log of portfolio growth when a given discrete-time periodic rebalance frequency is used. For a certain class of portfolio assets, we compute the optimal rebalance frequency. We show that it is possible to improve investor log utility using this quasi-passive or hybrid rebalancing strategy. Simulation studies show that an investor shall gain significantly by rebalancing periodically in discrete time, overcoming the limitations of continuous rebalancing.     

All Guts,No Glory: Trading and Diversification among Online Investors

I explore cross‐sectional portfolio performance in a sample containing 324,736 transactions conducted by 16,831 Swedish investors at an Internet discount brokerage firm during the period May 1999 to March 2002. On average, investors hold undiversified portfolios, show a strong preference for risk, and trade aggressively. I measure performance using a panel data model, and explain the cross‐sectional variation using investors' turnover, portfolio size and degree of diversification. I find that turnover is harmful to performance due to fees, and is therefore more predominant among investors with small portfolios. I argue that the degree of diversification is a proxy for investor skill, and it has a separate and distinct positive effect on performance. Investors underperform the market by about 8.5% per year on average, of which half can be attributed to trading costs.     

International capital market equilibrium with investment barriers

This paper outlines models of capital market equilibrium when there are explicit barriers to international investment in the form of a tax on holdings of assets in one country by residents of another country. There is a corresponding subsidy on short positions in foreign assets. Asset prices deviate from the predictions of the world capital asset pricing model. Investors do not hold a mixture of national market portfolios, but the mix of risky assets is the same for every investor in a country. Optimal portfolios tend to be heavy in domestic assets, and light in foreign assets. Tax free investors, however, tend to hold assets anywhere in the world that are taxed heavily. Estimates of the magnitude of the average tax (or the magnitude of effective barriers to international investment) can be made by comparing the average return on the minimum variance zero β portfolio, z, with the average across countries and time of the short-term interest rate. When barriers are ineffective, the expected return on portfolio z will be the average short-term interest rate, and the world capital asset pricing model will hold.     

An Empirical Investigation of the Option-Adjusted Realized Return

The issue of meaningful evaluation of professionally managed portfolios remains to be resolved satisfactorily within the investment community. The fact that many of the current procedures for evaluating portfolio performance are deeply rooted in conventional mean-variance (M-V) analysis raises serious concerns from a theoretical perspective. The primary objective of this paper is an empirical investigation (as differentiated from a thorough empirical test) of an ordinal portfolio performance measure, called the Option-adjusted Realized (average rate of) Return or ORR, developed recently by Smith and Kokoska (1998). The ORR is a leverage- and risk-adjusted average realized rate of return that can be used directly in evaluating portfolio performance.Using returns data for June 1992 to May 1998, we estimate ORRs for two portfolios—the CREF Stock Fund and a hypothetical market index portfolio whose composition is identical to that of the S&P 500 Index. Also, we estimate Sharpe and Treynor ratio values for each portfolio and compare rankings provided by these methods for the two portfolios with rankings provided by the ORR method. For the interval of time from June 1995 to May 1998, the rankings provided by the three methods are not consistent. The ORR rankings for this time period indicate the CREF Fund underperformed the S&P Index on a risk-adjusted basis. Additional partitioning of the data creates other multiple intervals or holding periods for which the evaluation results (ex post) support at least moderate likelihood of unambiguous inconsistency ex ante. We argue that, given our set of assumptions, the ORR rankings, founded in option-pricing theory, are more reliable than the others that are M-V based.     

On portfolio optimization: Imposing the right constraints

We reassess the recent finding that no established portfolio strategy outperforms the naively diversified portfolio, 1/N, by developing a constrained minimum-variance portfolio strategy on a shrinkage theory based framework. Our results show that our constrained minimum-variance portfolio yields significantly lower out-of-sample variances than many established minimum-variance portfolio strategies. Further, we observe that our portfolio strategy achieves higher Sharpe ratios than 1/N, amounting to an average Sharpe ratio increase of 32.5% across our six empirical datasets. We find that our constrained minimum-variance strategy is the only strategy that achieves the goal of improving the Sharpe ratio of 1/N consistently and significantly. At the same time, our developed portfolio strategy achieves a comparatively low turnover and exhibits no excessive short interest.     

Worst case portfolio vectors and diversification effects

We consider the problem of identifying the worst case dependence structure of a portfolio X ₁,…,X _n of d-dimensional risks, which yields the largest risk of the joint portfolio. Based on a recent characterization result of law invariant convex risk measures, the worst case portfolio structure is identified as a μ-comonotone risk vector for some worst case scenario measure μ. It turns out that typically there will be a diversification effect even in worst case situations. The only exceptions arise when risks are measured by translated max correlation risk measures. We determine the worst case portfolio structure and the worst case diversification effect in several classes of examples as, e.g. in elliptical, Euclidean spherical, and Archimedean type distribution classes.     

