Asset Selection with Margin Constraints and Income

IN MY judgment," maintained William McChesney Martin, Jr., Chairman of the Board of Governors, Federal Reserve System, "we can never under the present margin regulations have the same result that occurred in terms of a financial crash in 1929 through undermargined accounts, low margins resulting in a financial debacle."' A widely used elementary economics textbook claimed, "Margin requirements have exercised an important restrictive influence on security speculation, as contrasted with the uncontrolled period of the late 1920's... Nearly everyone agrees that Federal Reserve margin requirements exercise a healthy restraint on speculative stock purchases in a boom" (Bach, 1963, p. 116). But what evidence is there that margin requirements have the effects claimed? At the December meetings of the American Economic Association, George J. Stigler, in the Presidential address, called on economists to test their assumptions that state regulation of private activity has indeed been successful (Stigler, 1965). This article brings together some data on the efficacy of margin requirements. While the figures can only be considered preliminary, and more data should be collected to test margin requirements, the data that are available and presented here indicate that not one of the aims of the legislation establishing margin requirements has been accomplished.2

This paper deals with two problems of optimal portfolio strategies in continuous time. The first one studies the optimal behavior of a firm who is forced to withdraw funds continuously at a fixed rate per unit time. The second one considers a firm that is faced with an uncontrollable stochastic cash flow, or random risk process. We assume the firm's income can be obtained only from the investment in two assets: a risky asset (e.g., stock) and a riskless asset (e.g., bond). Therefore, the firm's wealth follows a stochastic process. When the wealth is lower than certain legal level, the firm goes bankrupt. Thus how to invest is the fundamental problem of the firm in order to avoid bankruptcy. Under the case of different lending and borrowing rates, we obtain the optimal portfolio strategies for some reasonable objective functions that are the piecewise linear functions of the firm's current wealth and present some interesting proofs for the conclusions. The optimal policies are easy to be operated for any relevant investor.

We integrate two approaches to portfolio management problems: that of Morton and Pliska (1995) for a portfolio with risky and riskless assets under transaction costs, and that of Cadenillas and Pliska (1999) for a portfolio with a risky asset under taxes and transaction costs. In particular, we show that the two surprising results of the latter paper, results shown for a taxable market consisting of only a single security, extend to a financial market with one risky asset and one bond: it can be optimal to realize not only losses but also gains, and sometimes the investor prefers a positive tax rate.

Worst-Case Portfolio Optimization with Proportional Transaction Costs

This paper examines an optimal investment–consumption problem in a setting where the financial environment is influenced by both stochastic factors and delayed effects. The investor, endowed with Constant Relative Risk Aversion (CRRA) preferences, allocates wealth between a risk-free asset and a single risky asset. The short rate follows a Vasiˇček-type term structure model, while the risky asset price dynamics are driven by a delayed Heston specification whose variance process evolves according to a Cox–Ingersoll–Ross (CIR) diffusion. Delayed dependence in the wealth dynamics is incorporated through two auxiliary variables that summarize past wealth trajectories, enabling us to recast the naturally infinite-dimensional delay problem into a finite-dimensional Markovian framework. Using Bellman’s dynamic programming principle, we derive the associated Hamilton–Jacobi–Bellman (HJB) partial differential equation and demonstrate that it generalizes the classical Merton formulation to simultaneously accommodate delay, stochastic interest rates, stochastic volatility, and consumption. Under CRRA utility, we obtain closed-form expressions for the value function and the optimal feedback controls. Numerical illustrations highlight how delay and market parameters impact optimal portfolio allocation and consumption policies.

This work considers a perturbed risk process with investment, where the investments are either into invested in risky and risk-less assets. A third order differential equation for the ruin probability is derived from the resulting integrodifferential equation. This equation is further decomposed into two equations describing the contributions of the claim and oscillation to the ruin probability. These two equations are solved separately using suitable transformations as well as theory of Kummer confluence hypergeometric equations.We further investigated these solutions and were able to conclude that the higher the fraction of investment into risky assets, the lower the ruin probability, provided all other parameters are kept constant. Keywords: Risk Reserve; Ruin Probability; Interest; Stochastic Investment; Exponential distribution; Kummer hyper-geometric equation AMS 2010 Mathematics Subject Classification : 60J25; 60J60

ABSTRACTIn this article, we study a multi-period portfolio selection model in which a generic class of probability distributions is assumed for the returns of the risky asset. An investor with a power utility function rebalances a portfolio comprising a risk-free and risky asset at the beginning of each time period in order to maximize expected utility of terminal wealth. Trading the risky asset incurs a cost that is proportional to the value of the transaction. At each time period, the optimal investment strategy involves buying or selling the risky asset to reach the boundaries of a certain no-transaction region. In the limit of small transaction costs, dynamic programming and perturbation analysis are applied to obtain explicit approximations to the optimal boundaries and optimal value function of the portfolio at each stage of a multi-period investment process of any length.

