Asset Prices Variability and Pricing Model - Essay Example

Asset Prices Variability and Pricing Model INTRODUCTION Net Present Value is the most common equation and formula in the entire finance which identifies and calculates the value of an asset at the present time. This net present value is the discounted value of a series of its payoffs at the present time of point. This equation is of core significance in corporate finance as net present value helps to evaluate the projects from the perspective of investment. In general, net present value is related to value projects whose market prices are not observable. The purpose of this paper is unusual from corporate finance to some extent, but the idea is consistent with it. In this study, relationship of net present value is determined as the market equilibrium condition that can be influenced by changing asset prices. Asset markets are dishonorable as they encounter occasional short periods of optimism followed by pessimism, which results in high increments in prices and the consequent breakdowns in prices. The course of intense price fluctuations is sometimes referred to as bubbles. In this paper, the compatibility with net present value relationship is examined with regards to several examples of asset prices fluctuations. ASSET PRICING: Asset price is defined as the amount that an individual pay to buy an asset. This price indicates the sum of value the market has allocated to an asset either fairly or unfairly. The most common mode for expressing prices is money, however, mode of expression of prices can be changed such as expressing through barter system which includes trading of one chicken in exchange of two fishes. The regulation behind this asset pricing phenomenon is the trend of supply and demand prevailing in the market, which depicts that asset prices change with the change in supply and demand. The price of an asset rises with the increased demand and lesser supply (Berk and Binsbergen, 2013). The outcome of this fact is that commoditization changes the prices and drives them down as the supply increases with a greater extent while the demand remains constant. Similarly, prices begin to rise as the value of money turns down. In such situations, government can take alternatives to control the prices of some assets (not all the assets) by setting regulations or subsidy. This measure is considered as anti-inflationary which tends to alter the law of demand and supply instead of eliminating the law. This is the reason it is mostly not sustainable as an instrument to manage the prices (Hordahl and Packer, 2007). NET PRESENT VALUE: The main aim of this section is to develop the net present value relationship. Net present value equation is open to misapprehension but if the equation is developed carefully, it provides several in-depth information about evaluation of asset prices as well as enlightens few odd complications in the equation. The basic assumption states that the future returns are obtainable and can be determined which comes under certainty. This may seem unrealistic, but assumptions regarding deterministic returns are considered as the basics of present value. Certainty: The common equation of rate of return on the assets and its payoff is expressed as: … (1) Where P = asset’s price and V = payoff of assets While developing relationship of net present value, payoffs of assets and rates are known with certainty and remain the same over the period or time. In this process, time is taken as a continuous variable instead of discrete intervals. On the other hand, payoffs split into two parts that are dividends or coupons and market price of one unit of asset. Now equation can be written as: … (2) To measure current price, it can be rearranged as: … (3) This equation can be written in net present value format: … (4) By using a discount factor, total of each dividend is discounted back to the present value. The above equation signifies the non-existence of arbitrage prospects. If this equation does not put together, the investors might have possibly made arbitrage (unbounded) profits by simply borrowing at risk-free rate and purchasing the assets, if the price of assets is lower than the discounted present value of its potential future returns. If asset is not purchased then investors could do short-selling of assets and lending the proceeds at the risk-free rate (if the discounted present value of its potential future returns is lower than the price of assets). At times, the relationship of net present value is offered as a definition of asset’s value or sometimes as a definition of its internal rate of return. However, the equation is not a specific definition that explains the value of an asset or internal rate of return, but it is presented as an equilibrium condition. In order to create generalization in NPV, so as to allow for a risk-free rate of return, the discount factor is defined as: … (5) And to form NPV condition, it is written as: … (6) And when N represents the infinite numbers, the equation will modify into following: … (7) That means; NPV presents the long series of dividends which is the sum of the series of discounted dividends. These infinite series do not allow convergence as it is insufficient. Also, due to infinity, it neglects some major aspects of NPV and allows unbounded life for an asset which presents the irrelevant equilibrium. With the infinitely lived assets, a special case has been designed where interest rate is constant, and the dividends produce at constant growth rate, as shown in equation below: … (8) If rate of return is less than or equal to growth rate, the NPV cannot be defined. In this case, the payment of every return becomes unbounded in the far future since the growth rate of dividends is much higher. Hence, their sum is accumulated as unbounded and thus NPV remains undefined. This model plays a significant role in applied finance with which equity prices can be forecasted based on assumptions related to future growth of dividends for defined interest rate and current dividends. Uncertainty: The NPV relationship will be modified by adding expected value of each return if uncertainty changes the assumptions of identifiable future returns: … (9) This equation identifies the expectation on information available today of the returns that are to be received in future, for example, dividend growth forms of share prices indicate the same expressions as in the equation above. However, this information that is based on expectations usually communicates investor’s belief which differs among various investors. But this equation does not involve individual based assumptions. In the case of identifiable returns, the nonexistence of unbounded opportunities implies the relationship of NPV. The expectations in the NPV relationship that are implying the probabilities is known to be artificial ‘martingale probabilities.' These are considered as the part of derivatives but do not relate to investors’ assumptions. Secondly, the assumption about investors of being risk-neutral and undisputed regarding their beliefs in potential expectations is an alternative way to justify the equation. In such scenarios, market equilibrium entails that rate of return of every asset must be equal to the risk-free rate, or else investors would prefer to buy assets with greater expected rate