Low Risk-free Rate Research Articles

Habit persistence, impediments to production factor adjustments, and asset returns in general equilibrium models with self-fulfilling expectations

I examine asset returns in the context of real dynamic stochastic general equilibrium economies with multiple equilibria (indeterminacy) that allow for aggregate fluctuations due to non-fundamental belief shocks. The two models include habit formation in preferences. Model 1 combines restrictions on factor mobility and adjustment costs in a one-sector economy. Model 2 uses restrictions on factor mobility in a two-sector economy. Results demonstrate that Model 1 fails to match the stylized financial facts. Model 2 replicates the low risk-free rate and the standard deviation of the return on the risk-free asset, but underestimates the equity premium and standard deviation of the return on equity.

Asset Returns and Scheduled Macroeconomic News Announcements

Stock market excess returns are significantly higher on days when the government is scheduled to announce inflation statistics, unemployment statistics, and interest rate decisions. The average announcement day excess return from 1958 to 2007 is 10.6 basis points versus 1.4 basis points for all the other days. In contrast, the risk-free rate (measured as the daily return on a 30-day T-bill) is detectably lower on announcement days, consistent with a precautionary saving motive. We show that a simple equilibrium model with deterministically varying aggregate risk can generate higher risk premia and lower risk-free rates around announcements. Our results demonstrate the required trade-off between macroeconomic risk and financial asset returns.

Consensus Consumer and Intertemporal Asset Pricing with Heterogeneous Beliefs

The aim of the paper is to analyze the impact of heterogeneous beliefs in an otherwise standard competitive complete market economy. The construction of a consensus probability belief, as well as a consensus consumer, are shown to be valid modulo an aggregation bias, which takes the form of a discount factor. In classical cases, the consensus probability belief is a risk-tolerance weighted average of the individual beliefs, and the discount factor is proportional to the beliefs dispersion. This discount factor makes the heterogeneous beliefs setting fundamentally different from the homogeneous beliefs setting, and it is consistent with the interpretation of belief heterogeneity as a source of risk. We then use our construction to rewrite in a simple way the equilibrium characteristics (market price of risk, risk premium, risk-free rate) in a heterogeneous beliefs framework and to analyze the impact of belief heterogeneity. Finally, we show that it is possible to construct specific parametrizations of the heterogeneous beliefs model that lead to globally higher risk premia, lower risk-free rates, and risk premia that are lower for assets with higher belief dispersion.

Applying portfolio optimisation to the harvesting decisions of non-industrial private forest owners

The non-industrial private forest owner's optimal harvesting and investment strategies are studied at forest holding level by including individual forest stands in an asset class portfolio. The forest owner can either clearcut mature stands and invest the capital in financial or real asset classes (bank deposits, government bonds, stocks, apartments) or postpone clearcutting and retain capital in standing trees. Forest inventory data from actual forest holdings in Southwest Finland, the simulation–optimisation software MELA, and statistics on timber prices are utilised to compute the return series for forest stands. The numerical results show that the optimal level of clearcutting decreases markedly with initial non-forest wealth, especially at low risk-free rates of interest. It may therefore be rational for non-industrial private forest owners to consider shorter rotation periods than those of investors with diversified portfolios. The correlations between returns from forest stands are high, implying that increasing the variety of stand structures achieved by planting different species is not likely to bring substantial diversification benefits. The favoured investment outlet for harvesting revenues (apartments, government bonds or stocks) is sensitive to the period of historical data used to compute the return series and risk-free rate of interest. The value growth of forest stand can be used to estimate annual returns only for those stands that are readily mature. An alternative method of computing returns on stands in any development phase is proposed, based on net present value of stand adjusted for fluctuations in forest land prices. This method applies if selling forest land is considered an option. If selling is not an option, the ratio of maximised net present value to value at immediate harvest can be used as a ‘maturity index’ for ranking the stands for portfolio optimisation.

THE EQUITY PREMIUM PUZZLE AND EMOTIONAL ASSET PRICING

Since the equity premium as well as the risk-free rate puzzle question the concepts central to financial and economic modeling, we apply behavioral decision theory to asset pricing in view of solving these puzzles. US stock market data for the period 1960–2003 and German stock market data for the period 1977–2003 show that emotional investors who act in accordance to Bell's [6] disappointment theory — a special case of prospect theory — and additionally administer mental accounts demand a high equity premium. Furthermore, these investors reason a low risk-free rate. However, Barberis et al. [5] already showed that limited rational investors demand a high equity premium. But as opposed to them, our approach additionally supports dividend smoothing.

