In finance, diversification is the process of allocating capital in a way that reduces the exposure to any one particular asset or risk. A common path towards diversification is to reduce risk or volatility by investing in a variety of assets. If asset prices do not change in perfect synchrony, a diversified portfolio will have less variance than the weighted average variance of its constituent assets, and often less volatility than the least volatile of its constituents.Diversification is one of two general techniques for reducing investment risk. The other is hedging.ExamplesThe simplest example of diversification is provided by the proverb "Don't put all your eggs in one basket". Dropping the basket will break all the eggs. Placing each egg in a different basket is more diversified. There is more risk of losing one egg, but less risk of losing all of them. On the other hand, having a lot of baskets may increase costs.In finance, an example of an undiversified po
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In finance, the capital asset pricing model (CAPM) is a model used to determine a theoretically appropriate required rate of return of an asset, to make decisions about adding assets to a well-dive
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
Investment is traditionally defined as the "commitment of resources to achieve later benefits". If an investment involves money, then it can be defined as a "commitment of money to receive more money
The course provides a market-oriented framework for analyzing the major financial decisions made by firms. It provides an introduction to valuation techniques, investment decisions, asset valuation, financing decisions, and other financial decisions of firms.
The course provides a market-oriented framework for analyzing the major financial decisions made by firms. It provides an introduction to valuation techniques, investment decisions, asset valuation, financing decisions, and other financial decisions of firms.
The modeling of the probability of joint default or total number of defaults among the firms is one of the crucial problems to mitigate the credit risk since the default correlations significantly affect the portfolio loss distribution and hence play a significant role in allocating capital for solvency purposes. In this article, we derive a closed-form expression for the default probability of a single firm and probability of the total number of defaults by time t in a homogeneous portfolio. We use a contagion process to model the arrival of credit events causing the default and develop a framework that allows firms to have resistance against default unlike the standard intensity-based models. We assume the point process driving the credit events is composed of a systematic and an idiosyncratic component, whose intensities are independently specified by a mean-reverting affine jump-diffusion process with self-exciting jumps. The proposed framework is competent of capturing the feedback effect. We further demonstrate how the proposed framework can be used to price synthetic collateralized debt obligation (CDO). Finally, we present the sensitivity analysis to demonstrate the effect of different parameters governing the contagion effect on the spread of tranches and the expected loss of the CDO.
The impact of capital mobility restrictions on the diversification benefit for risk at the group level of a financial conglomerate is an important aspect in risk management. In this paper we propose a new bottom-up approach for realizing diversification benefits using some predetermined capital and risk transfer instruments, taking counter-party default risk into account.
In this paper we compare the current Solvency II standard and a genuine bottom-up approach to risk aggregation. This is understood to be essential for developing a deeper insight into the possible differences between the diversification assumptions between the standard approach and internal models.