Time-varying Investment Opportunities Research Articles

Optimal asset allocation and consumption rules for commodity-based sovereign wealth funds

This paper studies the optimal asset allocation for a sovereign wealth fund (SWF) subject to a stochastic stream of commodity-based income, where, without loss of generality, we focus on oil-based SWFs. Using CRRA utility, we assume the fund’s objective is to maximize the discounted utility of intertemporal consumption in the presence of time-varying investment opportunities, and given non-zero correlations between shocks to oil income and asset return innovations. We use the log-linear approximation method of Campbell (1993) to solve for the model’s optimal asset allocation and consumption rules. Using historical data, we estimate the model parameters using the maximization-by-parts algorithm of Song et al. (2005). We then calibrate the model to study the optimal allocation and consumption for varying levels of risk aversion, time preference and oil income volatility. Our results are of interest to SWFs seeking optimal portfolio choice in the face of changing investment opportunities which correlate with their stochastic stream of income.

Tail behavior of Bitcoin, the dollar, gold and the stock market index

This paper studies whether Bitcoin can be classified as a currency, a commodity or an investment asset. Inspired by the movement that tail behavior is the key feature to determine the property of asset and for market participants to perceive the asset, I compare the tail behavior of daily return on Bitcoin to that of daily return on the US dollar, gold and the stock market index. Based on the conditional autoregressive Value at Risk proposed by Engle and Manganelli (2004), I find the similarity of the tail behavior between Bitcoin and the dollar, the stock market index with respect to contemporaneous correlation. Additionally, the tail of stock market return turns out to be associated with the risk premium on Bitcoin’s return while Bitcoin is proved to be the element of the time-varying investment opportunity set on the basis of Merton’s (1973) ICAPM setting. These findings suggest that Bitcoin is traded as an alternative for a medium of exchange and a means of investment, being far from a commodity.

Optimal Portfolios under Time-Varying Investment Opportunities, Parameter Uncertainty, and Ambiguity Aversion

We study the implications of predictability on the optimal asset allocation of ambiguity-averse long-term investors and analyze the term structure of the multivariate risk–return trade-off considering parameter uncertainty. We calibrate the model to real returns of U.S. stocks, long-term bonds, cash, real estate, and gold using the term spread and the dividend–price ratio as additional predictive variables, and we show that over long horizons, the optimal asset allocation is significantly influenced by the covariance structure induced by estimation errors. The ambiguity-averse long-term investor optimally tilts his or her portfolio toward a seemingly inefficient portfolio, which shows maximum robustness against estimation errors.

Long-Term Asset Allocation under Time-Varying Investment Opportunities: Optimal Portfolios with Parameter and Model Uncertainty

We study the implications of predictability on the optimal asset allocation of ambiguity averse long-term investors. We analyze the term structure of the multivariate risk-return trade-off in a VAR model under full consideration of parameter uncertainty, and we decompose the predictive covariance along different sources of risk/uncertainty. We calibrate the model to real returns of US stocks, US long-term government bonds, cash, real-estate and gold using term spread and dividend yields as additional predictive variables. While over short periods the model-implied conditional covariance structure of asset-class returns determines the optimal allocation, we find that over longer horizons the optimal asset allocation is significantly influenced by the covariance structure induced by estimation errors. As a consequence, the ambiguity averse long-term investor tilts her portfolio not simply toward the global minimum-variance portfolio but shrinks portfolio weights toward a seemingly inefficient portfolio which shows maximum robustness against estimation errors. Most interestingly, we find that even though time diversification of stock returns vanishes after consideration of estimation errors, real long-term bond returns are even more affected, making stocks an important asset class for the ambiguity averse long-term investor.

Dynamic Asset Allocation with Liabilities

AbstractWe develop an analytical solution to the dynamic multi‐period portfolio choice problem of an investor with risky liabilities and time varying investment opportunities. We use the model to compare the asset allocation of investors who take liabilities into account, assuming time varying returns and a multi‐period setting with the asset allocation of myopic ALM investors. In the absence of regulatory constraints on asset allocation weights, there are significant gains to investors who have access to a dynamic asset allocation model with liabilities. The gains are smaller under the typical funding ratio constraints faced by pension funds.

Pension Fund Asset Allocation in Low Interest Rate Environment

We analyze changes in portfolios of pension funds since the start of current low interest rate environment. We find that they have on average decreased the allocation to equity and increased the allocation to fixed income, which is inconsistent with the literature on strategic asset allocation. Next, more generally, we empirically investigate the relationship between variables that predict asset returns and portfolio allocation in levels as well as changes. We find that dividend-price ratio shows the strongest relationship among other variables. However, we find a negative relationship as opposed to a positive one predicted by the literature. Overall, the results suggest that pension funds are unable to incorporate predictive information in their strategic asset allocation, but they take active decisions by under or over-weighting their portfolio relative to the stated strategic portfolio to benefit from time-varying investment opportunities.