Rare Disasters and Asset Markets in the Twentieth Century*

The potential for rare economic disasters explains a lot of asset-pricing puzzles. I calibrate disaster probabilities from the twentieth century global history, especially the sharp contractions associated with World War I, the Great Depression, and World War II. The puzzles that can be explained include the high equity premium, low risk-free rate, and volatile stock returns. Another mystery that may be resolved is why expected real interest rates were low in the United States during major wars, such as World War II. The model, an extension of work by Rietz, maintains the tractable framework of a representative agent, timeadditive and isoelastic preferences, and complete markets. The results hold with i.i.d. shocks to productivity growth in a Lucas-tree type economy and also with the inclusion of capital formation. The Mehra-Prescott [1985] article on the equity risk-premium puzzle has received a great deal of attention. An article published three years later by Rietz [1988] purported to solve the puzzle by bringing in low-probability economic disasters, such as the Great Depression. I think that Rietz’s basic reasoning is correct, but the profession seems to think differently, as gauged by the continued attempts to find more and more complicated ways to resolve the equity-premium puzzle. I think the major reason for skepticism about Rietz’s argument is the belief that it depends on counterfactually high probabilities and sizes of economic disasters. Thus, a key aspect of my empirical analysis is the measurement of the frequency and sizes of the international economic disasters that occurred during the twentieth century. The three principal events are World War I, the Great Depression, and World War II, but post-World War II depressions have also been significant outside of OECD countries. My analysis of these events suggests a disaster probability of 1.5–2 percent per year with a distribution of declines in per capita GDP ranging between 15 percent and 64 percent. I construct a model of the equity premium that extends Lucas

Extrapolative Expectations: Implications for Volatility and Liquidity

This paper presents a model of liquidity and volatility in which investors extrapolate recent price movements to forecast the volatility of a risky asset. High perceived volatility leads to high risk premium, low current return, low risk-free rate and illiquid markets. Illiquidity amplifies supply shocks, increasing realized volatility of prices, which feeds into subsequent volatility forecasts. As a result, clustering of volatility and liquidity arises endogenously. The model helps to unify several known facts about liquidity and volatility, and I find support for its new prediction which links misperception of volatility to liquidity.

The equity premium in an overlapping-generations economy

In a recent paper, Constantinides, Donaldson and Mehra (CDM) present a convincing economic story that could simultaneously explain a high equity premium and a low risk-free rate. The argument is based on the effect of a borrowing restriction in an overlapping-generations model (OLG) with three generations. This paper investigates the effect of borrowing restrictions on the size of the equity premium in a model similar to CDM, but with a complete structure of contingent claims. The main conclusion of the analysis is that the results obtained by CDM follow from the particular market structure adopted in the model rather than the effects of the life cycle. Once the markets are completed, the equity premium and the risk-free rate in the OLG economy are identical to those obtained in a representative-agent (RA) economy.

Optimal Portfolio Balancing Under Conventional Preferences and Transaction Costs Explains the Equity Premium Puzzle

Following Constantinides' (1986) seminal approach and introducing transaction costs in the Pagano (1989) model, conventional CARA investors with heterogeneous endowments trade to construct optimal portfolios. We calibrate to the 1896-1994 equity and bond markets to show that gains from trade are high and, thus, investors require a high illiquidity premium even for a modest transactional charge. Excluding risk premia, exchange of equity and bonds by N strategic investors, as , under a mere 1% round-trip transaction cost induces a 6% illiquidity (equity) premium. Unlike existing literature, our findings are consistent with most stylized empirical facts. We recover the elasticity of trading demand from the excess equity return to confirm a major implication of the model. Among many other, so called, anomalies, we appear to explain the apparent irrational exuberance of equity markets, the 600% price premium for otherwise identical A stock over B stock in China, the low risk-free rate, the 20% letter stock premium and the lower return on the run bonds. Because illiquidity premia do not necessarily imply consumption volatility, variance bounds tests become irrelevant.

Direct Preference for Wealth in Aggregate Household Portfolios

According to standard theory, wealth should have no intrinsic value. Yet, conventional wisdom, recent theories, and data suggest it might. We verify whether or not households have direct preferences over wealth in selecting assets. The fully structural econometric model focuses on a multivariate Brownian motion in optimal consumption, portfolios and wealth. Using aggregate portfolio data, we find that wealth (i) is directly valued, (ii) reduces marginal utility and (iii) reduces risk aversion, while we reject the HARA, and CRRA restrictions. Consequently, wealth-dependent utility generates a larger IMRS risk, justifying a larger, more predictable risk premium and a lower risk-free rate.

