Small Portfolios Research Articles

A BAYESIAN JOINT MODEL FOR POPULATION AND PORTFOLIO-SPECIFIC MORTALITY

AbstractInsurance companies and pension funds must value liabilities using mortality rates that are appropriate for their portfolio. These can only be estimated in a reliable way from a sufficiently large historical dataset for such portfolios, which is often not available. We overcome this problem by introducing a model to estimate portfolio-specific mortality simultaneously with population mortality. By using a Bayesian framework, we automatically generate the appropriate weighting for the limited statistical information in a given portfolio and the more extensive information that is available for the whole population. This allows us to separate parameter uncertainty from uncertainty due to the randomness in individual deaths for a given realization of mortality rates. When we apply our method to a dataset of assured lives in England and Wales, we find that different prior specifications for the portfolio-specific factors lead to significantly different posterior distributions for hazard rates. However, in short-term predictive distributions for future numbers of deaths, individual mortality risk turns out to be more important than parameter uncertainty in the portfolio-specific factors, both for large and for small portfolios.

A review and simulation of business angel investment returns

Business angels are widely recognized as a significant source of entrepreneurial finance, particularly for early-stage businesses. However, rigorous investigation on angel investment performance has been limited. This paper examines investment returns of business angels in addressing the question of whether angel investing generates attractive returns. We review the few published studies which report on more than 100 investment exits to establish baseline returns expectations and clarify returns measurement limitations. We then use data from one of the largest studies of angel returns to populate a Monte Carlo simulation of returns profiles to explore the link between portfolio size and the probability of the desired level of returns. The study reveals that angel deal returns are highly skewed; smaller portfolios have higher average returns but dramatically lower median returns. In contrast with prior studies, our study shows that portfolios with more than 50 investments are required to significantly minimize risk of poor returns and that similar scale is required to maximize returns potential, as smaller portfolios have a lower average internal rate of return (IRR). We show that reinvestment rate is a critical element in measuring angel returns, and we demonstrate the limitations of IRR as a returns metric through the simulation.

Portfolio Optimization under Cardinality Constraints: A Comparative Study

The Cardinality Constraint-Based Optimization problem is investigated in this note. In portfolio optimization problem, the cardinality constraint allows one to invest in assets out of a universe of N assets for a prespecified value of K. It is generally agreed that choosing a “small” value of K forces the implementation of diversification in small portfolios. However, the question of how small must be K has remained unanswered. In the present work, using a comparative approach we show computationally that optimal portfolio selection with a relatively small or large number of assets, K, may produce similar results with differentiated reliabilities.

Sparse Structural Approach for Rating Transitions

In banking practice, rating transition matrices have become the standard approach of deriving multi-year probabilities of default (PDs) from one-year PDs, the latter normally being available from Basel ratings. Rating transition matrices have gained in importance with the newly adopted IFRS 9 accounting standard. Here, the multi-year PDs can be used to calculate the so-called expected credit losses (ECL) over the entire lifetime of relevant credit assets. A typical approach for estimating the rating transition matrices relies on calculating empirical rating migration counts and frequencies from rating history data. For small portfolios, however, this approach often leads to zero counts and high count volatility, which makes the estimations unreliable and unstable, and can also produce counter-intuitive prediction patterns such as non-parallel/crossing forward PD patterns. This paper proposes a structural model which overcomes these problems. We make a plausible assumption of an underlying autoregressive mean-reverting ability-to-pay process. With only three parameters, this sparse process can well describe an entire typical rating transition matrix, provided the one-year PDs of the rating classes are specified (e.g. by the rating master scale). The transition probabilities produced by the structural approach are well-behaved by design. The approach significantly reduces the statistical degrees of freedom of the estimated transition probabilities, which makes the rating transition matrix more reliable for small portfolios. The approach can be applied to data with as few as 50 observed rating transitions. Moreover, the approach can be efficiently applied to data consisting of continuous PDs (prior to rating discretization). In the IFRS 9 context, the approach offers an additional merit: it can easily account for the macroeconomic adjustments, which are required by the IFRS 9 accounting standard.

Does education strengthen the life skills of adolescents?

Life skills, sometimes referred to as noncognitive skills or personality traits (e.g. conscientiousness or locus of control—the belief to influence events and their outcomes), affect labor market productivity. Policy makers and academics are thus exploring whether such skills should be taught at the high school or college level. A small portfolio of recent studies shows encouraging evidence that education could strengthen life skills in adolescence. However, as no uniform approach exists on which life skills are most important and how to best measure them, many important questions must be answered before life skill development can become an integral part of school curricula.

