Measuring and Optimizing Portfolio Credit Risk: A Copula‐based Approach*

In this work, we present a methodology for measuring and optimizing the credit risk of a loan portfolio taking into account the non‐normality of the credit loss distribution. In particular, we aim at modelling accurately joint default events for credit assets. In order to achieve this goal, we build the loss distribution of the loan portfolio by Monte Carlo simulation. The times until default of each obligor in portfolio are simulated following a copula‐based approach. In particular, we study four different types of dependence structure for the credit assets in portfolio: the Gaussian copula, the Student's t‐copula, the grouped t‐copula and the Clayton n‐copula (or Cook–Johnson copula). Our aim is to assess the impact of each type of copula on the value of different portfolio risk measures, such as expected loss, maximum loss, credit value at risk and expected shortfall. In addition, we want to verify whether and how the optimal portfolio composition may change utilizing various types of copula for describing the default dependence structure. In order to optimize portfolio credit risk, we minimize the conditional value at risk, a risk measure both relevant and tractable, by solving a simple linear programming problem subject to the traditional constraints of balance, portfolio expected return and trading. The outcomes, in terms of optimal portfolio compositions, obtained assuming different default dependence structures are compared with each other. The solution of the risk minimization problem may suggest us how to restructure the inefficient loan portfolios in order to obtain their best risk/return profile. In the absence of a developed secondary market for loans, we may follow the investment strategies indicated by the solution vector by utilizing credit default swaps.     

Risk index based models for portfolio adjusting problem with returns subject to experts' evaluations

This paper discusses a portfolio adjusting problem with additional risk assets and a riskless asset in the situation where security returns are given by experts' evaluations rather than historical data. Uncertain variables are employed to describe the security returns. Using expected value and risk index as measurements of portfolio return and risk respectively, we propose two portfolio optimization models for an existing portfolio in two cases, taking minimum transaction lot, transaction cost, and lower and upper bound constraints into account. In one case the riskless asset can be both borrowed and lent freely, and in another case the riskless asset can only be lent and the borrowing of riskless asset is not allowed. The adjusting models are converted into their crisp equivalents, enabling the users to solve them with currently available programming solvers. For the sake of illustration, numerical examples in two cases are also provided. The results show that under the same predetermined maximum tolerable risk level the expected return of the optimal portfolio is smaller when the riskless asset can only be lent than when the riskless asset can be both borrowed and lent freely.     

Portfolio choice and pricing in illiquid markets

This paper studies portfolio choice and pricing in markets in which immediate trading may be impossible. It departs from the literature by removing restrictions on asset holdings, and finds that optimal positions depend significantly and naturally on liquidity: When expected future liquidity is high, agents take more extreme positions, given that they do not have to hold those positions for long when they become undesirable. Consequently, larger trades should be observed in markets with more frequent trading. Liquidity need not affect the price significantly, however, because liquidity has offsetting impacts on different agents' demands. This result highlights the importance of unrestricted portfolio choice. The paper draws parallels with the transaction-cost literature and clarifies the relationship between the price level and the realized trading frequency in this literature.     

Resuscitating businessman risk: A rationale for familiarity-based portfolios

This paper studies two frequently observed portfolio behaviors that are seemingly inconsistent with rational portfolio choice. The first is the tendency of workers and entrepreneurs to hold their companyʼs stock. The second is the propensity of workers to limit their equity holdings through time. The explanation offered here for both of these behaviors lies in the option to switch jobs when oneʼs company does poorly. This is equivalent to holding put options on oneʼs own company stock and call options on the other companyʼs stock, where both options must be exercised at the same time. Given these initial undiversified implicit financial holdings, workers need to allocate a relatively large share of their regular financial assets to their own companyʼs stock and a relatively small share to the stock of their alternative employment simply to restore overall portfolio balance. Although this effect can only create some hedging demand for companyʼs stock, it is a factor of potentially major import for assessing the suitability of workersʼ financial decisions. I find that, under certain conditions, workers optimally hold almost 40% of their financial wealth in their companyʼs stock.     

Precautionary Saving,Financial Risk,and Portfolio Choice

Relying on a direct question about the desired amount of precautionary wealth from the 2002 wave of the Italian “Survey of Household Income and Wealth,” I assess the main determinants of the precautionary motive for saving, focusing on the role played by financial risk on households' saving decisions. Households that invest mainly in safe assets do not need to protect themselves against future and unexpected financial losses. Consequently, once we control for households' sources of risk beside financial ones, the amount of precautionary savings of a household investing exclusively in safe assets should be lower compared to households who detain a non‐negligible share of risky assets in their portfolio. Results show that, as expected, a strong and negative correlation exists between the desired amount of precautionary wealth and the ownership of a portfolio made exclusively of safe assets.     