Understanding Dynamic Mean Variance Asset Allocation

We provide a new portfolio decomposition formula that sheds light on the economics of portfolio choice for investors following the mean-variance (MV) criterion. We show that the number of components of a dynamic portfolio strategy can be reduced to two: the first is preference free and hedges the risk of a discount bond maturing at the investor's horizon while the second hedges the time variation in pseudo relative risk tolerance. Both components entail strong horizon effects in the dynamic asset allocation as a result of time-varying risk tolerance and investment opportunity sets. We also provide closed-form solutions for the optimal portfolio strategy in the presence of market return predictability. The model parameters are estimated over the period 1963 to 2012 for the U.S. market. We show that:(i) intertemporal hedging can be very large, (ii) the MV criterion hugely understates the true extent of risk aversion for high values of the risk aversion parameter, and the more so the shorter the investment horizon and, (iii) the efficient frontiers seem problematic for investment horizons shorter than one year but satisfactory for large horizons. Overall, adopting the MV model leads to acceptable results for medium and long term investors endowed with medium or high risk tolerance, but to very problematic ones otherwise.

Optimal retirement planning with a focus on single and joint life annuities

We optimize the asset allocation, consumption and bequest decisions of a couple with an uncertain lifetime. The asset menu consists of zero coupon bonds and pure endowments with different maturities, whole life annuities and stocks. The pure endowments pay either fixed or variable benefits, and, similarly to the whole life annuities, are contingent on either a single or a joint lifetime. We model the stock returns and the parameters for the term structure with a vector autoregressive model, thus considering time-varying investment opportunities. To find the optimal solution we use a multi-stage stochastic programming approach, which allows for including complex surrender charges on pure endowments and annuities, as well as transaction costs on stocks and bonds. Our findings indicate that despite high surrender charges, households should invest in a wide combination of life contingent products with different maturities and underlying financial risk.

The Liquidity Risk Premium Demanded by Large Investors: Dynamic Portfolio Choice with Stochastic Illiquidity

textabstractRecent empirical work documents large liquidity risk premiums in stock markets. We calculate the liquidity risk premiums demanded by large investors by solving a dynamic portfolio choice problem with stochastic price impact of trading, CRRA utility and a time-varying investment opportunity set. We find that, even with high trading-cost rates and substantial trading motives, the theoretically demanded liquidity risk premium is negligible, less than 3 basis points per year. Assuming forced selling during market downturn enlarges the liquidity risk premium to maximally 20 basis points per year, which is well below existing empirical estimates of the liquidity risk premium.

Inefficient Investment Waves

We show that firms' individually optimal liquidity management results in socially inefficient boom-and-bust patterns. Financially constrained firms decide on the level of their liquid resources facing cash-flow shocks and time-varying investment opportunities. Firms' liquidity management decisions generate simultaneous waves in aggregate cash holdings and investment, even if technology remains constant. These investment waves are not constrained efficient in general, because the social and private value of liquidity differs. The resulting pecuniary externality affects incentives differentially depending on the state of the economy, and often overinvestment occurs during booms and underinvestment occurs during recessions. In general, policies intended to mitigate underinvestment raise prices during recessions, making overinvestment during booms worse. However, a well-designed price-support policy will increase welfare in both booms and recessions.

Modeling Covariance Risk in Merton's ICAPM

We propose a new method for constructing the hedge component in Merton's ICAPM that uses a daily summary measure of economic activity to track time-varying investment opportunities. We then use nonparametric projections to compute a robust estimate of the conditional covariance between stock market returns and our daily economic activity index. We find that the new conditional covariance risk measure plays an important role in explaining time variation in the equity risk premium. Specification tests as well as out-of-sample forecasts of aggregate stock returns suggest that the new covariance risk measure performs well compared to alternative covariance measures previously proposed in the literature.

Inefficient Investment Waves

We show that firms’ individually optimal liquidity management results in socially inefficient boom-and-bust patterns. Financially constrained firms decide on the level of their liquid resources facing cash-flow shocks and time-varying investment opportunities. Firms; liquidity management decisions generate simoultaneous waves in aggregate cash holdings, in market value of liquidity and in investment even if technology remains constant, consistently with firm-level and aggregate evidence. These investment waves are not constrained efficient in general, because the social and private value of liquidity differs. The resulting pecuniary externality affect incentives differentially depending on the state of the economy. There is often overinvestment in booms and underinvestment in recessions. In general, policies targeted to raise prices in recessions to mitigate underinvestment, make overinvestment in booms worse. However, a well designed price-support policy will increase welfare both in booms and in recessions.

Is the investment factor a proxy for time-varying investment opportunities? The US and international evidence

Motivated from Fama’s (1991) conjecture of an explicit link between the cross-sectional and time-series stock return predictability, we investigate whether the investment factor constructed from the cross-section of stocks also has time-series predictive power for stock returns within Merton’s (1973) ICAPM framework. The evidence from both US and other G-7 countries (except Japan) suggests that the investment factor is a proxy for time-varying investment opportunities. We also find that the risk-return relation is positive and statistically significant after controlling for the covariance between the market factor and the investment factor.