Extreme Portfolio Loss Correlations in Credit Risk

The stability of the financial system is associated with systemic risk factors such as the concurrent default of numerous small obligors. Hence it is of utmost importance to study the mutual dependence of losses for different creditors in the case of large, overlapping credit portfolios. We analytically calculate the multivariate joint loss distribution of several credit portfolios on a non-stationary market. To take fluctuating asset correlations into account we use an random matrix approach which preserves, as a much appreciated side effect, analytical tractability and drastically reduces the number of parameters. We show that for two disjoint credit portfolios diversification does not work in a correlated market. Additionally we find large concurrent portfolio losses to be rather likely. We show that significant correlations of the losses emerge not only for large portfolios with thousands of credit contracts but also for small portfolios consisting of a few credit contracts only. Furthermore we include subordination levels, which were established in collateralized debt obligations to protect the more senior tranches from high losses. We analytically corroborate the observation that an extreme loss of the subordinated creditor is likely to also yield a large loss of the senior creditor.

The Influence of Internal and External Factors to the Indian Stock Market

This paper has been undertaken with the aim of testing the applicability of Fama and French three factor model (1993) in explaining cross-sectional average return for Stocks in Indian equity market for the time frame of 5 years from 2011-2016.The sample includes firms that traded on NIFTY 50 index from 2011-2016. Monthly data has been used to assess the performance of various stocks which have been categorized into big and small portfolios. Monthly data gives a better picture as compared to annual data when the time horizon for study is short.

On Setting Day-Ahead Equity Trading Risk Limits: VaR Prediction at Market Close or Open?

This paper investigates the information content of the ex post overnight return for one-day-ahead equity Value-at-Risk (VaR) forecasting. To do so, we deploy a univariate VaR modeling approach that constructs the forecast at market open and, accordingly, exploits the available overnight close-to-open price variation. The benchmark is the bivariate VaR modeling approach proposed by Ahoniemi et al. that constructs the forecast at the market close instead and, accordingly, it models separately the daytime and overnight return processes and their covariance. For a small cap portfolio, the bivariate VaR approach affords superior predictive ability than the ex post overnight VaR approach whereas for a large cap portfolio the results are reversed. The contrast indicates that price discovery at the market open is less efficient for small capitalization, thinly traded stocks.

Santa Claus Rally and firm size

Purpose – Several articles in the popular press have detailed an end-of-year anomaly known as the Santa Claus Rally, a period best defined as the last five trading days of December and the first two trading days of January. The purpose of this paper is to examine US stock market returns over this period from 1926 to 2014. Design/methodology/approach – The authors examine the Santa Claus Rally by relating it to firm size in the stock markets of the USA. The Santa Claus Rally consists of the last five trading days in December and the first two in January. The authors use t-tests, non-parametric test and regression analysis to determine if investors in small firms get superior returns over the period 1926-2014. Findings – The authors find that returns are generally higher during the period and that the effect is considerably stronger for small-firm portfolios relative to large capitalization portfolios. The authors also provide convincing evidence that the three most important trading days (especially for small stock portfolios) are the last trading day in December and the first two trading days in January. Research limitations/implications – The authors only check the markets in the USA. Market makers can use this to get significantly high returns during the Christmas-New Year period. The study shows for the first time that there is a size effect as part of the Santa Claus Rally. Practical implications – This is the first study to show that Santa Claus Rally exists for a long time in the USA. It is the first study to show that there is a size effect in Santa Claus Rally. Market participants could get significantly higher returns by investing or being invested in the stock market during this period. Social implications – The impact of the holiday season on stock market returns. Originality/value – This is the first major academic study to examine Santa Claus Rally in this much detail. The authors not only show that the rally exists, the authors show that it is based on firm size and has been in existence for nearly 90 years in the USA.

Market Sentiment Dynamics and Return Volatility in the Indian Equity Market

In this study, we constructed a composite index of irrational market sentiment to ascertain the impact of market sentiment upon return volatility in the Indian equity market using monthly data spanning the time period from April 2007 to January 2015 of four major indices of Bombay Stock Exchange such as : BSE Sensex, BSE 500, BSE Mid-cap, BSE Small-cap. The Sentindex significantly portrayed the fluctuations in accordance with the events that took place in the market during the period of analysis, and at the same time, its movements were found to be uncorrelated with that of economic fundamentals. Though the graphical analysis showed indications of higher fluctuations in returns in times of pessimistic sentiments and moderate and calm period of volatility regimes with moderate positive sentiment in the market, from further investigation, we observed that the effect of sentiment was significant only in case of the volatilities in medium and small cap portfolio returns. On examination of temporal dependency, based on ARDL modeling, we noticed significant long-term relationship between return volatility and irrational sentiments in case of such portfolios. An initial shock in the sentiment component was found to create varying magnitude of responses in volatility over the months and was observed to be disappearing after four to five months. These observations necessitate the incorporation of sentiment factors in the pricing models of assets as well as in risk estimation, especially in case of those stocks with the characteristics that are sensitive to market sentiment. Along with this, in order to pinpoint the causes of the persistence of sentiment effects, further investigations on : the nature and trading behavior of investors who participate in such market segments, level of trading and fund flows, sophistication of trading mechanism, and effectiveness of policy level initiatives to eliminate market inefficiency in these segments is recommended.

