Confidence regions for the mean-variance efficient set: An alternative approach to estimation risk

The mean-variance efficient set is used extensively in portfolio analysis and in addition underlies many of the models and tests of asset pricing. Despite this vital role, little direct attention has been paid to efficient frontier estimation. This article illustrates that an estimator for the efficient set hyperbola is composed of three mutually independent statistics whose distributions are known. This result is used to develop a confidence region for the efficient set hyperbola in (σ, μ) space. Two alternative approaches are used to define a confidence region. The first approach can be used to obtain an expression for a confidence region for σ given μ or for μ given σ. The second approach defines a confidence region in (σ, μ) space that contains the true hyperbola with a specified probability. In addition, anF test for mean-variance efficiency is used to generate a sample acceptance region. The sample acceptance region and the two confidence regions are compared graphically. A simulation experiment is used to examine the properties of the various procedures.     

Simple Construction of the Efficient Frontier

We provide simple methods of constructing known results. At the core of our methods is the identification of a simple concise basis that spans the Capital Market Line (CML). We show that a portfolio whose risky assets weights are the product of the inverse variance‐covariance matrix of (nonredundant) security rates of return times the vector of the excess expected rates of return over the risk‐free rate is a CML portfolio. This portfolio and the risk‐free security span the CML. In addition, with this basis, there is immediate construction of the efficient frontier of risky assets (the 'hyperbola'), 'tangency' portfolios, 'reflection' portfolios, and a CAPM relationship. Our method is quick and simple. It is easy to derive, teach, implement, interpret, and remember.     

On statistical inference on the mean-variance efficient set

A proof of the asymptotic distribution of the estimated mean-variance frontier is given. A Bayesian prediction interval is derived for the capital asset pricing model. Numerical illustrations show that the prediction intervals for the CAPM are smaller than those for the constant mean model, if the fit of the CAPM is better than that of the constant mean model.     

Owner-Occupied Housing and the Composition of the Household Portfolio: The Case of France

This paper investigates the impact of housing demand on the composition of the optimal portfolios of homeowners in France, following the methodology developed by Flavin and Yamashita (NBER Working Paper 6389, 2002). We use historical data on housing prices and financial assets returns to estimate the mean return and covariance matrix of a set of assets including housing. We then calculate mean-variance efficient frontiers associated to various levels of the housing-to-net wealth ratio, corresponding to the average ratios observed for different age groups in the 1998 French Wealth Survey sample. Our numerical results fit the average portfolios in different age brackets quite well. Also, returns of housing and its covariance with the other assets indicate there is room in France for housing price derivatives.     

REITs风险收益特征及其资产配置作用

REITs具有“长期收益率高于股票、波动性低于股票”的风险／收益特征，更为重要的是REITs与股票、债券的相关系数低。机构投资者的传统组合中通常只包括债券、股票类证券，加AREITs可使组合优化，即组合有效边界向左上方移动，意味着在相同风险水平下，增加REITs后的组合可获得更高收益，或是为取得相同收益水平，增加REITs后的组合只承担更低风险。     

Applying Portfolio Change and Conditional Performance Measures: The Case of Industry Rotation via the Dynamic Investment Model

This paper applies portfolio change and conditional performance measures to assess the performance of the dynamic investment model in various industry-rotation settings spanning the 1934–1995 period. The dynamic investment model employs the empirical probability assessment approach in raw form. In addition, it incorporates three adjustments for estimation error: James–Stein, Bayes–Stein, and CAPM-based corrections. The tests are unanimous in their conclusion that the excess returns attained by the (unadjusted) historic, the Bayes–Stein, and the James–Stein estimators are (sometimes highly) statistically significant over the 1966–1995 and 1966–1981 sub-periods. This lends support to the idea that the joint empirical probability assessment approach based on the recent past, with and without Stein-based corrections for estimation error, contains information that can be profitably exploited. The relationship of these findings to the extant literature on momentum and contrarian strategies is addressed.     

Stochastic Interest Rates and the Bond-Stock Mix

The optimal bond-stock mix is examined in light of an apparentinconsistency between the Tobin Separation Theorem and the adviceof popular investment advisors which has been pointed out byCanner et al. (1997).It is shown that the apparent inconsistencyis largely explicable in terms of the hedging demands of optimisinglong-term investors in an environment in which the investmentopportunity set is subject to stochastic shocks. The analysispoints to the importance of considering investors' time horizonsin analyzing optimal portfolio policies.     

