Consumption-wealth Ratio Research Articles

Predicting consumption-wealth ratio changes and stock market returns

We show that the ability of Lettau and Ludvigson’s cay ratio to predict stock market returns could be greatly improved when adjustment is made for variations in expected cay ratio changes. We use the present-value identity of Campbell and Mankiw (1989) to derive the appropriate form of the adjustment and model the adjustment using a handful of macroeconomic variables. We find that the expected cay ratio changes vary in a predictable manner. Using our model to adjust cay improves the annual R̄2 values from 4.42% to 9.55% for in-sample prediction of excess market returns, and the out-of-sample pseudo R2 values increase from -1.88% and -1.72% to 2.38% and 3.69% with the first estimations using information up to 1985 and 1990, respectively. The superior performance also exists in medium-term market return predictions.

Existence of the Wealth-Consumption Ratio in Asset Pricing Models with Recursive Preferences

Abstract Modern asset pricing models combine recursive preferences with complex dynamics for the underlying consumption process. The existence of solutions is for many of these models an unsettled question. This paper introduces a novel technique to prove existence and nonexistence, as well as uniqueness for models with recursive preferences. The approach applies to many models of interest, including those with long-run consumption risks, with stochastic volatility and jumps, with time-varying consumption disasters, and with smooth ambiguity aversion and learning. Collectively, the proven results settle the existence question for many of today’s leading asset pricing models.

Dynamic spending and portfolio decisions with a soft social norm

We explore the implications of a preference ordering for an investor-consumer with a strong preference for keeping consumption above an exogenous social norm, but who is willing to tolerate occasional dips below it. We do this by splicing two CRRA preference orderings, one with high curvature below the norm and the other with low curvature at or above it. We find this formulation appealing for many endowment funds and sovereign wealth funds, including the Norwegian Government Pension Fund Global, which inspired our research. We derive an analytical solution, which we use to describe key properties of the policy functions for consumption and portfolio allocation. We find that annual spending should not only be significantly lower than the expected financial return, but mostly also procyclical. In particular, financial losses should, as a rule, be followed by larger than proportional spending cuts, except when some smoothing is needed to keep spending from falling too far below the social norm. Yet, at very low wealth levels, spending should be kept particularly low in order to build sufficient wealth to raise consumption above the social norm. Financial risk taking should also be modest and procyclical, so that the investor sometimes may want to “buy at the top” and “sell at the bottom.” Many of these features are shared by habit-formation models and other models with some lower bound for consumption. However, our specification is more flexible and thus more easily adaptable to actual fund management. The nonlinearity of the policy functions may present challenges regarding delegation to professional managers. However, simpler rules of thumb with constant or slowly moving equity share and consumption-wealth ratio can reach almost the same expected discounted utility. Nevertheless, the constant levels will then look very different from the implications of expected CRRA utility or Epstein–Zin preferences in that consumption is much lower.

Consumption and asset allocation with information learning and capital gains tax

<p style='text-indent:20px;'>In this study, we explore the consumption and asset allocation problem with random horizon in which stock returns are unobservable and capital gains are taxed. The agent with recursive utility could apply the historical stock prices and her private information to learn the expected returns on the stock. We obtain a semi-analytical solution to this problem. Numerical results show that the weights in the non-concealed risky asset and the safe asset increases and decreases with the expected return learnt, respectively. Besides, as the accuracy of estimation gets improved, the agent will reduce her consumption and riskless asset investment and enhance her investment in the non-concealed risky asset. However, information learning does not affect the tax evasion strategy. We also find that the effect of risk aversion on consumption-wealth ratio is significantly affected by the estimation accuracy.</p>

Long-Run Risk Unwrapped: An Analytical Expression of the Wealth-Consumption Ratio

Long-Run Risk Unwrapped: An Analytical Expression of the Wealth-Consumption Ratio

Aggregate consumption and wealth in the long run: The impact of financial liberalization

SummaryThis paper investigates the impact of financial liberalization on the relationship between consumption and total wealth (i.e., the sum of asset wealth and human wealth). Financial liberalization is persistent and may signal changes in expected future consumption growth rates and/or in rates of return on wealth that, through the intertemporal budget constraint, affect the current consumption–wealth ratio. We estimate the long‐run relationship between consumption, total wealth, and financial liberalization by state space methods using quarterly US data. The results show that the trend in the consumption–wealth ratio is well‐captured by our baseline liberalization indicator. We find that the increase in this indicator over the sample period has increased the consumption–wealth ratio with about 10%. Investigating the responsible channel, additional estimates show that financial liberalization has predictive power for aggregate consumption growth rather than for returns, a result that supports an incomplete markets interpretation of the link between liberalization and the consumption–wealth ratio.

Robust leverage decision under locked wealth and high-water mark contract

This paper investigates the effects of ambiguity on the optimal fund leverage and the private risk-taking of a hedge fund manager with a high-water mark contract and locked wealth in the fund. We derive a closed-form solution that predicts an increase in ambiguity about the market risk has a U-shaped effect on the optimal fund leverage but a monotonic decreasing effect on the private risk-taking. An increase in ambiguity about the idiosyncratic risk reduces the optimal fund leverage and raises the private risk-taking. According to the simulation, ambiguity erodes the fund wealth and the private wealth of the manager. Consumption-wealth ratio and welfare of the manager are both reduced as ambiguity increases.