Size, Value, and Momentum Effects in Stock Returns: Evidence from India

We examine in this article if stock returns show a pattern which indicates certain anomalies predominantly size, value, and momentum effects. We also examine whether asset pricing models capture mean excess returns on portfolios constructed based on size–value and size–momentum factors. We find that average stock returns exhibit patterns that have size, value, and momentum effects. We also show evidence that the empirical results do not fully support asset-pricing models. Capital asset-pricing model (CAPM) does not capture average returns on portfolios. Fama–French three-factor model partly explains average returns on size–value sorted portfolios while Carhart four-factor model captures returns on size–momentum sorted portfolios mainly small size-winner portfolio. Hence, size, value and momentum factors continue to exist in Indian stock market and they are found to be profitable investment strategies which would maximize invested wealth of the investors.

Characterization of gas and oil portfolios of exploration and production assets using a methodology that integrates value, risk and time

Asset portfolio modelling and optimization are critical activities for upstream (exploration and production) gas and oil companies in order for decision makers to establish the combined value of their assets and to select assets for further development, divestment and/or acquisition. However, it is an activity that is typically not conducted in a standardized and systematic way, with many companies relying on simple deterministic discounted cash flow asset-value-roll-up analysis, but missing vital insight to the subtle, but significant characteristics of their portfolios. A more systematic, multi-stage stochastic methodology is proposed to reveal detailed characterization of gas and oil asset portfolios in terms of value, risk and timing. The non-linear nature of risk is taken into account in an approach to risk analysis that begins at the asset level and progresses through to the pre-corporate rolled-up asset portfolio to post-tax portfolio factoring in the corporate financial dimension. The proposed methodology emphasizes the importance of considering financial and non-financial metrics (i.e. production, reserves and timing) over each year of a planning horizon. In addition, those same metrics summed over all the years of a planning horizon, expressed in terms of risked value and downside risk of the portfolio failing to achieve certain strategic targets identifies feasible envelopes for possible asset combinations. The downside risk measures apply important modifications to standard risk-variance analysis, introducing flexibility into the approach to suit diverse strategic objectives of potential portfolio holders. Further analysis of those risk versus risked value feasible envelopes reveals the efficient frontiers representing the asset combinations that achieve the highest value for specific levels of downside risk. Characterizing a portfolio of gas and oil assets with such a methodology helps to frame multi-objective optimization algorithms tailored to suit the unique characteristics of each asset portfolio. Excel spreadsheets driven by visual basic for applications (VBA) macros offer the advantages of flexibility, transparency and customization to characterize asset portfolios with the methodology proposed. A small portfolio involving eleven exploration, appraisal, development and production gas and oil assets (Portfolio X) is presented to illustrate the benefits of the proposed approach to gas and oil asset portfolio characterization. The diversity in character of conventional and unconventional upstream gas assets makes a portfolio approach to their understanding extremely worthwhile.

Sparse Mean-Variance Portfolios: A Penalized Utility Approach

This paper considers mean-variance optimization under uncertainty, specifically when one desires a sparsified set of optimal portfolio weights. From the standpoint of a Bayesian investor, our approach produces a small portfolio from many potential assets while acknowledging uncertainty in asset returns and parameter estimates. We demonstrate the procedure using static and dynamic models for asset returns.

Higher Order Stochastic Dominance and Aggregate Investor Preferences

This paper finds necessary and sufficient conditions of Nth-order stochastic dominance (SD) for risk aversion and develops linear tests for Nth-order SD. We introduce a linear FDSD (fourth-order SD and decreasing absolute risk aversion SD) test for standard risk aversion. A positive research shows that higher order risk attitude cannot explain pricing errors of the small size and high value benchmark portfolios. The empirical results also suggests that any Nth-order SD criterion might not be superior to MV rule when the MV kernel does not violate non-satiation. FDSD has the best discriminate power and substantially improves the pricing kernel.

Financing drug discovery via dynamic leverage

We extend the megafund concept for funding drug discovery to enable dynamic leverage in which the portfolio of candidate therapeutic assets is predominantly financed initially by equity, and debt is introduced gradually as assets mature and begin generating cash flows. Leverage is adjusted so as to maintain an approximately constant level of default risk throughout the life of the fund. Numerical simulations show that applying dynamic leverage to a small portfolio of orphan drug candidates can boost the return on equity almost twofold compared with securitization with a static capital structure. Dynamic leverage can also add significant value to comparable all-equity-financed portfolios, enhancing the return on equity without jeopardizing debt performance or increasing risk to equity investors.

