Loss aversion,asymmetric market comovements,and the home bias

Loss aversion has been used to explain why a high equity premium might be consistent with plausible levels of risk aversion. The intuition is that the first-order-different utility impact of wealth gains and losses leads loss-averse investors to behave similarly to investors with high risk aversion. But if so, should those agents not perceive larger gains from international diversification than standard expected-utility investors with plausible levels of risk aversion? They might not, because comovements in international stock markets are asymmetric: correlations are higher in market downturns than in upturns. This asymmetry dampens the gains from diversification relatively more for loss-averse investors. We analyze the portfolio problem of such an investor who has to choose between home and foreign equities in the presence of asymmetric comovement in returns. Perhaps surprisingly, in the context of the home bias puzzle we find that loss-averse investors behave similarly to those with standard expected-utility preferences and plausible levels of risk aversion. We argue that preference specifications that appear to perform well with respect to the equity premium puzzle should be subjected to this “test”.     

A Generalisation of the Mean-Variance Analysis

In this paper we consider a decision maker whose utility function has a kink at the reference point with different functions below and above this reference point. We also suppose that the decision maker generally distorts the objective probabilities. First we show that the expected utility function of this decision maker can be approximated by a function of mean and partial moments of distribution. This 'mean-partial moments' utility generalises not only mean-variance utility of Tobin and Markowitz, but also mean-semivariance utility of Markowitz. Then, in the spirit of Arrow and Pratt, we derive an expression for a risk premium when risk is small. Our analysis shows that a decision maker in this framework exhibits three types of aversions: aversion to loss, aversion to uncertainty in gains, and aversion to uncertainty in losses. Finally we present a solution to the optimal capital allocation problem and derive an expression for a portfolio performance measure which generalises the Sharpe and Sortino ratios. We demonstrate that in this framework the decision maker's skewness preferences have first-order impact on risk measurement even when the risk is small.     

Utilitarianism and fairness in portfolio positioning

The paper introduces the theory of optimal positioning of financial products. It is illustrated in the context of long-term intertemporal portfolio allocation and can be applied for example to asset allocation funds. We embed this problem in location theory: the portfolio is optimized within the investors’risk aversion dimension. For the CRRA utility functions, we compute explicitly the distance functions. For the first (utilitarian criterion), the average utility of the investors is maximized. For the second one (fairness criterion), the choice of portfolio is optimized so that the average monetary loss due to the lack of customization is minimized. Given the distribution of investors’ risk aversion, we provide a solution method and an algorithm to optimally position standardized portfolio along one of these two criteria.     

Investment strategies in the long run with proportional transaction costs and a HARA utility function

We consider an agent who invests in a stock and a money market in order to maximize the asymptotic behaviour of expected utility of the portfolio market price in the presence of proportional transaction costs. The assumption that the portfolio market price is a geometric Brownian motion and the restriction to a utility function with hyperbolic absolute risk aversion (HARA) enable us to evaluate interval investment strategies. It is shown that the optimal interval strategy is also optimal among a wide family of strategies and that it is optimal also in a time changed model in the case of logarithmic utility.     

Robust portfolio choice with uncertainty about jump and diffusion risk

We analyze the portfolio planning problem of an ambiguity averse investor. The stock follows a jump-diffusion process. We find that there are pronounced differences between ambiguity aversion with respect to diffusion risk and jump risk. Ignoring ambiguity with respect to jump risk causes larger losses in an incomplete market, whereas ignoring ambiguity with respect to diffusion risk is more severe in a complete market. For a deterministic jump size we show that the loss from market incompleteness is always increasing in the level of ambiguity aversion with respect to one risk factor and decreasing in the level of ambiguity aversion with respect to the other risk factor.     

Dynamic Portfolio Choice with Stochastic Wage and Life Insurance

We study optimal insurance, consumption, and portfolio choice in a framework where a family purchases life insurance to protect the loss of the wage earner's human capital. Explicit solutions are obtained by employing constant absolute risk aversion utility functions. We show that the optimal life insurance purchase is not a monotonic function of the correlation between the wage and the financial market. Meanwhile, the life insurance decision is explicitly affected by the family's risk preferences in general. The model also predicts that a family uses life insurance and investment portfolio choice to hedge stochastic wage risk.     

Portfolio turnpike theorems for constant policies

This paper develops general overtaking techniques for studying the asymptotic properties of portfolio policies optimal with respect to a terminal utility valuation. For a restricted class of utility functions the sequence of optimal constant (non-revised) portfolio policies formed as the horizon recedes into the future is shown to converge. Furthermore, for utility functions unbounded above and below, this turnpike policy need not be the policy associated with the minimal constant relative risk aversion function that bounds the valuation function from above. Finally, an analogy between the portfolio turnpike problem and the turnpike problem of growth theory is studied.     