Sustainability in a Risky World

We view sustainability as a requirement that welfare should not be expected to decline over time. We impose this requirement as a prior constraint on the consumption-savings-investment problem, and study its implications for saving, risky investment, and the social discount rate. The constraint does not distort portfolio choice, but it imposes an upper bound on the sustainable time preference rate and on the sustainable consumption-wealth ratio, which we show must lie between the riskless rate and the expected return on optimally invested wealth.

Sustainability in a Risky World

We view sustainability as a requirement that welfare should not be expected to decline over time. We impose this requirement as a prior constraint on the consumption-savings-investment problem, and study its implications for saving, risky investment, and the social discount rate. The constraint does not distort portfolio choice, but it imposes an upper bound on the sustainable time preference rate and on the sustainable consumption-wealth ratio, which we show must lie between the riskless rate and the expected return on optimally invested wealth.

Linking U.S. State-level housing market returns, and the consumption-(Dis)Aggregate wealth ratio

Using state-level data for the U.S. housing market over the period of 1975:Q1-2012:Q2, we show that the consumption-wealth ratios derived from aggregate wealth (cay) and disaggregate (i.e. financial and housing) wealth (cday) are strong predictors of real housing returns (and their volatility). Additionally, we find that, barring the extreme ends of their respective conditional distributions, such effect is stronger for housing return volatility than housing returns. All in all, our findings show that state-level regressions can recover a large degree of heterogeneity that country-level exercises typically ignore. Such heterogeneity is prominent not only in terms of consumption smoothing behavior, but also with regard to housing return predictability.

Regularizing Bayesian predictive regressions

Regularizing Bayesian predictive regressions provides a framework for prior sensitivity analysis via the regularization path. We jointly regularize both expectations and covariance matrices using a pair of shrinkage priors. Our methodology applies directly to vector autoregressions and seemingly unrelated regressions (SUR). By exploiting a duality between penalties and priors, we reinterpret two classic macrofinance studies: equity premium predictability and macroforecastability of bond risk premia. We find those plausible prior specifications for predictability for excess S&P 500 returns exist, using predictors as book-to-market ratios, consumption–wealth ratio, and T-bill rates. We evaluate our forecasts using a market-timing strategy and show how ours outperforms buy-and-hold. We also predict multiple bond excess returns involving a high-dimensional set of macroeconomic fundamentals with a regularized SUR model. We find the predictions from latent factor models such as PCA are sensitive to prior specifications. Finally, we conclude with directions for future research.

Bequest Motives in Consumption-Portfolio Problems with Recursive Utility

This paper studies consumption-portfolio decisions with recursive utility on a finite time horizon. We postulate essential properties that a bequest motive must satisfy. We show that the parameter which serves as weight of bequest in setups with time-additive utility is both quantitatively and qualitatively a poor measure of the relative strength of bequest. To obtain realistic distributions between consumption and bequest, this parameter takes extreme values and varies between 0 and $10^{32}$ depending on the calibration of the model. Besides, it violates the monotonicity requirement that the strength of bequest should be positively related to the amount of wealth bequeathed. We thus derive two alternative representations of the bequest motive that are in line with the postulated properties. Our representations are parametrized by the terminal wealth-consumption ratio or a normalized version hereof which serve as the strength of the bequest motive. We obtain clear-cut interpretations of strength.

Aggregate Consumption and Wealth in the Long Run: The Impact of Financial Liberalization

This paper investigates the impact of financial liberalization on the relationship between consumption and total wealth (i.e., the sum of asset wealth and human wealth). Financial liberalization is persistent and may signal changes in expected future consumption growth rates and/or in rates of return on wealth that, through the inter-temporal budget constraint, affect the current consumption-wealth ratio. We estimate the long-run relationship between consumption, total wealth and financial liberalization by state space methods using quarterly US data. The results show that the trend in the consumption-wealth ratio is well-captured by our baseline liberalization indicator. We find that the increase in this indicator over the sample period has increased the consumption-wealth ratio with about ten to sixteen percent. Investigating the responsible channel, additional estimates show that financial liberalization has predictive power for aggregate consumption growth rather than for returns, a result that supports an incomplete markets interpretation of the link between liberalization and the consumption-wealth ratio.