Power mapping with dynamical adjustment for improved portfolio optimization

For financial risk management it is of vital interest to have good estimates for the correlations between the stocks. It has been found that the correlations obtained from historical data are covered by a considerable amount of noise, which leads to a substantial error in the estimation of the portfolio risk. A method to suppress this noise is power mapping. It raises the absolute value of each matrix element to a power q while preserving the sign. In this paper we use the Markowitz portfolio optimization as a criterion for the optimal value of q and find a K/T dependence, where K is the portfolio size and T the length of the time series. Both in numerical simulations and for real market data we find that power mapping leads to portfolios with considerably reduced risk. It compares well with another noise reduction method based on spectral filtering. A combination of both methods yields the best results.     

On optimal portfolio diversification with respect to extreme risks

Extreme losses of portfolios with heavy-tailed components are studied in the framework of multivariate regular variation. Asymptotic distributions of extreme portfolio losses are characterized by a functional γ _ξ =γ _ξ (α,Ψ) of the tail index α, the spectral measure Ψ, and the vector ξ of portfolio weights. Existence, uniqueness, and location of the optimal portfolio are analysed and applied to the minimization of risk measures. It is shown that diversification effects are positive for α>1 and negative for α<1. Strong consistency and asymptotic normality are established for a semiparametric estimator of the mapping ξ ↦ γ _ξ . Strong consistency is also established for the estimated optimal portfolio.     

Jump robust two time scale covariance estimation and realized volatility budgets

We estimate the daily integrated variance and covariance of stock returns using high-frequency data in the presence of jumps, market microstructure noise and non-synchronous trading. For this we propose jump robust two time scale (co)variance estimators and verify their reduced bias and mean square error in simulation studies. We use these estimators to construct the ex-post portfolio realized volatility (RV) budget, determining each portfolio component’s contribution to the RV of the portfolio return. These RV budgets provide insight into the risk concentration of a portfolio. Furthermore, the RV budgets can be directly used in a portfolio strategy, called the equal-risk-contribution allocation strategy. This yields both a higher average return and lower standard deviation out-of-sample than the equal-weight portfolio for the stocks in the Dow Jones Industrial Average over the period October 2007–May 2009.     

Does futures trading increase stock market volatility? The case of the Nikkei stock index futures markets

We propose new tests to examine whether stock index futures affect stock market volatility. These tests decompose spot portfolio volatility into the cross-sectional dispersion and the average volatility of returns on the portfolio's constituent securities. Our tests show that for Nikkei stocks spot portfolio volatility increased and cross-sectional dispersion decreased compared with average volatility when Nikkei futures began trading on the Osaka Securities Exchange, but not on the Singapore International Monetary Exchange. For non-Nikkei stocks, no shift occurred when futures trading began on either exchange. These findings are consistent with the hypotheses that futures trading increases spot portfolio volatility but that there is no volatility “spillover” to stocks against which futures are not traded. However, the increase in volatility attributable to futures trading is small compared with volatility shifts induced by changes in broad economic factors.     

Maximizing an equity portfolio excess growth rate: a new form of smart beta strategy?

It has been claimed that, for dynamic investment strategies, the simple act of rebalancing a portfolio can be a source of additional performance, sometimes referred to as the volatility pumping effect or the diversification bonus because volatility and diversification turn out to be key drivers of the portfolio performance. Stochastic portfolio theory suggests that the portfolio excess growth rate, defined as the difference between the portfolio expected growth rate and the weighted-average expected growth rate of the assets in the portfolio, is an important component of this additional performance (see Fernholz [Stochastic Portfolio Theory, 2002 (Springer)]). In this context, one might wonder whether maximizing a portfolio excess growth rate would lead to an improvement in the portfolio performance or risk-adjusted performance. This paper provides a thorough empirical analysis of the maximization of an equity portfolio excess growth rate in a portfolio construction context for individual stocks. In out-of-sample empirical tests conducted on individual stocks from 4 different regions (US, UK, Eurozone and Japan), we find that portfolios that maximize the excess growth rate are characterized by a strong negative exposure to the low volatility factor and a higher than 1 exposure to the market factor, implying that such portfolios are attractive alternatives to competing smart portfolios in markets where the low volatility anomaly does not hold (e.g. in the UK, or in rising interest rate scenarios) or in bull market environments.     

In which financial markets do mutual fund theorems hold true?

The mutual fund theorem (MFT) is considered in a general semimartingale financial market S with a finite time horizon T, where agents maximize expected utility of terminal wealth. The main results are:

Portfolio Returns,Market Volatility,and Seasonality

This paper examines three important issues related to the relationship between stock returns and volatility. First, are Duffee's (1995) findings of the relationship between individual stock returns and volatility valid at the portfolio level? Second, is there a seasonality of the market return volatility? Lastly, do size portfolio returns react symmetrically to the market volatility during business cycles? We find that the market volatility exhibits strong autocorrelation and small size portfolio returns exhibit seasonality. However, this phenomenon is not present in large size portfolios. For the entire sample period of 1962–1995, the highest average monthly volatility occurred in October, followed by November, and then January. Examining the two sub-sample periods, we find that the average market volatility increases by 15.4% in the second sample period of 1980–1995 compared to the first sample period of 1962–1979. During the contraction period, the average market volatility is 60.9% higher than that during the expansion period. Using a binary regression model, we find that size portfolio returns react asymmetrically with the market volatility during business cycles. This paper documents a strongly negative contemporaneous relationship between the size portfolio returns and the market volatility that is consistent with the previous findings at the aggregate level, but is inconsistent with the findings at the individual firm level. In contrast with the previous findings, however, we find an ambiguous relationship between the percentage change in the market volatility and the contemporaneous stock portfolio returns. This ambiguity is attributed to strongly negative contemporaneous and one-month ahead relationships between the market volatility and portfolio returns.