Can utility optimization explain the demand for structured investment products?

In this paper, we first show that for classical rational investors with correct beliefs and constant absolute or constant relative risk aversion, the utility gains from structured products over and above a portfolio consisting of the risk-free asset and the market portfolio are typically much smaller than their fees. This result holds irrespectively of whether the investors can continuously trade the risk-free asset and the market portfolio at no costs or whether they can just buy the assets and hold them to maturity of the structured product. However, when considering behavioural utility functions, such as prospect theory, or investors with incorrect beliefs (arising from probability weighting or probability misestimation), the utility gain can be sizable.     

Equilibrium analysis of volatility clustering

Volatility clustering is a pervasive feature of equity markets. This article studies volatility clustering in an equilibrium setting by generalizing the CRRA and CARA representative agent models of finance. In equilibrium, the market portfolio follows a volatility regime-switching process in which the volatility level is determined by the agent's local risk aversion. Using monthly data, the empirical tests reveal that at least four volatility regimes are necessary to fit the data. While one of the models explains the GARCH effects in the data, an analysis of the Euler equation pricing errors suggests that both models are likely misspecified. Since the models can be used to closely approximate any state-independent utility function, it is doubtful that there exists any representative agent equilibrium (with state-independent utility) that is consistent with the data. An equivalent interpretation is that the market portfolio price process is not a diffusion process of the type studied by Bick [Bick, A., On viable diffusion price processes of the market portfolio, J. Finance 45 (1990) 673–689] and He and Leland [He, H., Leland, H., On equilibrium asset price processes, Rev. Financ. Stud. 6 (1993) 593–617].     

Endogenous Life‐Cycle Housing Investment and Portfolio Allocation

This paper develops a life‐cycle portfolio allocation model to address the effects of housing investment on the portfolio allocation of households. The model employs a comprehensive housing investment structure, Epstein–Zin recursive preferences, and a stock market entry cost. Furthermore, rather than resorting to calibration we estimate the value of the relative risk aversion and elasticity of intertemporal substitution. The model shows that housing investment has a strong crowding out effect on investment in risky assets throughout the life‐cycle. We further find that the effect of the presence of housing investment on households portfolio allocation is larger than the effect of having EZ recursive preferences.     

Saving and investing for early retirement: A theoretical analysis

We study optimal consumption and portfolio choice in a framework where investors adjust their labor supply through an irreversible choice of their retirement time. We show that investing for early retirement tends to increase savings and reduce an agent's effective relative risk aversion, thus increasing her stock market exposure. Contrary to common intuition, an investor might find it optimal to increase the proportion of financial wealth held in stocks as she ages and accumulates assets, even when her income and the investment opportunity set are constant. The model predicts a decrease in risk aversion following strong market gains like those observed in the nineties.     

Rewards for downside risk in Asian markets

Distributional properties of emerging market returns may impact on investor ability and willingness to diversify. Investors may also place greater weighting on downside losses, compared to upside gains. Using individual equities in a range of emerging Asian markets, we investigate the potential contribution of downside risk measures to explain asset pricing in these markets. As realized returns are used as a proxy for expected returns, we separately examine conditional returns in upturn and downturn periods, in order to successfully identify risk and return relationships. Results indicate that co-skewness and downside beta are priced by investors. Further testing confirms a separate premium for each measure, confirming that they capture different aspects of downside risk. Robustness tests indicate that, when combined with other risk measures, both retain their explanatory power. Tests also indicate that co-skewness may be the more robust measure.     

Asset Allocation and the Liquidity Premium for Illiquid Annuities

Academics and practitioners alike have developed numerous techniques for benchmarking investment returns to properly adjust seemingly high numbers for excessive levels of risk. The same, however, cannot be said for liquidity, or the lack thereof. This article develops a model for analyzing the ex ante liquidity premium demanded by the holder of an illiquid annuity. The annuity is an insurance product that is akin to a pension savings account with both an accumulation and decumulation phase. We compute the yield (spread) needed to compensate for the utility welfare loss, which is induced by the inability to rebalance and maintain an optimal portfolio when holding an annuity. Our analysis goes beyond the current literature, by focusing on the interaction between time horizon (both deterministic and stochastic), risk aversion, and preexisting portfolio holdings. More specifically, we derive a negative relationship between a greater level of individual risk aversion and the demanded liquidity premium. We also confirm that, ceteris paribus, the required liquidity premium is an increasing function of the holding period restriction, the subjective return from the market, and is quite sensitive to the individual's endowed (preexisting) portfolio.     

