An equity wealth preservation strategy: Following the macro trend

Financial crisis have happened in the past and will continue to do so in the future. In the most recent 2008 crisis, global equities (as measured by the MSCI ACWI index) lost a staggering 54.2% in USD, on the year. During those periods wealth preservation becomes at the top of most investor’s concerns. The purpose of this paper is to develop a strategy that protects the investment during bear markets and significant market corrections, generates capital appreciation, and that can support Millennium BCP’s Wealth Management Unit on their asset allocation procedures. This strategy extends the Dual Momentum approach introduced by Gary Antonacci (2014) in two ways. First, the investable set of securities in the equities space increases from two to four. Besides the US it will comprise the Japanese, European (excl. UK) and EM equity indices. Secondly, it adds a volatility filter as well as three indicators related to the business cycle and the state of the economy, which are relevant to decide on the strategy’s exposure to equities. Overall the results attest the resiliency of the strategy before, during and after historical financial crashes, as it drastically reduces the downside exposure and consistently outperforms the benchmark index by providing higher mean returns with lower variance.

Forecasting volatility using a continuous time model

This paper evaluates the forecasting performance of a continuous stochastic volatility model with two factors of volatility (SV2F) and compares it to those of GARCH and ARFIMA models. The empirical results show that the volatility forecasting ability of the SV2F model is better than that of the GARCH and ARFIMA models, especially when volatility seems to change pattern. We use ex-post volatility as a proxy of the realized volatility obtained from intraday data and the forecasts from the SV2F are calculated using the reprojection technique proposed by Gallant and Tauchen (1998).

Three essays on the psychology of investment and financial markets

Préface My thesis consists of three essays where I consider equilibrium asset prices and investment strategies when the market is likely to experience crashes and possibly sharp windfalls. Although each part is written as an independent and self contained article, the papers share a common behavioral approach in representing investors preferences regarding to extremal returns. Investors utility is defined over their relative performance rather than over their final wealth position, a method first proposed by Markowitz (1952b) and by Kahneman and Tversky (1979), that I extend to incorporate preferences over extremal outcomes. With the failure of the traditional expected utility models in reproducing the observed stylized features of financial markets, the Prospect theory of Kahneman and Tversky (1979) offered the first significant alternative to the expected utility paradigm by considering that people focus on gains and losses rather than on final positions. Under this setting, Barberis, Huang, and Santos (2000) and McQueen and Vorkink (2004) were able to build a representative agent optimization model which solution reproduced some of the observed risk premium and excess volatility. The research in behavioral finance is relatively new and its potential still to explore. The three essays composing my thesis propose to use and extend this setting to study investors behavior and investment strategies in a market where crashes and sharp windfalls are likely to occur. In the first paper, the preferences of a representative agent, relative to time varying positive and negative extremal thresholds are modelled and estimated. A new utility function that conciliates between expected utility maximization and tail-related performance measures is proposed. The model estimation shows that the representative agent preferences reveals a significant level of crash aversion and lottery-pursuit. Assuming a single risky asset economy the proposed specification is able to reproduce some of the distributional features exhibited by financial return series. The second part proposes and illustrates a preference-based asset allocation model taking into account investors crash aversion. Using the skewed t distribution, optimal allocations are characterized as a resulting tradeoff between the distribution four moments. The specification highlights the preference for odd moments and the aversion for even moments. Qualitatively, optimal portfolios are analyzed in terms of firm characteristics and in a setting that reflects real-time asset allocation, a systematic over-performance is obtained compared to the aggregate stock market. Finally, in my third article, dynamic option-based investment strategies are derived and illustrated for investors presenting downside loss aversion. The problem is solved in closed form when the stock market exhibits stochastic volatility and jumps. The specification of downside loss averse utility functions allows corresponding terminal wealth profiles to be expressed as options on the stochastic discount factor contingent on the loss aversion level. Therefore dynamic strategies reduce to the replicating portfolio using exchange traded and well selected options, and the risky stock.

Can a Lucas model with habit generate realistic conditional volatility in exchange rate returns?

