Chih-Ying Hsiao

Stochastic Correlation and Risk Premia in Term Structure Models

This paper proposes and analyses a term structure model that allows for both stochastic correlation between underlying factors and an extended market price of risk specification. The issues of invariant transformation and different normalization are then considered so that a comparison between different restrictions can be made. We show that significant improvement in bond fitting is obtained by both allowing the market price of risk to have an extended affine form, and allowing the correlation between underlying factors to be stochastic as well as of variable sign. The overall model fit is more negatively impacted by the restriction on the market price of risk than the restriction of correlated factors. However, the stochastic correlation is priced significantly by market participants, though its impact on the risk premia reduces gradually as time to maturity increases. In addition, stochastic correlation is vital in obtaining good hedged portfolio positions. Certainly, the best hedged portfolio is the one that is built based on the model that takes into account both stochastic correlation and extended market price of risk.

Asset Accumulation and Portfolio Decisions Under Inflation Risk

This chapter studies intertemporal investment strategies under inflation risk by extending the dynamic programming we have used so far, to include a stochastic price index. The stochastic price index gives rise to a two-tier evaluation system: agents maximize their utility of consumption in real terms while investment activities and wealth evolution are evaluated in nominal terms.

Asset Accumulation and Portfolio Decisions with Time Varying Asset Returns and Labor Income

Next we will include labor income into our asset accumulation and asset allocation decisions. This brings us to the problem of pension funds and retirement income. Academics, journalists and politicians have recently discussed in particular the issue of uncovered future retirement and pension fund liabilities. Many questions are being raised in this context.

Dynamic Saving and Portfolio Decisions-Theory

In this chapter, we illustrate the use of dynamic programming (DP) and the HJB equation for a simple model. We focus on dynamic saving and asset allocation, formulated in continuous time. We first introduce a model with one asset and constant returns. Usually in the literature, the problem is formulated as consumption and asset allocation decision. In this context, the objective of the investor is then to maximize his or her welfare given by some preferences over consumption, resulting in corresponding saving rates affecting the size of the assets.

Forecasting and Low Frequency Movements of Asset Returns

In this chapter we provide an overview on forecasting asset returns and low frequency movements in asset returns. Saving and asset allocation decision, usually focus on low frequency movements in asset returns and how they are expected to behave in the future. Thus, the prevailing consensus in the context of portfolio theory, is of the view that the estimates of the mean, variance and covariance should be forward looking rather than purely historically.

Continuous and Discrete Time Modeling

As mentioned, the transition of a continuous time model into a discrete time model is not an easy issue. We discuss here various discretization procedures to turn continuous time into discrete time models. There are many methods to convert continuous time models into discrete time variants. The main discretization methods are the Euler method, the Milstein method and a new local linearization method. All those will be illustrated here to obtain discrete-time approximate models.

Portfolio Modeling with Sustainability Constraints

As mentioned in Chap. 1 following the events of the world-wide financial crisis over the periods 2007–2009, the risk profile of some assets changed drastically and many assets exhibited large losses. These events have reinforced thinking about proper portfolio models that not only avoid large losses, but also allow to impose some constraints. This chapter will introduce standard static portfolio models that however also impose some constraints. Asset accumulation through saving or consumption decisions, will not be discussed in this chapter, so we will assume that the funds are given and only asset allocations have to be made. More generally, portfolio decisions under constraints are important for practitioners that invest on behalf of institutions with some ethical or social guidelines. For example, investment decisions of wealth funds, pension funds or university endowments, are often supposed to follow multiple guidelines and procedures rather than only choosing one procedure, such as an optimizing procedure without constraints. This is a point emphasized by Danthine and Donaldson (2005). They note that one step corresponds to the choice of instruments, another decision corresponds to the country or sector allocation or the choice of specific individual assets based on available information—to all of them maybe some constraints attached.

Asset Accumulation with Estimated Low Frequency Movements of Asset Returns

As discussed in Chap. 2 academic research on asset returns seems to converge toward the view that a proper formation of expected asset returns are essential for saving and asset allocation decisions. As also shown in Chap. 4 the use of time varying asset returns, following low frequency movements, appears to be quite suitable for the purpose of such decisions. In this chapter harmonic estimations are used to estimate low frequency movements of time series data on asset returns. We employ U.S. data sets and undertake a harmonic fitting of the actual time series data.

Continuous and Discrete Time Modeling of Short-Term Interest Rates

In modern finance theory, the short-term interest rate is important in characterizing the term structure of interest rates and in pricing interest-rate-contingent-claims. There is some pioneering work in the continuous-time framework, for example by Vasicek (1997) and Cox et al. (1985). A survey of is provided by Chan et al. (1992). Chan et al. (1992) show that a wide variety of well-known one-factor models for short rates can be nested within the following stochastic different equation (SDE):