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.     

International exchange risk and asset substitutability

This paper estimates subsitutability/complementarity relations among financial assets denominated in foreign currencies. Utilizing a representative investor and a flexible functional form methodology, a mean-variance utility function was estimated and used to determine expected return and variance elasticities between assets in the world portfolio. The hypothesis that international assets are perfect substitutes was rejected. It was also found that relative changes in variance tended to have a bigger impact on asset demand than did relative changes in expected returns. Substituability/complementarity relationships were not strong except in specific cases where strong relationships were expected a priori.     

The Illiquidity Discount of Life Insurance Investments

We incorporate an illiquid life insurance investment in the multi-period investment strategy of an investor with constant relative risk aversion and independent and identically distributed returns. In our setup, the liquid and the illiquid assets are risky and correlated and the illiquid investment cannot be rebalanced. We calculate the illiquidity discount as the difference in certainty equivalent rates of return between the optimal strategy with all assets being rebalanced in each period and the strategy with the illiquid investment. Calibrating our model to data of the German market we find a negative relationship between the level of risk aversion and the illiquidity discount when the investor does not rebalance at all. However, when the investor rebalances his liquid assets in each period to hedge against the illiquid investment the illiquidity discount becomes economically negligible.     

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.     

A knowledge‐based framework for incorporating investor's preference into portfolio decision‐making

This paper describes a framework for the integration of a rule‐based system capable of identifying an investor's risk preference into a quantitative portfolio model based on risk and expected return. By inferring rules consisting of an investor's objective and subjective risk preferences, the integrated methodology provides the assets suitable for the preferences. Through investment in the portfolio composed of the assets, the investor is able to obtain the following bene?ts: reduction of costs and time spent to determine target assets, and alleviation of anxiety from ‘out‐of‐favor’ assets. The framework is applied to the development of a knowledge‐based portfolio system for constructing an investor's preference‐oriented portfolio. In the procedure of the system for ?nding an optimal portfolio, the system uses an arti?cial intelligence method of a case‐based reasoning to obtain preference thresholds for an investor when the investor's past investment records are available. Experimental results show that the framework contributes signi?cantly to the construction of a better portfolio from the perspective of an investor's bene?t/cost ratio than that produced by the existing portfolio models. Copyright © 2004 John Wiley & Sons, Ltd.     

Profitability,investment and average returns

Valuation theory says that expected stock returns are related to three variables: the book-to-market equity ratio (B_t/M_t), expected profitability, and expected investment. Given B_t/M_t and expected profitability, higher expected rates of investment imply lower expected returns. But controlling for the other two variables, more profitable firms have higher expected returns, as do firms with higher B_t/M_t. These predictions are confirmed in our tests.     

The 1/n Pension Investment Puzzle

Abstract

This paper examines the so-called 1/n investment puzzle that has been observed in defined contribution plans whereby some participants divide their contributions equally among the available asset classes. It has been argued that this is a very naive strategy since it contradicts the fundamental tenets of modern portfolio theory. We use simple arguments to show that this behavior is perhaps less naive than it at first appears. It is well known that the optimal portfolio weights in a mean-variance setting are extremely sensitive to estimation errors, especially those in the expected returns. We show that when we account for estimation error, the 1/n rule has some advantages in terms of robustness; we demonstrate this with numerical experiments. This rule can provide a risk-averse investor with protection against very bad outcomes.     

Portfolio optimization under a generalized hyperbolic skewed t distribution and exponential utility

In this paper, we show that if asset returns follow a generalized hyperbolic skewed t distribution, the investor has an exponential utility function and a riskless asset is available, the optimal portfolio weights can be found either in closed form or using a successive approximation scheme. We also derive lower bounds for the certainty equivalent return generated by the optimal portfolios. Finally, we present a study of the performance of mean–variance analysis and Taylor’s series expected utility expansion (up to the fourth moment) to compute optimal portfolios in this framework.     

Conditions for Myopic Valuation and Serial Independence of the Market Excess Return in Discrete Time Models

In a multiperiod pure exchange world with investors displaying HARA-preferences, conditions for period-by-period application of one-period asset pricing models are derived first. The future investment opportunity set may be uncertain, provided that in every period a specific market portfolio variable depending on preferences is known as of the preceding date. This variable need not be completely deterministic. Second, conditions for a serially independent market excess return are derived. These conditions render serial independence very unlikely. Hence estimation methods assuming serial independence are likely to yield biased results.     