In this paper, we attempt to give a theoretical underpinning to the well established empirical stylized fact that asset returns in general and the spot FOREX returns in particular display predictable volatility characteristics. Adopting Moore and Roche s habit persistence version of Lucas model we nd that both the innovation in the spot FOREX return and the FOREX return itself follow "ARCH" style processes. Using the impulse response functions (IRFs) we show that the baseline simulated FOREX series has "ARCH" properties in the quarterly frequency that match well the "ARCH" properties of the empirical monthly estimations in that when we scale the x-axis to synchronize the monthly and quarterly responses we find similar impulse responses to one unit shock in variance. The IRFs for the ARCH processes we estimate "look the same" with an approximately monotonic decreasing fashion. The Lucas two-country monetary model with habit can generate realistic conditional volatility in spot FOREX return.

Revisiting Shiller’s excess volatility hypothesis

One of the cornerstone of financial anomalies is that there exists money making opportunities. Shiller’s excess volatility theory is re-investigated from the perspective of a trading strategy where the present value is computed using a series of simple econometric models to forecast the present value. The results show that the excess volatility may not be exploited given the data available until time t. However, when learning is introduced empirically, the simple trading strategy may offer profits, but which are likely to disappear once transaction costs are considered.

Revisiting Shiller’s excess volatility hypothesis

One of the cornerstone of financial anomalies is that there exists money making opportunities. Shiller’s excess volatility theory is re-investigated from the perspective of a trading strategy where the present value is computed using a series of simple econometric models to forecast the present value. The results show that the excess volatility may not be exploited given the data available until time t. However, when learning is introduced empirically, the simple trading strategy may offer profits, but which are likely to disappear once transaction costs are considered.

Three essays in international finance

Executive Summary The first essay of this dissertation investigates whether greater exchange rate uncertainty (i.e., variation over time in the exchange rate) fosters or depresses the foreign investment of multinational firms. In addition to the direct capital financing it supplies, foreign investment can be a source of valuable technology and know-how, which can have substantial positive effects on a host country's economic growth. Thus, it is critically important for policy makers and central bankers, among others, to understand how multinationals base their investment decisions on the characteristics of foreign exchange markets. In this essay, I first develop a theoretical framework to improve our knowledge regarding how the aggregate level of foreign investment responds to exchange rate uncertainty when an economy consists of many firms, each of which is making decisions. The analysis predicts a U-shaped effect of exchange rate uncertainty on the total level of foreign investment of the economy. That is, the effect is negative for low levels of uncertainty and positive for higher levels of uncertainty. This pattern emerges because the relationship between exchange rate volatility and 'the probability of investment is negative for firms with low productivity at home (i.e., firms that find it profitable to invest abroad) and the relationship is positive for firms with high productivity at home (i.e., firms that prefer exporting their product). This finding stands in sharp contrast to predictions in the existing literature that consider a single firm's decision to invest in a unique project. The main contribution of this research is to show that the aggregation over many firms produces a U-shaped pattern between exchange rate uncertainty and the probability of investment. Using data from industrialized countries for the period of 1982-2002, this essay offers a comprehensive empirical analysis that provides evidence in support of the theoretical prediction. In the second essay, I aim to explain the time variation in sovereign credit risk, which captures the risk that a government may be unable to repay its debt. The importance of correctly evaluating such a risk is illustrated by the central role of sovereign debt in previous international lending crises. In addition, sovereign debt is the largest asset class in emerging markets. In this essay, I provide a pricing formula for the evaluation of sovereign credit risk in which the decision to default on sovereign debt is made by the government. The pricing formula explains the variation across time in daily credit spreads - a widely used measure of credit risk - to a degree not offered by existing theoretical and empirical models. I use information on a country's stock market to compute the prevailing sovereign credit spread in that country. The pricing formula explains a substantial fraction of the time variation in daily credit spread changes for Brazil, Mexico, Peru, and Russia for the 1998-2008 period, particularly during the recent subprime crisis. I also show that when a government incentive to default is allowed to depend on current economic conditions, one can best explain the level of credit spreads, especially during the recent period of financial distress. In the third essay, I show that the risk of sovereign default abroad can produce adverse consequences for the U.S. equity market through a decrease in returns and an increase in volatility. The risk of sovereign default, which is no longer limited to emerging economies, has recently become a major concern for financial markets. While sovereign debt plays an increasing role in today's financial environment, the effects of sovereign credit risk on the U.S. financial markets have been largely ignored in the literature. In this essay, I develop a theoretical framework that explores how the risk of sovereign default abroad helps explain the level and the volatility of U.S. equity returns. The intuition for this effect is that negative economic shocks deteriorate the fiscal situation of foreign governments, thereby increasing the risk of a sovereign default that would trigger a local contraction in economic growth. The increased risk of an economic slowdown abroad amplifies the direct effect of these shocks on the level and the volatility of equity returns in the U.S. through two channels. The first channel involves a decrease in the future earnings of U.S. exporters resulting from unfavorable adjustments to the exchange rate. The second channel involves investors' incentives to rebalance their portfolios toward safer assets, which depresses U.S. equity prices. An empirical estimation of the model with monthly data for the 1994-2008 period provides evidence that the risk of sovereign default abroad generates a strong leverage effect during economic downturns, which helps to substantially explain the level and the volatility of U.S. equity returns.