Stochastic Interest Rates and the Bond-Stock Mix

The optimal bond-stock mix is examined in light of an apparent inconsistency between the Tobin Separation Theorem and the advice of popular investment advisors which has beenpointed out by Canner et al. (1997). It is shown that the apparent inconsistency is largely explicable in terms of the hedging demands of optimising long-term investors in an environment in which the investment opportunity set is subject to stochastic shocks. The analysis points to the importance of considering investors' time horizons in analyzing optimal portfolio policies.     

Determinants of Real Estate Asset Allocations in Private and Public Pension Plans

Numerous studies have examined the factors associated with allocation of corporate and government pension-plan assets. Yet to date there has been no attempt to identify the sponsor-related conditions that affect the percentage of U.S. private and public pension-fund assets invested in real estate. The purpose of this article is to examine various asset-and liability-matching hypotheses regarding pension-plan asset allocations. Models are specified for both corporate and government defined-benefit plans that relate the characteristics of each plan to the percentage allocated to real estate investments. Our results confirm the existence of a significant size effect for both corporate and government pension plans, although we find mean levels of real estate allocation to be much lower than those suggested in previous real estate allocation studies. The article, however, contains some anomalous findings. In particular, our findings suggest that pension-plan sponsors do not hedge their real estate risk. We also find that pension-plan sponsors do not invest in real estate, as theory might suggest, to minimize the noise level in their pension liabilities.     

Valuation of global IPOs: a stochastic frontier approach

This paper studies the impact of global offerings on US IPO firms’ offer price using the stochastic frontier approach. We find that the offer price valuation efficiency for global IPOs exceeds that of IPOs with purely domestic offers by 3.1%. In particular, the global offering approach is most appropriate to those IPO firms, which offer larger proportion of new shares to international investors, underwritten by less prestigious investment banks and with larger firm-specific return variance. Our findings are consistent with the demand inelasticity, certification effect and investor recognition arguments that account for the benefits of global offering.

Robustness of the inference procedures for the global minimum variance portfolio weights in a skew-normal model

In this paper, we study the influence of skewness on the distributional properties of the estimated weights of optimal portfolios and on the corresponding inference procedures derived for the optimal portfolio weights assuming that the asset returns are normally distributed. It is shown that even a simple form of skewness in the asset returns can dramatically influence the performance of the test on the structure of the global minimum variance portfolio. The results obtained can be applied in the small sample case as well. Moreover, we introduce an estimation procedure for the parameters of the skew-normal distribution that is based on the modified method of moments. A goodness-of-fit test for the matrix variate closed skew-normal distribution has also been derived. In the empirical study, we apply our results to real data of several stocks included in the Dow Jones index.     

My global fund portfolio is not yours: the effect of home bias on European- and US-managed convertible bond fund exposures

This paper shows that global convertible bond funds (CBFs) and their resulting equity-bond exposures are regionally biased. Global bond fund managers display home bias, resulting in CBFs that are not only tilted towards the home market but also reflect the different bond-equity exposures of European and US convertibles. More specifically we find that global funds managed by a European asset management firm are more bond-like than global funds managed by a US-based asset manager. Hence, investors have to account for the asset management company's origin to avoid that the performance of the fund and its correlation with other assets is not in line with investor's ex ante expectations about globally managed portfolios. Our results also indicate that for investors of European-based CBFs this home bias has resulted in an ex post opportunity cost up to 1.38% per year, depending on the sample period.     

Consumption and Investment Motives and the Portfolio Choices of Homeowners

This article investigates the portfolio choices of homeowners, taking into account the investment constraint introduced by Henderson and Ioannides (1983). This constraint requires housing investment by homeowners to be at least as large as housing consumption. It is shown that when the constraint is binding, the homeowner's optimal portfolio is ineffcient in a mean-variance sense. Thus, portfolio inefficiency is not an indication that consumers are irrational or careless in their financial decisions. Instead, inefficiency can be seen as the result of a rational balancing of the consumption benefits and portfolio distortion associated with housing investment.     

Exploring the benefits of using stock characteristics in optimal portfolio strategies

I examine the benefits of using stock characteristics to model optimal portfolio weights in stock selection strategies using the characteristic portfolio approach of Brandt, Santa-Clara, and Valkanov. [2009. “Parametric Portfolio Policies: Exploiting Characteristics in the Cross-section of Equity Returns.” Review of Financial Studies 22: 3411–3447]. I find that there are significant out-of-sample performance benefits in using characteristics in stock selection strategies even after adjusting for trading costs, when investors can invest in the largest 350 UK stocks. Imposing short selling restrictions on the characteristic portfolio strategy leads to more consistent performance. The performance benefits are concentrated in the earlier part of the sample period and have disappeared in recent years. I find that there no performance benefits in using stock characteristics when using random subsets of the largest 350 stocks.     