Nonlinearly weighted convex risk measure and its application

We propose a new class of risk measures which satisfy convexity and monotonicity, two well-accepted axioms a reasonable and realistic risk measure should satisfy. Through a nonlinear weight function, the new measure can flexibly reflect the investor’s degree of risk aversion, and can control the fat-tail phenomenon of the loss distribution. A realistic portfolio selection model with typical market frictions taken into account is established based on the new measure. Real data from the Chinese stock markets and American stock markets are used for empirical comparison of the new risk measure with the expected shortfall risk measure. The in-sample and out-of-sample empirical results show that the new risk measure and the corresponding portfolio selection model can not only reflect the investor’s risk-averse attitude and the impact of different trading constraints, but can find robust optimal portfolios, which are superior to the corresponding optimal portfolios obtained under the expected shortfall risk measure.     

Idiosyncratic Risk in Emerging Markets

In this study, I examine the properties and portfolio management implications of value‐weighted idiosyncratic volatility in 24 emerging markets. This paper provides evidence against the view that the rise of idiosyncratic risk is a global phenomenon. Furthermore, specific and market risks jointly predict market returns as there is a negative (positive) relation between idiosyncratic (market) risk and subsequent stock returns. Idiosyncratic volatility is the most important component of tracking error volatility, and it does not exhibit either an upward or a downward trend. Thus, investors do not have to increase, on average, the number of stocks they hold to keep the active risk constant.     

Liquidity risk and stock returns around the world

The recent global financial crisis demonstrates that market liquidity is a prominent systematic risk globally. We find that local liquidity risk, in addition to the local market, value and size factors, demands a systematic premium across stocks in 11 developed markets. This local pricing premium is smaller in countries where the country-level corporate boards are more effective and where there are less insider trading activities. We also discover that global liquidity risk is a significant pricing factor across all developed country market portfolios after controlling for global market, value, and size factors. The contribution of this risk to the return on a country market portfolio is economically and statistically significant within and across regions.     

The world price of liquidity risk

This paper empirically tests the liquidity-adjusted capital asset pricing model of Acharya and Pedersen (2005) on a global level. Consistent with the model, I find evidence that liquidity risks are priced independently of market risk in international financial markets. That is, a security’s required rate of return depends on the covariance of its own liquidity with aggregate local market liquidity, as well as the covariance of its own liquidity with local and global market returns. I also show that the US market is an important driving force of global liquidity risk. Furthermore, I find that the pricing of liquidity risk varies across countries according to geographic, economic, and political environments. The findings show that the systematic dimension of liquidity provides implications for international portfolio diversification.     

Does adding up of economic capital for market- and credit risk amount to conservative risk assessment?

There is a tradition in the banking industry of dividing risk into market risk and credit risk. Both categories are treated independently in the calculation of risk capital. But many financial positions depend simultaneously on both market risk and credit risk factors. In this case, an approximation of the portfolio value function separating value changes into a pure market risk plus pure credit risk component can result not only in an overestimation, but also in an underestimation of risk. We discuss this compounding effect in the context of foreign currency loans and argue that a separate calculation of economic capital for market risk and for credit risk may significantly underestimate true risk.     

Global equity fund performance, portfolio concentration, and the fundamental law of active management

This paper investigates the relation between portfolio concentration and the performance of global equity funds. Concentrated funds with higher levels of tracking error display better performance than their more broadly diversified counterparts. We show that the observed relation between portfolio concentration and performance is mostly driven by the breadth of the underlying fund strategies; not just by fund managers’ willingness to take big bets. Our results indicate that when investors strive to select the best-performing funds, they should not only consider fund managers’ tracking-error levels. More important is that they take into account the extent to which fund managers carefully allocate their risk budget across multiple investment strategies and have concentrated holdings in multiple market segments simultaneously.     

Optimal growth portfolios reconciling theory and practice

Modern portfolio theory dictates diversification among assets that are not perfectly correlated (that is, asset diversification). Professional investors, on the other hand, contend that one can simply diversify across time (that is, time diversification). The controversy of time diversification versus asset diversification is examined in this article by empirically analyzing the optimum investment strategies for a myopic utility function (the extreme case that supports across asset diversification) under varying degrees of relative risk aversion. While Merton and Samuelson (1974) and Samuelson (1990) show that with a myopic utility function the investment diversification strategy does not change with an increase in the investment horizon, the recommendation of professional investors is also found to hold since for a wide range of relative risk-aversion measures, the optimum portfolio is shown to consist almost entirely of equities.