Equilibrium asset prices and savings of heterogeneous agents in the presence of incomplete markets and portfolio constraints

We study the quantitative properties of a dynamic general equilibrium model in which agents face both idiosyncratic and aggregate income risk, state-dependent borrowing constraints that bind in some but not all periods and markets are incomplete. Optimal individual consumption-savings plans and equilibrium asset prices are computed under various assumptions about income uncertainty. Then we investigate whether our general equilibrium model with incomplete markets replicates two empirical observations: the high correlation between individual consumption and individual income, and the equity premium puzzle. We find that, when the driving processes are calibrated according to the data from wage income in different sectors of the US economy, the results move in the direction of explaining these observations, but the model falls short of explaining the observed correlations quantitatively. If the incomes of agents are assumed independent of each other, the observations can be explained quantitatively.

Option pricing under stochastic volatility and stochastic interest rate in the Spanish case

Among the underlying assumptions of the Black-Scholes option pricingmodel, those of a fixed volatility of the underlying asset and of aconstantshort-term riskless interest rate, cause the largest empirical biases. Onlyrecently has attention been paid to the simultaneous effects of thestochasticnature of both variables on the pricing of options. This paper has tried toestimate the effects of a stochastic volatility and a stochastic interestrate inthe Spanish option market. A discrete approach was used. Symmetricand asymmetricGARCH models were tried. The presence of in-the-mean and seasonalityeffectswas allowed. The stochastic processes of the MIBOR90, a Spanishshort-terminterest rate, from March 19, 1990 to May 31, 1994 and of the volatilityofthe returns of the most important Spanish stock index (IBEX-35) fromOctober1, 1987 to January 20, 1994, were estimated. These estimators wereused onpricing Call options on the stock index, from November 30, 1993 to May30, 1994.Hull-White and Amin-Ng pricing formulas were used. These prices werecomparedwith actual prices and with those derived from the Black-Scholesformula,trying to detect the biases reported previously in the literature. Whereasthe conditional variance of the MIBOR90 interest rate seemed to be freeofARCH effects, an asymmetric GARCH with in-the-mean and seasonalityeffectsand some evidence of persistence in variance (IEGARCH(1,2)-M-S) wasfoundto be the model that best represent the behavior of the stochasticvolatilityof the IBEX-35 stock returns. All the biases reported previously in theliterature were found. All the formulas overpriced the options inNear-the-Moneycase and underpriced the options otherwise. Furthermore, in most optiontrading, Black-Scholes overpriced the options and, because of thetime-to-maturityeffect, implied volatility computed from the Black-Scholes formula,underestimatedthe actual volatility.

On the relevance of modeling volatility for pricing purposes

This paper presents a two-factor (Vasicek-CIR) model of the term structure of interest rates and develops its pricing and empirical properties. We assume that default free discount bond prices are determined by the time to maturity and two factors, the long-term interest rate and the spread. Assuming a certain process for both factors, a general bond pricing equation is derived and a closed-form expression for bond prices is obtained. Empirical evidence of the model's performance in comparisson with a double Vasicek model is presented. The main conclusion is that the modeling of the volatility in the long-term rate process can help (in a large amount) to fit the observed data can improve - in a reasonable quantity - the prediction of the future movements in the medium- and long-term interest rates. However, for shorter maturities, it is shown that the pricing errors are, basically, negligible and it is not so clear which is the best model to be used.