Investing for the Long-run in European Real Estate

We calculate optimal portfolio choices for a long-horizon, risk-averse investor who diversifies among European stocks, bonds, real estate, and cash, when excess asset returns are predictable. Simulations are performed for scenarios involving different risk aversion levels, horizons, and statistical models capturing predictability in risk premia. Importantly, under one of the scenarios, the investor takes into account the parameter uncertainty implied by the use of estimated coefficients to characterize predictability. We find that real estate ought to play a significant role in optimal portfolio choices, with weights between 12 and 44%. Under plausible assumptions, the welfare costs of either ignoring predictability or restricting portfolio choices to traditional financial assets only are found to be in the order of 150–300 basis points per year. These results are robust to changes in the benchmarks and in the statistical framework.      

The Optimal Construction of Internationally Diversified Equity Portfolios Hedged Against Exchange Rate Uncertainty

Much of the empirical work on hedging exchange rate exposure in portfolios of financial assets has used a unitary hedge ratio, or a currency overlay. Alternatively, the currencies themselves can be treated as assets and the position in them optimized. This study empirically tests whether the ex post results of recent studies, which conclude that currencies should themselves be optimized, stand up under parameter uncertainty. It may very well be that ex ante, when parameter inputs must be estimated from historical data, the attempt to determine the optimal currency weights results in inferior performance in comparison to using a simple unitary hedging strategy, or even unhedged international investment. The results suggest that a local currency return unitary hedging strategy works best in the presence of parameter uncertainty.     

Assessing the Economic Significance of Return Predictability: A Research Note

The predictability of stock returns is often assessed using classical statistical significance from predictive regressions. Statistical inference, however, can belie the economic importance with which investors regard various predictors. This paper examines the influence that predictors have on an investor's optimal portfolio allocations. The results show that return predictability is sufficient to induce horizon effects in optimal allocations. After incorporating estimation risk, however, little evidence of predictability remains. We also assess the relative importance of three predictor variables. While dividend yield is the most important predictor, optimal allocations are also sensitive to the term spread and the relative bill rate.     

Returns to scale at large banks in the US: A random coefficient stochastic frontier approach

This paper investigates the returns to scale of large banks in the US over the period 1997–2010. This investigation is performed by estimating a random coefficient stochastic distance frontier model in the spirit of Tsionas (2002) and Greene (2005, 2008). The primary advantage of this model is that its coefficients can vary across banks, thereby allowing for unobserved technology heterogeneity among large banks in the US We find that failure to consider unobserved technology heterogeneity results in a misleading ranking of banks and mismeasured returns to scale. Our results show that the majority of large banks in the US exhibit constant returns to scale. In addition, our results suggest that banks of the same size can have different levels of returns to scale and there is no clear pattern among large banks in the US concerning the relationship between asset size and returns to scale, due to the presence of technology heterogeneity.     

Investment beliefs of endowments

United States university and college endowments now hold close to one‐third of their portfolios in private equity and hedge funds. We estimate the implied beliefs of endowments on these alternative assets’ returns relative to equities and bonds. At the end of 2012, the typical endowment believes that its private equity investments will outperform a portfolio of conventional assets by 3.9% per year, and hedge funds will outperform by 0.7% per year. Taking into account the implied equity exposures in alternative asset positions, the effective equity holding of endowments is approximately 60%.     

Utility and the Skewness of Return in Gambling

This paper demonstrates that the intuitively appealing argument based on the postulated trade-off between expected return, variance and skewness of return of a risk-averse gambler does not provide an explanation of observed betting behaviour. It is shown how the expected utility of a representative gambler faced with a single-prized outcome event can be expressed in terms of the mean and variance of return, the mean and skewness of return or, generally, of the mean and any other single moment of return: and the standard practice of taking a Taylor series expansion/approximation of the expected utility involving moments of return is usually incorrect. Previous analyses have suggested that a punter will accept a lower mean return for higher skewness and this work seems to have involved invalid expansions of the utility function. The upshot is that with certain utility functions which have been used in a number of studies, any analysis based on expansion and estimation of the derivatives of the utility function may be valid only for data based on odds-on favourites and not for longshots.