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Concept# Modern portfolio theory

Summary

Modern portfolio theory (MPT), or mean-variance analysis, is a mathematical framework for assembling a portfolio of assets such that the expected return is maximized for a given level of risk. It is a formalization and extension of diversification in investing, the idea that owning different kinds of financial assets is less risky than owning only one type. Its key insight is that an asset's risk and return should not be assessed by itself, but by how it contributes to a portfolio's overall risk and return. It uses the past variance of asset prices as a proxy for future risk.
Economist Harry Markowitz introduced MPT in a 1952 essay, for which he was later awarded a Nobel Memorial Prize in Economic Sciences; see Markowitz model.
Mathematical model
Risk and expected return
MPT assumes that investors are risk averse, meaning that given two portfolios that offer the same expected return, investors will prefer the less risky one. Thus, an investor will take on increa

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Susanne Johanna Petronella Léonie Vissers

This thesis examines how banks choose their optimal capital structure and cash reserves in the presence of regulatory measures. The first chapter, titled Bank Capital Structure and Tail Risk, presents a bank capital structure model in which bank assets are subject to both diffusion and tail risk. Of these two types of risk, tail risk causes uninsured deposits to be risky, as the bank's asset value can unexpectedly fall below the value of deposits in case of default. The model shows that tail risk, rather than diffusion risk, is the main driver of the risk on deposits when the bank is unregulated and of the endogenous deposit insurance premium when the bank is regulated. Keeping total volatility constant, the model shows that a high tail risk component leads to higher credit spreads, default risk, and magnitude of bank losses in default than a high diffusion risk component.The second chapter, titled Bank Regulation and Market Discipline in the Presence of Risk-Taking Incentives, presents a bank capital structure model in which equity holders can increase asset risk once debt is in place. I study the effects of capital requirements and subsidized deposit insurance on the bank's privately optimal funding and operational risk level. The model predicts that there are synergetic effects of regulation and market discipline. When the regulator sets the capital charge and deposit insurance premium payments sufficiently high for a risky portfolio, the bank commits to the low-risk asset portfolio by setting a lower leverage ratio and substituting market debt for deposits. This market discipline effect disappears when the regulatory costs become too high. In the third chapter that is titled Dividend Restrictions and Asymmetric Information, we develop a dynamic model of a bank whose management has superior information about the impact of a pending shock to the bank's cash holdings and can signal the bank's type through its dividend policy. Banks that will be adversely affected by the shock have incentives to pool with unaffected banks to increase their market value. To avoid being mimicked, the unaffected banks can credibly signal via a more aggressive payout strategy. Dividend payout restrictions have the potential to prevent a separating equilibrium from forming. This leads to the bad type adopting a more aggressive payout policy with a higher risk of default but mitigates the distortion of the good type's policy. We identify a number of scenarios where this trade-off presents an opportunity for regulatory intervention and some where it does not.

Julien Hugonnier, Florian Pelgrin, Pascal St-Amour

Richer and healthier agents tend to hold riskier portfolios and spend proportionally less on health expenditures. Potential explanations include health and wealth effects on preferences, expected longevity or disposable total wealth. Using HRS data, we perform a structural estimation of a dynamic model of consumption, portfolio and health expenditure choices with recursive utility, as well as health-dependent income and mortality risk. Our estimates of the deep parameters highlight the importance of health capital, mortality risk control, convex health and mortality adjustment costs and binding liquidity constraints to rationalize the stylized facts. They also provide new perspectives on expected longevity and on the values of life and health.

2010This thesis is a contribution to financial statistics. One of the principal concerns of investors is the evaluation of portfolio risk. The notion of risk is vague, but in finance it is always linked to possible losses. In this thesis, we present some measures allowing the valuation of risk with the help of Bayesian methods. An exploratory analysis of data is presented to describe the sampling properties of financial time series. This analysis allows us to understand the origins of the daily returns studied in this thesis. Moreover, a discussion of different models is presented. These models make strong assumptions on investor behaviour, which are not always satisfied. This exploratory analysis shows some differences between the behaviour anticipated under equilibrium models, and that of real data. The Bayesian approach has been chosen because it allows one to incorporate all the variability, in particular that associated with model choice. The models studied in this thesis allow one to take heteroskedasticity into account, as well as particular shapes of the tails of returns. ARCH type models and models based on extreme value theory are studied. One original aspect of this thesis is its use of Bayesian analysis to detect change points in financial time series. We suppose that a market has two phases, and that it switches from a state to the other at random. Another new contribution is a model integrating heteroskedasticity and time dependence of extreme values, by superposition of the model proposed by Bortot and Coles (2003) and a GARCH process. This thesis uses simulation intensively for the estimation of risk measures. The drawback of simulation is the amount of time needed to obtain accurate estimates. However, simulation allows one to produce results when direct calculation is not feasible. For example, simulation allows one to compute risk estimates for time horizons greater than one day. The methods presented in this thesis are illustrated on simulated data, and on real data from European and American markets. This thesis involved the construction of a library containing C and S code to perform risk analysis using GARCH and extreme value theory models. The results show that model uncertainty can be incorporated, and that risk measures for time horizons greater than one can be obtained by simulation. The methods presented in this thesis have a natural representation involving conditioning. Thus, they permit the computation of both conditional and unconditional risk estimates. Three methods are described: the GARCH method; the two-state GARCH method; and the HBC method. Unconditional risk estimation using the GARCH method is satisfactory on data which seem stationary, but not reliable on data which are non-stationary, such as data with change points. The two-state GARCH model does a little better, but gives very satisfactory results when the risk is estimated conditionally on time. The HBC method does not give satisfactory results.

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