On the Viability of Robo-Advising for Individual Investors

The development of robo-advising allows investors to receive advice on investments that were considered too small by traditional human advisers. In this paper, the viability of robo-advising for individual investors is discussed by investigating one of the basic strategies of portfolio management, diversification. We formulate a mean-variance portfolio problem with a constraint on investment size, and find that most of risk reduction from diversification is achieved even with a small portfolio. The consistency of our finding provides insight on the feasibility of robo-advising for all investors regardless of their level of wealth.

Carteiras Igualmente Ponderadas com Poucas Ações e o Pequeno Investidor

Este artigo analisa carteiras igualmente ponderadas (1/N) com foco no investidor sem sofisticação, com carteiras de pequenas de ações. A quantidade de ações incluídas nas carteiras 1/N foi de 6 a 16, e o rebalanceamento, feito apenas três vezes ao ano. O período de análise incluiu retornos diários e mensais, entre 1998 e 2011. O desempenho das carteiras 1/N foi comparado ao de fundos de investimento em ações (FIAs), a uma carteira de mínima variância global com limite de 10% sobre os pesos positivos (MVP 10%) e ao Ibovespa. As comparações empregaram testes não paramétricos, medidas de retorno ajustado ao risco e consideram custos de transação. Os resultados, por sua vez, indicam que os FIAs selecionados apresentam desempenho, na melhor das hipóteses, equivalente ao das carteiras 1/N, apesar de apresentarem desvio padrão menor. Não se constatou retorno mediano das carteiras 1/N significativamente diferente do da Ibovespa e do da MVP 10%. O critério de seleção das ações, segundo ordenamento pelo Índice de Sharpe do período anterior, é relevante, mas o rebalanceamento pode ser feito menos de três vezes ao ano. As carteiras 1/N são, portanto, uma alternativa atraente em relação aos FIAs para investidores com carteiras pequenas de ações, apesar de seus custos de transação poderem ultrapassar 400 pontos base por ano.

Dynamic asset allocation

This article analyzes whether dynamically adjusting a portfolio with multiple asset classes can lead to superior returns. This article utilizes mean reverting behavior of different asset classes and applies a relative valuation technique to dynamically allocate funds to six different asset classes. The dynamic asset allocation (DAA) strategy generates a positive annualized geometric mean return differential over 20–30 year horizons on a geometric mean basis. The standard deviation of the DAA strategy was lower than that of the six individual asset classes while the Sharpe ratios and Max Drawdown for DAA also compared favorably to large and small cap stocks portfolios. The approach developed in this study can be useful to investors in identifying the most undervalued asset class at a particular point in time. This strategy may also be very well suited for retirement portfolios that are inherently long term in nature.

Optimal Trade Execution for Time-Inconsistent Mean-Variance Criteria and Risk Functions

Liquidation of large portfolios in practice requires a longer time and smaller relative selling speed than the liquidation of small portfolios. Mean-variance optimal liquidation however results in the same relative selling speed and time horizon for small and large positions. We discuss three approaches that remedy this effect and show that they are equivalent: In the first approach, the optimal strategy is found by trading off mean performance with a function of total variance. This results in time-inconsistency which we resolve through continuous recalibration. In the second approach we consider the same trade-off but resolve time-inconsistency through equilibrium strategies. The third approach is to choose the optimal strategy by trading off mean performance with the time integral of a risk function of the asset position.

A Theory of Market Design: The Split Market Paradigm.

The cost of systemic risk in the over-the-counter (OTC) derivatives market is described and estimated. Modern portfolio theory (MPT), applied to OTC derivatives, predicts this cost, which has been growing since 1970. This cost grew because Congress blocked MPT’s predicted market forces. Without Congressional intervention, derivatives dealers would either have held dramatically smaller portfolios or made OTC derivatives negotiable. We estimate the global market has reached an un-booked negative market value, the implied capital cost of derivatives’ credit risk, substantially in excess of $250 billion today. At the banking lobby’s behest, Congress serially altered the bankruptcy code, transferring derivatives’ implied credit risk from derivatives dealers to others. However, the burden of the transferred credit risk was not reassigned. Thus the risk is not accounted for and not supported by bank capital. Worse, since derivatives are credit-riskless for derivatives dealers, these dealers create more derivatives than if they bore the cost, creating systemic risk.This risk, and the resulting changes in bankruptcy code, are unnecessary. If the dealer community were to modify the structure of OTC derivative instruments, derivatives’ credit risk would be dramatically reduced. Without Congress’ intervention, this might have happened long ago.The article is organized as follows. The introduction summarizes the article. The second section describes how OTC derivatives create temporary excess credit risk. The third section describes government intervention in this market and the resulting permanent systemic risk. Section four estimates the current size of systemic risk. The final section concludes.