Optimal portfolio and spending rules for endowment funds

We investigate the role of different spending rules in a dynamic asset allocation model for university endowment funds. In particular, we consider the fixed consumption-wealth ratio (CW) rule and the hybrid rule which smoothes spending over time. We derive the optimal portfolios under these two strategies and compare them with a theoretically optimal (Merton) strategy. We show that the optimal portfolio with habit is less risky compared to the optimal portfolio without habit. A calibrated numerical analysis on U.S. data shows, similarly, that the optimal portfolio under the hybrid strategy is less risky than the optimal portfolios under both the CW and the classical Merton strategies, in typical market conditions. Our numerical analysis also shows that spending under the hybrid strategy is less volatile than the other strategies. Thus, endowments following the hybrid spending rule use asset allocation to protect spending. However, in terms of the endowment’s wealth, the hybrid strategy comparatively outperforms the conventional Merton and CW strategies when the market is highly volatile but under-performs them when there is strong stock market growth and low volatility. Overall, the hybrid strategy is effective in terms of stability of spending and intergenerational equity because, even if it allows short-term fluctuation in spending, it ensures greater stability in the long run.

Consumption, asset wealth, equity premium, term spread, and flight to quality

AbstractWe link transitory deviations of consumption from its equilibrium relationship with aggregate wealth and labor income to equity returns on the one hand, and to two characteristics of bond investors—the premium demanded to hold long‐term assets, and “flight to quality” behavior—on the other hand. Using a panel of 10 euro area countries over the period 1984Q1–2017Q4, we show that a rise in the consumption–wealth ratio predicts both higher equity returns and the future term spread, while a fall in the consumption–wealth ratio explains a large fraction of the rise in the spread between the “risky” and the “safe‐haven” bond.

An Intertemporal Preference with Risk and Loss Aversion: Equilibrium Analysis

We study a pure exchange economy with two groups of agents who exhibit different consumption patterns: one changes consumption immediately in response to shocks and the other exhibits stickiness in consumption change. This heterogeneity in the timing and the amount of consumption changes affects the equilibrium dynamics of wealth, and generates business cycles without a major shock to the endowment process. The model is fully tractable in that optimal allocations and the stationary densities of major asset pricing variables are obtained in closed form. The model generates counter-cyclical variation in risk aversion without having an external habit component in the utility function, by which we can explain why the Sharpe ratio, the risk premium, and the stock volatility are counter-cyclical and why the consumption-wealth (or price-dividend, inversely) ratio can predict future returns. The asset pricing moments and yield curves generated by the model match well with the data. Finally, the model also predicts that a (sudden) significant change in the government bond price is accompanied by major consumption revisions by households with sticky consumption without any change in the monetary policy.

An Intertemporal Preference with Risk and Loss Aversion

We study the consumption and portfolio selection problem of an agent who faces consumption irreversibility: there is disutility from changing consumption levels. The derived preference exhibits intertemporal loss aversion toward consumption changes with the previous consumption level being the reference point. The optimization problem involves the non-monotonic and non-concave utility function. By combining a duality method and the super-contact principle, we derive the closed-form solution. We show that the consumption policy involves an inaction interval for the consumption-wealth ratio, which can explain the four stylized facts about consumption at once. The optimal portfolio choice exhibits a U-shape in the inaction interval, which sheds light on the empirical debate on the relationship between a household's financial wealth and the share invested in risky assets.

Time-inconsistent preferences, consumption, investment and life insurance decisions

ABSTRACTIn this paper, we study a consumption, investment and life insurance strategy model in which agent has time-inconsistent preferences. We numerically find that time-inconsistent preferences lead agent to more consumption–wealth ratio and less insurance–wealth ratio, and that time-inconsistent agent purchases life insurance in advance. Moreover, both the consumption–wealth ratio and amount of life insurance purchased for naive agent are less than for sophisticated one, while total available wealth for naive agent is more than for sophisticated one. In particular, total amount of life insurance purchased increases when agent is young, but the situation reverses when she is older.

European equity markets: Who is the truly representative investor?

While most asset pricing models assume the perspective of the representative investor, the globalization of financial markets makes it difficult to know who the investors whose marginal utility determines market prices really are. Since the majority of investment in European financial markets comes from European countries, we study the performance of the consumption-capital asset pricing model (CCAPM) in the equity markets of the three largest European economies: France, Germany and the United Kingdom. For each nation, we price 25 portfolios sorted by size and book-to-market equity, 30 industry portfolios and 25 portfolios sorted by ROE and asset growth, using both domestic and foreign consumption growth as factors. In order to account for the variability of the parameters over time, we employ a scaled factor model, with the domestic consumer confidence index (CCI) and the consumption-wealth ratio (cay) as instruments. We show that the multi-CCAPM scaled by the CCI performs significantly better than the classic CCAPM, providing results comparable to those of the Fama-French five-factor model.

Learning from the Consumption-Wealth Ratio

Mixed-Frequency Predictive Regressions ∗ Markus Leippold † and Hanlin Yang ‡ January 21, 2019 Abstract This paper explores the performance of mixed-frequency predictive regressions for stock re- turns from the perspective of a Bayesian investor. We develop a parameter learning approach for sequential estimation, allowing for belief revisions. Empirically, we find that mixed-frequency models improve predictability, not only because of the combination of predictors with different frequencies but also due to the preservation of the time-variation in the volatility of predictors. Mixed-frequency models produce higher volatility timing benefits, compared to temporally aggregate models.Therefore, our results highlight the importance of consistently incorporating predictors of mixed frequencies and correctly specifying the volatility dynamics in predictive regressions