Essays on asset allocation
- Autores: Gabriel Ignacio Penagos Londoño
- Directores de la Tesis: Francisco Sogorb Mira (dir. tes.), Gonzalo Rubio Irigoyen (dir. tes.)
- Lectura: En la Universidad Cardenal Herrera-CEU ( España ) en 2013
- Idioma: español
- Tribunal Calificador de la Tesis: Alfonso Santiago Novales Cinca (presid.), Mariano González Sánchez (secret.), Pedro Jose Serrano Jimenez (voc.), Juan M. Nave Pineda (voc.), Ana González Urteaga (voc.)
- Materias:
- Enlaces
- Tesis en acceso abierto en: Repositorio Institucional CEU
- Resumen
The aim of this work is to study the portfolio decisions of an investor who face a risky market, a topic that is a current subject of research in finance. In this regard, Modern Portfolio Theory provides us with the solution to the short term portfolio problem. The resulting strategy is suitable for one period horizon investments, reason by which it is named myopic. Similar results can be obtained if we extend the model to the more realistic situation of an investor in a multi period environment who is able to rebalancing the portfolio composition. This is true, for instance, in an economy where the investment opportunities does not change over time, and whose individual¿s risk preferences are represented by a power utility function. In particular it holds when some statistical characteristics of the rates of return such as the mean and the variance are identical and independently distributed. Despite the mathematical tractability of this approach, the real financial market does not behaves in such a way. A judicious study of financial time series suggest the presence of common properties, the so called stylized facts, which are irrespective of markets or instruments. As examples of these we find fluctuation over time of rates of return, heavy tails, volatility clustering, and leverage effects, among others. These changing market conditions are reflected in the portfolio decisions and accounted for by a new term in the portfolio allocation solution, the inter temporal hedging demand. In that context, we intend to study the financial market in order to determine the consequences of those factors on portfolio decisions. We do this by varying the underlying mathematical specification of the model in such a way that the aforementioned characteristics are modeled explicitly. The first chapter is motivated by the recent turmoil in the financial markets, where we have observed large losses across markets. This phenomena, regarded as systemic risk, is the risk of occurrence of rare, large, and highly correlated jumps whose mechanism relies on the interactions between markets. To deal with this, 2 we define a continuos multivariate model that includes a common jump component to all assets. The jump accounts for instantaneous and simultaneous occurrence of unexpected events in the market. The asset specific jump amplitude are defined as an independent random variable, reflecting the individual response to the severity of the shock. To gauge the impact of systemic risk to the portfolio, we match the first two moments of the jump-diffusion model to that of the pure diffusion model and compare the solutions. As market data we use the monthly series of a low book-to-market (growth stocks) portfolio, the high book-to-market (value stocks) portfolio, and an intermediate portfolio of Fama and French. We find that the effects of systemic jumps may be potentially substantial as long as market equity returns experiment very large average (negative) sizes. However, it does not seem to be relevant that stock markets experience very frequent jumps if they are not large enough to impact the most levered portfolios. All potentially relevant effects are concentrated in portfolios financed with a considerable amount of leverage. In fact, for conservative investors with low leverage positions the potential effects of systemic jumps on the optimal allocation of resources is not substantial even under large average size jumps. Finally, the value premium is particularly high when the average size of the jumps of value stocks is positive, large and relatively infrequent, while the average size of growth stocks is also very large but negative. It seems therefore plausible to conclude that the magnitude of the value premium is closely related to the characteristics of the jumps experienced by value and growth stocks. In chapter two, we follow the same line of including additional features of financial series to the model, and consider a time varying volatility. We also expect to enhance the the jump model¿s ability to capture skewness. Thus, besides to the jump term, we include a stochastic volatility term to the asset price dynamics. As in chapter one, this specification results in an incomplete market model. And, although dynamic 3 programing method is still available to address the problem, we sought to solve the model through the use of duality methods which leads to deeper insights to the portfolio solution. From the theoretical point of view, we obtain the expression for the portfolio allocation rule along with the market price of risk, the market price of volatility risk and the market price of jump risk. We also find the explicit expressions for the the mean, standard deviation, skewness and excess kurtosis in terms of the market model parameters. The portfolio rule reduces to the standard myopic rule when the correlation between the asset prices and volatility is zero, and the frequency of extreme event vanishes. The market price of risk is found to be composed by the Brownian market price of risk plus a jump contribution. The market price of volatility risk is approximately proportional to the market price of risk for a very low risk adverse investor and vanishes if the innovations in the returns are perfectly correlated with the instantaneous volatility. For the empirical analysis, besides the growth and value series, we also include the Standard and Poor¿s Composite index for comparison purposes. The numerical results show that series¿ mean is dominated by the diffusion mean compensated by the long run variance. Volatility depends on model¿s volatility parameters, i.e., jump volatility, long term volatility, volatility of stochastic volatility, and mean reversion. Finally, skewness and kurtosis strongly depends on jump mean, and on jump volatility respectively, and also on Poisson intensity. A closer look at Growth and Value series reveals that the largest variance of Growth series is mainly due to the low frequency of unexpected large events in Value series. Additionally, the long term volatility of the Growth series is larger. It is worth to mention that shocks with small jump mean¿s absolute value happen more frequently than larger shocks, in agreement with the results in the first chapter. The portfolio weights are found to be low compared with those of a standard diffu4 sion model. This is because the investor perceives more risk coming from jumps and stochastic volatility. We calculate a myopic demand as the ratio of the risk premium over the instantaneous volatility times the risk aversion. It proves to be greater than the total portfolio weight. The discrepancy could be explained if we define an intertemporal hedging demand as the difference between the total portfolio weight and the myopic contribution. Given that the expectations of asset performance worsen, the intertemporal hedging demand is negative thus reducing the participation of the myopic component. This reduction diminishes as increases for Growth and Value series, and is constant for the S&P500. In the third chapter we deal with time varying excess returns, we aim to set the basis of study for the time varying relative risk aversion as a useful tool for portfolio allocation. To that end, we estimate the consumption based, external habit model of Campbell and Cochrane. This model accounts for time varying and countercyclical expected returns, as well as the high equity premium with a low and steady riskfree rate. This model has the feature of deliver a counter cyclical varying risk aversion, and allows predictability of asset returns. Afterwards, we test two specifications of pricing models that includes surplus and risk aversion, under contemporaneous and ultimate consumption risk. As market data we examine the 25 portfolios formed on size and book to market by Fama and French. Numerical results shows that curvature exhibits low values, in spite of the high relative risk aversion. Its magnitude lessens as the lag of the ultimate consumptions series increases. We render the surplus ratio, the stochastic discount factor, and the time varying relative risk aversion. The linear relationship between the price over dividend and the surplus ratio in the Campbell and Cochrane model is most closely followed under ultimate consumption series for twelve months lags. The stochastic discount factor exhibits a business cycle, attaining maxima at the start of recessions and dropping at the end of them. Finally, the risk aversion 5 proved to be time varying and countercyclical. We estimate two factor pricing models derived from the habit model specification. The data analysis suggest that ultimate consumption risk specification with time varying aversion seems to explain relatively well the cross section of average returns. Additionally, we conclude that the excess returns seems to be more sensitive to risk aversion than to consumption growth. However, the estimated intercept for the models is statistically significant indicating an overall rejection of them.