Optimal portfolio selection with maximal risk adjusted return

We investigate the portfolio diversification problem by maximizing the risk adjusted return (RAR) of the underlying portfolio. The model in this article has two primary advantages over the original portfolio selection model with maximal RAR: (1) it considers the set of available assets containing any number of assets instead of only two assets, which is more reasonable in practical applications and (2) it incorporates the general linear constraint other than the simple budget constraint, which can deal with additional constraints for rational investors. An application including in-sample and out-of-sample tests is provided where the results illustrate that the portfolios selected by our method lead to considerable increases of RAR in comparison with those by the minimization of variance approach, and the outperformance persists using different sample frequencies.     

Incentives and Voluntary Investment in Employer Shares

Using a partial equilibrium model, this paper makes a first attempt to provide an explanation based on rational behaviour for the basic big puzzle of why workers have large holdings of the shares of their employer in their defined contribution (DC) pension plans. The primary explanations in the literature seem to be behavioural ones that involve sub‐optimal behaviour. This paper attempts to see how far a standard optimizing setting in a principal–agent type framework can go in explaining the same phenomenon. It uses an incentive approach involving two agents, senior managers and workers to show how portfolio weights can be voluntarily shifted away from what would be first best in the absence of an incentive problem.     

A simple portfolio allocation model of financial wealth

This paper introduces a simple but highly flexible portfolio allocation model which provides a convenient framework for testing and imposing considerable structure on the data. The model is estimated with Australian data for four financial assets, fixed deposits, savings bank deposits, building society deposits and holdings of a class of government bonds. In contrast to previous findings, interest rate coefficients are estimated precisely and indicate quite a high degree of substitutability.     

Portfolio choice, attention allocation, and price comovement

This paper models the attention allocation of portfolio investors. Investors choose the composition of their information subject to an information flow constraint. Given their expected investment strategy in the next period, which is to hold a diversified portfolio, in equilibrium investors choose to observe one linear combination of asset payoffs as a private signal. When investors use this private signal to update information about two assets, changes in one asset affect both asset prices and may lead to asset price comovement. The model also has implications for the transmission of volatility shocks between two assets.     

Multiplicity in general financial equilibrium with portfolio constraints

This paper explores the role of portfolio constraints in generating multiplicity of equilibrium. We present a simple financial market economy with two goods and two households, households who face constraints on their ability to take unbounded positions in risky stocks. Absent such constraints, equilibrium allocation is unique and is Pareto efficient. With one portfolio constraint in place, the efficient equilibrium is still possible; however, additional inefficient equilibria in which the constraint is binding may emerge. We show further that with portfolio constraints cum incomplete markets, there may be a continuum of equilibria; adding incomplete markets may lead to real indeterminacy.     

The effects of portfolio size on international equity home bias puzzle

This paper investigates a new explanation for the international equity home bias puzzle based on an endogenous asymmetric information model. Using a cross-sectional mutual fund data set, it is found that the degrees of home bias across fund managers are negatively correlated to the asset sizes under their management. This result is consistent with the theoretical prediction in the endogenous asymmetric information model—the portfolio managers with the larger assets tend to acquire more information regarding foreign equity and, hence, hold more foreign equity holdings.     

THE PRICE LEVEL, THE QUANTITY THEORY OF MONEY, AND THE FISCAL THEORY OF THE PRICE LEVEL

This paper examines price‐level determination from the perspective of portfolio choice. Arbitrages among money balances, bonds, and investment goods determine their relative demands. Returns to real balance holdings and after‐tax returns to investment goods determine the relative values of nominal and real assets. Because expectations of government policies ultimately determine the expected returns to both nominal and real assets, the price level depends on interactions among current and expected future monetary and fiscal policies. The quantity theory and the fiscal theory emerge as special cases produced by restricting both the margins and the policies considered.     

On trees and logs

In this paper we contrast the main workhorse model in asset pricing theory, the Lucas (1978) tree model (LT-Model), to a benchmark model in financial equilibrium theory, the real assets model (RA-Model). It is commonly believed that the two models entail similar conclusions since the LT-Model is a special case of the RA-Model. But this is simply wrong: implications of these models can be strikingly at odds. Indeed, under the widely used log-linear specification of households’ preferences, we show that for a large set of initial endowments the LT-Model—even with potentially complete financial markets—admits only peculiar financial equilibria in which the stock market is completely degenerate, in that all stocks offer the same investment opportunity—and yet, allocation is Pareto optimal. We investigate why the LT-Model is so much at variance with the RA-Model, and uncover new results on uniqueness of financial equilibria and introduction of portfolio constraints obtaining in the LT-Model, but not in the RA-Model.     