Multiperiod Mean-Variance Portfolio Optimization with General Correlated Returns

Cheridito (Finance Stoch 7:533–553, 2003) studies a financial market that consists of a money market account and a risky asset driven by a fractional Brownian motion. It is shown that arbitrage possibilities in such markets can be excluded by suitably restricting the class of allowable trading strategies. In this note, we show an analogous result in a multi-asset market where the discounted risky asset prices follow more general non-semimartingale models. In our framework, investors are allowed to trade between a risk-free asset and multiple risky assets by following simple trading strategies that require a minimal deterministic waiting time between any two trading dates. We present a condition on the discounted risky asset prices that guarantee absence of arbitrage in this setting. We give examples that satisfy our condition and study its invariance under certain transformations.

Investment in Education and Strategic Asset Allocation

PurposeThe study aims to show that ambiguity aversion exerts a non-negligible effect on the investors' decisions, especially due to the possibility of sharp declines in stock prices.Design/methodology/approachThe vast majority of previous studies on life-cycle consumption and asset allocation assume that the equity premium is constant. This study evaluates the impact of rare disasters that shift the stock market to a low return state on investors' consumption and portfolio decisions. The author assumes that investors are averse to ambiguity relative to the current state of the economy and must incur a per period cost to participate in the stock market and solve their optimal consumption and asset allocation problem using dynamic programming.FindingsThe results show that most young investors choose not to invest in stocks because they have low accumulated wealth and the potential return from their stock market investments would not cover the participation costs. Furthermore, ambiguity-averse investors hold considerably fewer stocks throughout their lifetime than ambiguity-neutral ones. The fraction of wealth invested in stocks over the typical consumer's life is hump-shaped: it is low for a young individual, peaks at his early 30s and then decreases until his retirement age.Originality/valueTo the best of the author’s knowledge, this is the first study that assesses the impact of negative stock price jumps on the optimal portfolio of an ambiguity-averse investor.

PurposeThis study aims to investigate the association between Muslim individuals’ portfolio allocation choice and Islamic religiosity (levels and dimensions), controlling for risk tolerance and sociodemographic factors.Design/methodology/approachThe study uses primary data collected via survey questionnaires from a sample of 751 Muslim working individuals in Kuala Lumpur, Malaysia. Owing to the ordinal nature of the dependent variable, which reflects the levels of proportions of risky assets in portfolios, the data were analyzed using an ordered probit regression model.FindingsThe findings reveal that Islamic religiosity levels in general were insignificantly related to portfolio allocation, but that two dimensions of religiosity (virtue and obligation) significantly impact the allocations of risky assets in the portfolio. The higher the level of virtue, the lower the propensity to allocate risky assets into the portfolio. On the contrary, the higher the level of obligation, the higher the propensity to allocate risky assets in the portfolio. Meanwhile, individuals with higher risk tolerance, income and education levels show greater propensity to allocate risky assets in the portfolio.Research limitations/implicationsThe sample is restricted to Muslims in Kuala Lumpur; hence, the findings are not easily generalized to Muslim investors in general. Findings may differ between Muslims across the world, so future research needs to expand from a country specific to an international analysis. In addition, future studies could include other determinants of portfolio allocation, such as financial literacy.Practical implicationsThe findings of this study may assist financial planners and policymakers to better understand the drivers of portfolio allocation among their Muslim clients.Originality/valueWhile other studies have tended to focus on the impact of religiosity on the holdings of specific financial assets, such as Islamic bank accounts or Takaful, the present study explores the effect of Islamic religiosity dimensions on the allocations of risky assets in the portfolio. The study also develops an ordinal measure of portfolio allocation and makes a methodological contribution by using an ordered probit regression analysis.

Optimal consumption and investment strategies with a perishable and an indivisible durable consumption good

We consider the portfolio optimization problem for an investor whose consumption rate process and terminal wealth are subject to downside constraints. In the standard financial market model that consists of d risky assets and one riskless asset, we assume that the riskless asset earns a constant instantaneous rate of interest, r > 0, and that the risky assets are geometric Brownian motions. The optimal portfolio policy for a wide scale of utility functions is derived explicitly. The gradient operator and the Clark–Ocone formula in Malliavin calculus are used in the derivation of this policy. We show how Malliavin calculus approach can help us get around certain difficulties that arise in using the classical “delta hedging” approach.

The return on assets depends on the joint behavior of all savers; if all sell the asset simultaneously, then there will be a financial "Armageddon." We assume that risk-neutral savers' information about aggregate investment is too vague to form precise probability estimates, so they have Knightian uncertainty, and thus act to maximize their minimum payoff. Savers invest in a risky asset (economy-wide production) and in a riskless asset (government bonds). In times of high uncertainty, savers hold too many government bonds, lowering output. A monetary policy of lowering the risk-free rate causes savers to save less in total but to invest more in the risky asset, and the policy is shown to be Pareto-improving; but the policy is unable to recapture the optimal allocations. To restore investment and total savings to their optimal levels, the government must also use a fiscal policy of distortionary taxes to discourage current consumption and leisure.