Optimal portfolio choice with asset return predictability and nontradable labor income

We study the optimal consumption and investment choice for long-horizon investors with nontradable labor income and time-varying investment opportunities. Our results suggest that the popular investment recommendation that more conservative investors should hold a higher bond/stock ratio may lack theoretical justification when labor income is considered. When labor income is positively correlated with stock returns, a more risk-averse investor holds a higher bond/stock ratio in her risky portfolio, but the reverse is true when labor income is positively correlated with bond returns. The allocation to stock inherits the inverted U-shaped pattern of labor income growth with respect to expected time until retirement. Investors with lower income growth, namely, younger workers or those near retirement, should invest less in risky assets than those who are in their mid career and have a higher income growth. Performance test shows that the welfare loss of ignoring asset return predictability in the presence of nontradable labor income can be economically significant.

Dynamic Optimization of Futures Portfolio Strategies under Downside Risk Control

We introduce a novel out-of-sample approach to solve a real-time investor's multiperiod portfolio choice problem in a setting with (time-varying) conditional predictability, multiple assets and downside risk control. The method involves defining a discrete set of one-period portfolio allocation policies and choosing among them at portfolio revision dates within a discrete-time stochastic dynamic programming approach so as to maximize an investor's expected utility. Our framing of the portfolio problem overcomes the curse of dimensionality that is associated with time-varying investment opportunity sets and multiple assets. We apply our technique to dynamic investment decision problems in futures markets and demonstrate its feasibility and usefulness.

A robust optimization approach to asset-liability management under time-varying investment opportunities

This paper presents an asset liability management model based on robust optimization techniques. The model explicitly takes into consideration the time-varying aspect of investment opportunities. The emphasis of the proposed approach is on computational tractability and practical appeal. Computational studies with real market data study the performance of robust-optimization-based strategies, and compare it to the performance of the classical stochastic programming approach.

Expected VIX Option Returns

We dissect the fine structure of volatility risks, as an important component of time-varying investment opportunities, by studying returns on VIX option portfolios. In particular, we provide model-free evidence regarding the two leading channels in modeling volatility risks: stochastic volatility-of-volatility and volatility jumps. We find that zero-delta straddles and delta-hedged portfolios of VIX options, which are neutral to changes in VIX but sensitive to volatility-of-volatility, underperform zero. In contrast, tail portfolios, which we construct by out-of-the-money and at-the-money VIX options and are only sensitive to tails risks of volatility, outperform zero. Therefore, risks in volatility-of-volatility and jump-induced volatility tails are priced, providing empirical support for both of the two leading channels. We further construct measures for volatility-of-volatility and volatility tail risks, by the whole set of out-of-the-money VIX options, to understand how they are priced relative to variance and equity risk premiums. We find that both measures predict short-horizon market returns, with the predictability from volatility-of-volatility risks subsumed by the variance premium but the volatility tail risk standing as a separate channel. Different from existing tail risk measures of merely market returns, our volatility tail index provides important information regarding how investors gauge the extreme volatility risks.

A method for solving general equilibrium models with incomplete markets and many financial assets

This paper presents a numerical method for solving stochastic general equilibrium models with dynamic portfolio choice. The method can be applied to models with heterogeneous agents, time-varying investment opportunity sets, and incomplete asset markets. We illustrate the method using a two-country model with production. We check the accuracy of our method by comparing the numerical solution to a complete markets version of the model against its known analytic properties. We then apply the method to an incomplete markets version where no analytic solution is available. In all versions the standard accuracy tests confirm the effectiveness of our method.

Dynamic Asset Allocation with Liabilities

We develop an analytical solution to the dynamic multi-period portfolio choice problem of an investor with risky liabilities and time varying investment opportunities. We use the model to compare the asset allocation of investors who take liabilities into account, assuming time varying returns and a multi-period setting with the asset allocation of myopic ALM investors. In the absence of regulatory constraints on asset allocation weights, there are significant gains to investors who have access to a dynamic asset allocation model with liabilities. The gains are smaller under the typical funding ratio constraints faced by pension funds.

Misunderstanding Risk and Return?

In a seminal contribution, Campbell (1996) [Campbell, J., 1996, Understanding Risk and Return, Journal of Political Economy 104(2), 298-345] proposed a methodology based on a VAR(1) process to test Merton’s Intertemporal CAPM. Innovations in predictors of portfolio returns are estimated and used as risk factors in an asset pricing model. One key element is the triangularization of the VAR system used to obtain orthogonal innovations. We show that this procedure makes the cross-sectional prices of risk associated with the predictors non identifiable. This is because they depend on the arbitrary ordering of the variables in the VAR. Moreover, since the factors are orthogonal to the market and to one another, the comparison with alternative multi-factor models is problematic. To illustrate, we revisit recent results that allegedly showed that innovations in the predictors drive the two Fama-French factors out in the cross section of portfolio excess returns and concluded that HML and SMB proxy for time-varying investment opportunities. We show that these results are mainly a statistical artifact of the methodology used to obtain orthogonal innovations.