Liquidity risk and bank portfolio management in a financial system without deposit insurance: Empirical evidence from prewar Japan

Using data from prewar Japan, this paper investigates the impact of a liquidity shock induced by depositors' behavior on bank portfolio management during financial crises in a system lacking deposit insurance. It is found that banks reacted to the liquidity shock sensitively through an increase in their cash holdings not by liquidating bank loans but by selling securities in the financial market. Moreover, banks exposed to local financial contagion adjusted the liquidity of their portfolio mainly by actively selling and buying their securities in the financial market. Finally, there is no evidence to conclude that the existence of the lender of last resort mitigated the liquidity constraints in bank portfolio adjustments.     

Cognitive abilities and portfolio choice

We study the relation between cognitive abilities and stockholding using the recent Survey of Health, Ageing and Retirement in Europe (SHARE), which has detailed data on wealth and portfolio composition of individuals aged 50+ in 11 European countries and three indicators of cognitive abilities: mathematical, verbal fluency, and recall skills. We find that the propensity to invest in stocks is strongly associated with cognitive abilities, for both direct stock market participation and indirect participation through mutual funds and retirement accounts. Since the decision to invest in less information-intensive assets (such as bonds) is less strongly related to cognitive abilities, we conclude that the association between cognitive abilities and stockholding is driven by information constraints, rather than by features of preferences or psychological traits.     

Does religious faith affect household financial market participation? Evidence from China

Based on the 2013 China Household Finance Survey data, this paper investigates the impact of religious faith on household financial market participation and portfolio choice. The results show that religious faith can significantly promote household financial market participation. Besides, religious faith can increase the proportion of risky assets held by households, including equities. We also find that the need for social interaction and human capital accumulation can significantly induce religious residents to participate in financial markets and hold risky assets. Overall, our results reveal how faith affects household finance activities in China.     

On the Endogeneity of the Mean-Variance Efficient Frontier

The endogeneity of the efficient frontier in the mean-variance model of portfolio selection is commonly obscured in the portfolio selection literature and in widely used textbooks. The authors demonstrate this endogeneity and discuss the impact of parameter changes on the mean-variance efficient frontier and on the beta coefficients of individual assets.     

Portfolio Choice and Liquidity Constraints*

We study the infinite‐horizon model of household portfolio choice under liquidity constraints and revisit the portfolio specialization puzzle. We show why the puzzle is robust to several model variations, and argue that positive correlation between earnings shocks and stock returns is unlikely to provide an empirically plausible resolution. We find that relatively small fixed costs for stock market entry are sufficient to deter stockholding because, for a plausible range of parameter values, households can achieve desired consumption smoothing with small or zero holdings of stocks. Such costs could arise from informational considerations, sign‐up fees, and investor inertia.     

A large CVaR-based portfolio selection model with weight constraints

Although the traditional CVaR-based portfolio methods are successfully used in practice, the size of a portfolio with thousands of assets makes optimizing them difficult, if not impossible to solve. In this article we introduce a large CVaR-based portfolio selection method by imposing weight constraints on the standard CVaR-based portfolio selection model, which effectively avoids extreme positions often emerging in traditional methods. We propose to solve the large CVaR-based portfolio model with weight constraints using penalized quantile regression techniques, which overcomes the difficulties of large scale optimization in traditional methods. We illustrate the method via empirical analysis of optimal portfolios on Shanghai and Shenzhen 300 (HS300) index and Shanghai Stock Exchange Composite (SSEC) index of China. The empirical results show that our method is efficient to solve a large portfolio selection and performs well in dispersing tail risk of a portfolio by only using a small amount of financial assets.     

WEALTH,ASSET PORTFOLIO,MONEY DEMAND AND POLICY RULE

I look at the linkages between monetary policy and asset wealth using quarterly data for the USA. I show that a positive interest rate shock leads to a fall in aggregate wealth and an important change in portfolio composition: housing wealth gradually decreases, but the effects are very persistent; and financial wealth quickly shrinks, but the impact is short‐lived. I also find that the money market can be characterized as follows: (i) the money demand has a large interest elasticity and a small output elasticity; and (ii) the estimated monetary policy reaction function highlights the special focus given by the central bank to developments in monetary aggregates. These features call for an approach whereby monetary authorities put more emphasis on tracking wealth developments, in particular, given the asset portfolio rebalancing between money holdings and financial and/or housing assets.