     

THE PERFORMANCE MEASUREMENT AND EVALUATION OF A CORPORATE RETIREMENT PLAN: A CASE STUDY

This paper is based on an actual study of a pooled profit-sharing plan sponsored by a Fortune 50 company from September 1978 to June 1983. The purpose of performance measurement is to identify skill at portfolio management and provide evidence indicating whether performance coincides with the investment skills claimed by the portfolio manager. The approach here is to apply the security market line analysis suggested by Fama. Characteristic lines were determined for the plan portfolio allowing the calculation for alpha, the Jensen differential performance index, beta, and R². Tests are made to determine if the investment manager was able to achieve superior performance by shifting portfolio market sensitivity in anticipation of major market moves (market-timing effect) and/or selecting undervalued securities (security-selection effect).     

Fine‐Tuning a Corporate Hedging Portfolio: The Case of an Airline

Industrial companies typically face a multitude of risks that could cause significant fluctuations in their cash flow. This is a case study of the hedging strategy adopted by an international air carrier to manage its jet‐fuel price exposure. The airline's hedging approach uses “strips” of monthly collars constructed with Asian options whose payoffs are based on average of “within‐prompt‐month” oil prices. Using the carrier's own implicit objective function based on an annual granularity, the authors show how the air carrier could fine‐tune its current hedge portfolio by adding tailored exotic options. The article describes annual average‐price options, provides an explicit valuation of them, and considers how such instruments may affect corporate liquidity. Consistent with its annual objective function, the airline made this exotic derivative the central tool to hedge across all potential realized values of annual jet‐fuel spot prices. The authors believe this modified portfolio is better suited to address the firm's hedging cost and its overall exposure to jet‐fuel price fluctuations.     

Luck versus Skill in the Cross‐Section of Mutual Fund Returns

The aggregate portfolio of actively managed U.S. equity mutual funds is close to the market portfolio, but the high costs of active management show up intact as lower returns to investors. Bootstrap simulations suggest that few funds produce benchmark‐adjusted expected returns sufficient to cover their costs. If we add back the costs in fund expense ratios, there is evidence of inferior and superior performance (nonzero true α) in the extreme tails of the cross‐section of mutual fund α estimates.     

Marketing Period Risk in a Portfolio Context: Comment and Extension

This paper re-examines and extends the findings of Bond et al., Journal of Real Estate Finance and Economics, 34, 447–461, (2007) who consider the theoretical model of Lin and Vandell, Real Estate Economics, 35, 291–330, (2007) to determine the extent to which individual real estate asset return characteristics caused by marketing period risk disappear in a large, diversified real estate portfolio. The effects of marketing period risk are found to disappear in the limit with growth in the size of the portfolio, with ex ante variance approaching ex post variance, but only if the portfolio consists of nonsystematic risk alone, in which case both approach zero. The marketing period risk factor (MPRF), representing the ratio of ex ante to ex post variance, however, does not in general approach zero in the limit, in fact could increase or decrease depending upon the illiquidity characteristics of the individual assets and the magnitude and degree of correlation among individual property returns and marketing periods. The results suggest that even large institutional real estate portfolio managers must consider the illiquidity present in their portfolios and cannot assume that its effect will be diversified away.

Random matrix models for datasets with fixed time horizons

This paper examines the use of random matrix theory as it has been applied to model large financial datasets, especially for the purpose of estimating the bias inherent in Mean-Variance portfolio allocation when a sample covariance matrix is substituted for the true underlying covariance. Such problems were observed and modeled in the seminal work of Laloux et al. [Noise dressing of financial correlation matrices. Phys. Rev. Lett., 1999, 83, 1467] and rigorously proved by Bai et al. [Enhancement of the applicability of Markowitz's portfolio optimization by utilizing random matrix theory. Math. Finance, 2009, 19, 639–667] under minimal assumptions. If the returns on assets to be held in the portfolio are assumed independent and stationary, then these results are universal in that they do not depend on the precise distribution of returns. This universality has been somewhat misrepresented in the literature, however, as asymptotic results require that an arbitrarily long time horizon be available before such predictions necessarily become accurate. In order to reconcile these models with the highly non-Gaussian returns observed in real financial data, a new ensemble of random rectangular matrices is introduced, modeled on the observations of independent Lévy processes over a fixed time horizon.