A Hull and White formula for a general stochastic volatility jump-diffusion model with applications to the study of the short-time behavior of the implied volatility

In this paper, generalizing results in Alòs, León and Vives (2007b), we see that the dependence of jumps in the volatility under a jump-diffusion stochastic volatility model, has no effect on the short-time behaviour of the at-the-money implied volatility skew, although the corresponding Hull and White formula depends on the jumps. Towards this end, we use Malliavin calculus techniques for Lévy processes based on Løkka (2004), Petrou (2006), and Solé, Utzet and Vives (2007).

A note on the Malliavin differentiability of the Heston volatility

We show that the Heston volatility or equivalently the Cox-Ingersoll-Ross process is Malliavin differentiable and give an explicit expression for the derivative. This result assures the applicability of Malliavin calculus in the framework of the Heston stochastic volatility model and the Cox-Ingersoll-Ross model for interest rates.

Essays in general equilibrium asset pricing

ABSTRACT : Research in empirical asset pricing has pointed out several anomalies both in the cross section and time series of asset prices, as well as in investors' portfolio choice. This dissertation aims to discover the forces driving some of these "puzzling" asset pricing dynamics and portfolio decisions observed in the financial market. Through the dissertation I construct and study dynamic general equilibrium models of heterogeneous investors in the presence of frictions and evaluate quantitatively their implications for financial-market asset prices and portfolio choice. I also explore the potential roots of puzzles in international finance. Chapter 1 shows that, by introducing jointly endogenous no-default type of borrowing constraints and heterogeneous beliefs in a dynamic general-equilibrium economy, many empirical features of stock return volatility can be reproduced. While most of the research on stock return volatility is empirical, this paper provides a theoretical framework that is able to reproduce simultaneously the cross section and time series stylized facts concerning stock returns and their volatility. In contrast to the existing theoretical literature related to stock return volatility, I don't impose persistence or regimes in any of the exogenous state variables or in preferences. Volatility clustering, asymmetry in the stock return-volatility relationship, and pricing of multi-factor volatility components in the cross section all arise endogenously as a consequence of the feedback between the binding of no-default constraints and heterogeneous beliefs. Chapters 2 and 3 explore the implications of differences of opinion across investors in different countries for international asset pricing anomalies. Chapter 2 demonstrates that several international finance "puzzles" can be reproduced by a single risk factor which captures heterogeneous beliefs across international investors. These puzzles include: (i) home equity preference; (ii) the dependence of firm returns on local and foreign factors; (iii) the co-movement of returns and international capital flows; and (iv) abnormal returns around foreign firm cross-listing events in the local market. These are reproduced in a setup with symmetric information and in a perfectly integrated world with multiple countries and independent processes producing the same good. Chapter 3 shows that by extending this framework to multiple goods and correlated production processes; the "forward premium puzzle" arises naturally as a compensation for the heterogeneous expectations about the depreciation of the exchange rate held by international investors. Chapters 2 and 3 propose differences of opinion across international investors as the potential resolution of several international finance `puzzles'. In a globalized world where both capital and information flow freely across countries, this explanation seems more appealing than existing asymmetric information or segmented markets theories aiming to explain international finance puzzles.

Market linkages and volatility spillover: evidence from BRIC countries

The aim of this study is to investigate volatility spillover-effect and market integration between BRIC countries. Motivated by existing literature of market integration between developed and emerging markets, we will investigate market linkages using multivariate asymmetric GARCH BEKK model. The increasing globalization of the financial markets and consequent higher volatility transfer between markets makes it more important to understand market integration between BRIC countries. We investigate the stock market integration and volatility transfer between the BRIC countries form 1998 to 2007, using daily data. The empirical results show that there are international diversification benefits among Brazil, Russia, China and India. U.S. influence to these countries has been week, even though U.S. economy has been leading the global financial markets. From Finnish point of view, diversification benefits are robust but we find some correlation with Russia and China.