Asset prices

The Capital Asset Pricing Model and other financial theories around diversification offer useful insights. If I give you a million dollars, you are a fool to invest in venture capital. But if you have a billion dollars, you are a fool if you don t invest in venture capital. 

The normal method of calculation for company funds is to use the capital asset pricing model (CAPM). This was developed by share analysts keen to have a defence against accusations of negligence in selecting shares for clients as a means of assessing the real value of any share, in the form of risk and desirability. It essentially demonstrates one version of the direct proportionality between risk and return. 

The first is the Cost of Equity. It is defined here as the return that a shareholder expects from the company over a certain period, in terms of dividend and the capital gain from a rise in the stock price. These are the actual expectations of income on which an investor bases his original purchase or reviews his portfolio. The Cost of Equity can be estimated using the Capital Asset Pricing Model (CAPM). 

CAPM —capital asset pricing model EDCs —European Discovery Capability Units... 

Capital asset pricing model An economic model of equilibrium in capital markets which predicts rates of return on all risky assets as a function of their correlation (or covariance) with the overall market portfolio. 

Note Average of VEBA s and VIAG s WACC and in 2000 before merger. Capital asset pricing model. 

Another very popular definition of risk is through the risk premium or beta. This is defined as the slope of the curve that gives market returns as a function of S P 500 Index returns in other words, comparing how the investment compares with the market. The concept of beta (the slope of the curve) is part of the capital asset pricing model (CAPM) proposed by Lintner (1969) and Sharpe (1970), which intends to incorporate risk into valuation of portfolios and it can also be viewed as the increase in expected return in exchange for a given increase in variance. However, this concept seems to apply to building stock portfolios more than to technical projects within a company. 

The minimum interest rate a company should earn on its invested capital is determined by the capital structure of the firm. The firm must earn an adequate return both to support the long-term debt and to compensate the stockholders adequately for their equity investment. This minimum interest rate, Cc, is calculated using the capital asset pricing model and is often referred to as the weighted cost of capital. 

The implications of this new model class are in contrast to most term structure models discussed in the literature, which assume that the bond markets are complete and fixed income derivatives are redundant securities. Collin-Dufresne and Goldstein [ 18] and Heiddari and Wu [36] show in an empirical work, using data of swap rates and caps/floors that there is evidence for one additional state variable that drives the volatility of the forward rates. Following from that empirical findings, they conclude that the bond market do not span all risks driving the term structure. This framework is rather similar to the affine models of equity derivatives, where the volatility of the underlying asset price dynamics is driven by a subordinated stochastic volatility process (see e.g. Heston [38], Stein and Stein [71] and Schobel and Zhu [69]). 

Duffle D (1996) Dynamic Asset Pricing Theory. Princeton University Press,... 

Fornari, F. and Mele, A. Recovering the probability density function of asset prices using GARCH as diffusion approximations. Journal of Empirical Finance, 8(1) 83-110, 2001. 

The first property that asset prices, which can be taken to include interest rates, are assumed to follow is that they are part of a continuous process. This means that the value of any asset can and does change at any time and from one point in time to another, and can assume any ffactiOTi of a unit of measurement. It is also assumed to pass through every value as it changes so, for example, if the price of a bond moves from 92.00 to 94.00, it must also have passed through every point in between. This feature means that the asset price does not exhibit jumps, which in fact is not the case in many markets, where price processes do exhibit jump behaviour. For now, however, we may assume that the price process is continuous. 

Models that seek to value options or describe a yield curve also describe the dynamics of asset price changes. The same process is said to apply to changes in share prices, bond prices, interest rates and exchange rates. The process by which prices and interest rates evolve over time is known as a stochastic process, and this is a fundamental concept in finance theory. Essentially, a stochastic process is a time series of random variables. Generally, the random variables in a stochastic process are related in a non-random manner, and so therefore we can capture them in a probability density function. A good introduction is given in Neftci (1996), and following his approach we very briefly summarise the main features here. 

The price processes of shares and bonds, as well as interest rate processes, are stochastic processes. That is, they exhibit a random change over time. For the purposes of modelling, the change in asset prices is divided into two components. These are the drift of the process, which is a deterministic element, also called the mean, and the random component known as the noise, also called the volatility of the process. 

For the piuposes of employing option pricing models, the d3mamic behaviour of asset prices is usually described as a function of what is known as a Wiener process, which is also known as Brownian motion. The noise or volatility component is described by an adapted Brownian or Wiener process, and involves introducing a random increment to the standard random process. This is described next. 

The successive values assumed by W are serially independent so from Equation (2.8), we conclude that changes in the variable W from time 0 to time T follow a normal distribution with mean 0 and a standard deviation of /T. This describes the Wiener process, with a mean of zero or a zero drift rate and a variance of T. This is an important result because a zero drift rate implies that the change in the variable (for which now read asset price) in the future is equal to the current change. This means that there is an equal chance of an asset return ending up 10% or down 10% over a long period of time. 

The standard Wiener process is a close approximation of the behaviour of asset prices but does not account for some specific aspects of market behaviour. In the first instance, the prices of financial assets do not start at zero, and their price increments have positive mean. The variance of asset price moves is also not always unity. Therefore, the standard Wiener process is replaced by the generalised Wiener process, which describes a variable that may start at something other than zero, and also has incremental changes that have a mean other than zero as well as variances that are not unity. The mean and variance are still constant in a generalised process, which is the same as the standard process, and a different description must be used to describe processes that have variances that differ over time these are known as stochastic integrals (Figure 2.3). 

The above discussion is used to derive a model of the behaviom of asset prices sometimes referred to as geometric Brownian motion. The dynamics of the asset price X are represented by the ltd process shown in Equation (2.18), where there is a drift rate of a and a variance rate of b X, ... 

The discrete time version of the asset price model states that the proportional return on the asset price X over a short time period is given by an expected return of aAt and a stochastic retimi of beAAt. Therefore, the returns of asset price... 

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