The effects of dividend yield and dividend policy on common stock prices and returns

This paper suggests that it is not possible to demonstrate, using the best available empirical methods, that the expected returns on high yield common stocks differ from the expected returns on low yield common stocks either before or after taxes. A taxable investor who concentrates his portfolio in low yield securities cannot tell from the data whether he is increasing or decreasing his expected after-tax return by so doing. A tax exempt investor who concentrates his portfolio in high yield securities cannot tell from the data whether he is increasing or decreasing his expected return. We argue that the best method for testing the effects of dividend policy on stock prices is to test the effects of dividend yield on stock returns. Thus the fact that we cannot tell, using the best available methods, what effects dividend yield has on stock returns implies that we cannot tell what effect, if any, a change in dividend policy will have on a corporation's stock price.     

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.     

Real Stock Returns and Inflation

This paper develops the relation between the real rate of return on the stock market and changes in the price level using a multiperiod economy with production. The observed relation between real ex post stock returns and inflation is shown to be consistent with equilibrium in an economy with rational investors. The relation between expected real returns and expected inflation is shown to depend on the form of the economy's production function and on the form of investor preferences. When the production function exhibits stochastic constant returns to scale, the model explains the negative relation between expected real returns and expected inflation which has frequently been observed in empirical studies.     

The implied Sharpe ratio

In an incomplete market, including liquidly traded European options in an investment portfolio could potentially improve the expected terminal utility for a risk-averse investor. However, unlike the Sharpe ratio, which provides a concise measure of the relative investment attractiveness of different underlying risky assets, there is no such measure available to help investors choose among the different European options. We introduce a new concept—the implied Sharpe ratio—which allows investors to make such a comparison in an incomplete financial market. Specifically, when comparing various European options, it is the option with the highest implied Sharpe ratio that, if included in an investor's portfolio, will improve his expected utility the most. Through the method of Taylor series expansion of the state-dependent coefficients in a nonlinear partial differential equation, we also establish the behaviour of the implied Sharpe ratio with respect to an investor's risk-aversion parameter. In a series of numerical studies, we compare the investment attractiveness of different European options by studying their implied Sharpe ratio.     

OPTIMAL PORTFOLIO SELECTION WITH A SHORTFALL PROBABILITY CONSTRAINT: EVIDENCE FROM ALTERNATIVE DISTRIBUTION FUNCTIONS

We propose a new approach to optimal portfolio selection in a downside risk framework that allocates assets by maximizing expected return subject to a shortfall probability constraint, reflecting the typical desire of a risk-averse investor to limit the maximum likely loss. Our empirical results indicate that the loss-averse portfolio outperforms the widely used mean-variance approach based on the cumulative cash values, geometric mean returns, and average risk-adjusted returns. We also evaluate the relative performance of the loss-averse portfolio with normal, symmetric thin-tailed, symmetric fat-tailed, and skewed fat-tailed return distributions in terms of average return, risk, and average risk-adjusted return.     

Predictability of stock markets with disequilibrium trading

This paper analyses the predictability of a hypothetical market with freely negotiated prices on which exists a censoring of one-period returns which are in excess of an arbitrary level (‘floor’ and ‘ceiling’). It is shown that the expected value of returns (adjusted for drift) conditional on last period information regarding the censoring are equal to zero (and therefore the market is not predictable in mean) if there is no intertemporal spillover on the market. A simple simulation model is proposed and applied for the analysis of the effects of intertemporal and cross-spillovers resulting from quantity constraints. Statistical predictability tests are proposed, based on the corrected Student-t statistic of a regression of returns of some information concerning the previous censoring. An illustrative empirical analysis of six main time series of returns on the Warsaw Stock Exchange confirms their ex-ante, but not ex-post, predictability.     