Human Capital, Business Cycles and Asset Pricing

I investigate the asset pricing and business cycle implications of a dynamic stochastic general equilibrium model with human capital and education. Key features of the model are (1) a higher consumption risk resulting from the representative agent's desire to smooth leisure and from the short-run inelasticities in physical and human capital investment, and (2) a countercyclical risk aversion induced by shocks to human capital. The model provides a good fit to a number of asset-pricing facts including a low risk-free rate, an upward-sloping yield curve, a higher equity premium, countercyclical dividend yields, and long-horizon predictability of excess stock returns. On the macroeconomic side, the model matches conventional business-cycle statistics as well as a standard model does, while generating a high volatility in hours worked and a negative correlation between the output and the time spent in education, both of which are consistent with the data.

Equilibrium Asset Pricing with Time-varying Pessimism

We study the equilibrium pricing effects of a sentiment for pessimism. Pessimism has the form of Knightian model uncertainty aversion for a neighborhood of indistinguishable model specifications that are constrained in their relative entropy from a given reference model. We fully characterise the equilibrium of a pessimistic, representative agent, exchange economy with intertemporal consumption, stochastic opportunity set, and a relative entropy constraint that can depend on the state of the economy. We find that Knightian pessimism generates substantial First Order Risk Aversion (FORA) effects that enhance excess equity returns by pushing riskfree rates down. However, we find that the structure of equity returns is virtually unaffected by a Knightian concern for model uncertainty. We compute and calibrate explicit equilibrium examples of a pessimistic economy with an amount of pessimism associated to an 11% upper probability bound of confusing the relevant worst-case model and the given reference model. Relative entropy is the key in fixing such a realistic amount of pessimism in our calibrations. Even for log utility, such small amount of pessimism generates some 55 basis points more of unconditional equity premium. Knightian pessimism provides an economically and observationally different description of excess equity returns. Our findings show that realistic amounts of both pessimism and standard risk aversion yield substantial equity premia and low riskfree rates.

Disappointment, Pessimism and the Equity Risk Premia

We analyze the implications of the introduction of disappointment averse agents on the financial markets. The underlying intuition is that agents take account for the potential disappointment of their decisions, in particular when they invest on the stock market. After having defined the concepts of disappointment aversion, we show that in our framework a disappointment averse agent is pessimistic. We then explore the consequences of disappointment aversion and pessimism on the CAPM and the C-CAPM. We finally study a Lucas asset pricing model that is standard, except that the representative agent is supposed to be disappointment averse. Using a constant marginal utility function, we show that the model can account for both large equity risk premia and low risk-free rates. It may so be viewed as a solution to the equity premium puzzle

Belief-dependent Utilities, Aversion to State-Uncertainty and Asset Prices

This paper reinterprets standard axioms in choice theory to introduce the concepts of belief dependent utility functions and to state-uncertainty, and it shows that this type of preferences helps to explain the various stylized facts of asset returns, including a high equity risk premium, a low risk-free rate, a high return volatility, stock return predictability and volatility clustering. In one particular specification consistent with habit formation preferences, I also argue that aversion to state gives rise to aversion to long run risk, that is, to the uncertainty surrounding the long run average of future consumption. In order to solve for asset prices and returns under general conditions about the hidden state variable, the paper also develops a discretization methodology to obtain approximate analytical solutions. In a parsimonious parametrization, I then show that the model calibrated to real consumption generates unconditional moments for asset returns that closely match the empirical ones. Finally, due to the estimated time-variation in the dispersion of the conditional distribution on the drift rate of consumption, the model also generates a time series of conditional return volatility in line with the ex-post integrated volatility of stock returns.

A Monetary Explanation of the Equity Premium, Term Premium, and Risk-Free Rate Puzzles

This paper develops and estimates a monetary model that offers an explanation of some puzzling features of observed returns on equities and default-free bonds. The key feature of the model is that some assets other than money play a special role in facilitating transactions, which affects the rate of return that they offer. The model is capable of producing a low risk-free rate, a high equity premium, and an average positive relationship between maturity and term premium for default-free bonds. The model's implications for the joint distribution of asset returns, velocity, inflation, money growth, and consumption growth are also compared to the behavior of these variables in the U.S. economy.

Explaining Financial Market Facts: The Importance of Incomplete Markets and Transaction Costs

In this article, I suggest that incomplete markets and transaction costs are crucial for explaining the high equity premium and the low risk-free rate. I first demonstrate the failure of the complete frictionless markets model in explaining these return puzzles and then show how introducing incomplete markets and transaction costs can lead to success. Additionally, I explain how these features lead to predictions concerning individual consumptions, wealths, portfolios, and asset market transactions that are in better agreement with the facts than the predictions of the complete frictionless markets model.