The Effect of Serial Dependence on Multiperiod Holding Period Return Performance

The impact of the investment time horizon on risk‐return properties of asset returns depends on the presence of serial correlation and higher order serial dependencies. We present a methodology for decomposing multiperiod holding period return covariance into serial and cross‐sectional components using a recursive multiplicative model that captures the effects of serial and cross‐sectional dependencies and their joint effects without requiring a distributional form assumption. Applying this model to historical monthly return series for commonly held financial assets and portfolios of assets, we investigate the significance of the investment time horizon, the existence and relevance of time diversification, the inflation‐hedging effectiveness of different assets, and the appropriateness of applying traditional capital market theory in a multiperiod framework.     

Computing optimal rebalance frequency for log-optimal portfolios in linear time

The pure form of log-optimal investment strategies are often considered to be impractical due to the inherent need for continuous rebalancing. It is however possible to improve investor log utility by adopting a discrete-time periodic rebalancing strategy. Under the assumptions of geometric Brownian motion for assets and approximate log-normality for a sum of log-normal random variables, we find that the optimum rebalance frequency is a piecewise continuous function of investment horizon. One can construct this rebalance strategy function, called the optimal rebalance frequency function, up to a specified investment horizon given a limited trajectory of the expected log of portfolio growth when the initial portfolio is never rebalanced. We develop the analytical framework to compute the optimal rebalance strategy in linear time, a significant improvement from the previously proposed search-based quadratic time algorithm.     

Estimating Portfolio and Consumption Choice: A Conditional Euler Equations Approach

This paper develops a nonparametric approach to examine how portfolio and consumption choice depends on variables that forecast time-varying investment opportunities. I estimate single-period and multiperiod portfolio and consumption rules of an investor with constant relative risk aversion and a one-month to 20-year horizon. The investor allocates wealth to the NYSE index and a 30-day Treasury bill. I find that the portfolio choice varies significantly with the dividend yield, default premium, term premium, and lagged excess return. Furthermore, the optimal decisions depend on the investor's horizon and rebalancing frequency.     

Does a Held-to-Maturity Strategy Impede Effective Portfolio Diversification for Islamic Bond (Sukuk) Portfolios? A Multi-Scale Continuous Wavelet Correlation Analysis

There is a critical gap in the literature in studying the portfolio diversification opportunities available to sukuk investors and evaluating these in light of held-to-maturity strategies usually adopted by these investors. This article has made an initial attempt to study the portfolio diversification strategies for sukuk portfolios across heterogeneous investment horizons. Our findings critically indicate that returns between local currency sukuk in different markets generally have low levels of correlations across different investor holding periods, thus enabling both short and long-run portfolio diversification benefits. However, in contrast, international currency sukuk issued in different markets exhibits high levels of correlations in the longer-term investor holding periods. Also, in the domestic market context, returns on different classes of domestic sukuk are found to exhibit strong correlations in the longer-holding periods. Our findings critically highlight the feasibility of held-to-maturity sukuk investment strategies from a portfolio diversification perspective.     

Corporate Portfolio Management Roundtable

The dean of a top ten business school, the chair of a large investment management firm, two corporate M&A leaders, a CFO, a leading M&A investment banker, and a corporate finance advisor discuss the following questions:

• ? What are today's best practices in corporate portfolio management? What roles should be played by boards, senior managers, and business unit leaders?
• ? What are the typical barriers to successful implementation and how can they be overcome?
• ? Should portfolio management be linked to financial policies such as decisions on capital structure, dividends, and share repurchase?
• ? How should all of the above be disclosed to the investor community?

After acknowledging the considerable challenges to optimal portfolio management in public companies, the panelists offer suggestions that include:

• ? Companies should establish an independent group that functions like a “SWAT team” to support portfolio management. Such groups would be given access to (or produce themselves) business‐unit level data on economic returns and capital employed, and develop an “outside‐in” view of each business's standalone valuation.
• ? Boards should consider using their annual strategy “off‐sites” to explore all possible alternatives for driving share‐holder value, including organic growth, divestitures and acquisitions, as well as changes in dividends, share repurchases, and capital structure.
• ? Performance measurement and compensation frameworks need to be revamped to encourage line managers to think more like investors, not only seeking value‐creating growth but also making divestitures at the right time. CEOs and CFOs should take the lead in developing a shared value creation model that clearly articulates how capital will be allocated.