of return than the risk-free rate and sell assets with lesser expected rate of return than the risk-free rate. This signifies that an NPV relationship must be formed for every asset. The market equilibrium cannot be gained if assumptions of risk neutrality are given relaxation in support of risk aversion. On ignoring the assumptions, risk premiums are to be supported, or else NPV would be replaced by CAPM and APT through adjustment of the discount factor to include the risk premium. These justifications help to interpret the empirical proof about asset price fluctuations. In the viewpoint, NPV relationship defines the way to determine the asset prices if investors behave in a rational manner. In other way, NPV relationship would not get affected by the performance of asset markets (Bailey, 2005). ASSET PRICES VARIABILITY: The variability in financial asset prices and its potentials to undermine the financial stability has been a major concern for few years. An approach is used that focuses on the variability in asset pricing to examine the NPV relationship with asset prices. Asset prices are claimed as extremely volatile which can be judged by creating NPV relationship as a benchmark (Copeland, Weston and Shastri, 1983). As the interest rate is served as the basis for discount factors that are applied to future returns, the NPV relationship is demonstrated as: … (10) In relation to this, Robert Shiller, an analyst of asset price volatility, describes the ex-post rational asset price as: … (11) which can also be written as, … (12) This equation is considered as an equilibrium, which depicts the prices forecasted by NPV relationship if investors’ expectations about future dividend are satisfied (Bailey, 2005). The relationship between asset price and market price is obtainable through this equation: … (13) The ex-post rational price is divided into two components y substituting from equation 13 into 11, … (14) The NPV of estimation error is defined by Therefore, equation 14 can be written as: … (15) This shows that the ex-post rational price is equivalent to experiential market price and forecast error. The market prices can also be expressed as the market’s estimation of the ex-post rational price. pt plays the role of estimation of p∗t in this model. According to some assumptions, practical asset prices are uncorrelated with the predicted errors, and this condition is most often referred to as orthogonality condition. According to these conditions, if variance of the current price of assets is less than or equivalent to the variance of ex-post rational asset price, then the standard deviation of the current price of assets will be less than or equivalent to the standard deviation of ex-post rational asset price. This inequality declares that variability of the current price that is forecasted must be less than that of ex-post rational asset price, until the forecast error becomes correlated with the forecast itself. Thus, asset prices are regarded as extremely variable and volatile if variability of current prices is greater or equal to ex-post rational asset price. Through NPV relationship, the variability of asset prices has successfully been measured. Even NPV relationship can also measure high volatile prices to the greater extent (Bailey, 2005). Moreover, this has been proved by Shiller’s attempt in 2003 for Standard and Poor’s Composite Index of US stock prices which were plotted on prices, along with ex-post rational prices, forecasted as NPV of future dividends. The share prices showed more variances than those of current prices. This depicts that ex-post rational prices that are based on real interest rate shows lesser variation than those prices which are based on market interest rates. However, stock prices are considered as more volatile than current prices and ex-post rational price as their prices are highly variable. It can be concluded that NPV relationship is influential in finance as: It calculates the current price of an asset in terms of discounted value of its series of future returns, and these discount factors are based on interest rates of borrowing or lending funds. If the series of future returns is identifiable (identified with certainty), the nonexistence of arbitrage opportunities cause to obtain the NPV relationship (Bailey, 2005). As suggested by empirical study, when investors take decisions based on the correct estimation of future dividends, the asset price becomes more volatile than expected by the NPV relationship. Asset price model can be successfully created that are based on either the survival of noise traders, investors who react on fashion and fads or imperfect estimation of future dividends (Barsky, and De Long, 1993). Tremendous fluctuations in prices of assets are well-matched with the NPV relationship. DERIVATIVES Financial markets have been constantly changing and evolving its product range. The evolutionary engineering of the products and instrument range is done in order to deal with the future uncertainty lying in the underlying instrument. In a similar fashion, the extension of the asset pricing has resulted in the development of the derivatives. Simply stating derivatives are financial securities. The contract of derivatives is developed between two parties on the basis of prices and fluctuation in prices of the underlying asset. Usually characterized with a high-level leverage, a derivative contract are developed for almost all types of financial products such as stocks, commodities, market indexes, currencies, interest rate, bond and so on.  Most common form of derivate includes options, forwards, futures, and Swaps, etc.   The derivative pricing model underwent constant and extended expansion since 1970. However, overreliance by ignoring the technical complexities has led to the various crashes in the financial markets as some of the analysts blame.  On the other hand, the use of different types of derivatives has increased in the financial markets all across the world, and derivatives have become an integral part of the portfolio held by various firms. This in turn has led to the direct impact of the pricing methodologies of derivatives on the portfolios of the organization. Financial experts have already and are constantly investing time and expertise in the development of pricing models for different derivatives effectively and efficiently to deal with the risk and uncertainty in the financial market. DERIVATIVE PRICING MODEL Similar to the fact that type of derivatives vary, different pricing models have been devised for the purpose. For instance, Black-Scholes is a derivative pricing model was developed in the year 1973 was developed on the basis of the general equilibrium as found in economics. Moreover, Black-Scholes is a closed form of option pricing, and it is a system that is free for the arbitrage-free for the valuation of equation. The model is preferred against another closed form of pricing model developed prior to it, as those models did not consider the general equilibrium factor (Kolb and Overdahl, 2009). An Exponential L´evy model is another derivative pricing model that takes into account the Black-Scholes general idea. While an Exponential L´evy model allows stock prices to jump, it also enables the stock return to maintain their stationary position as well as independence (Tankov, 2011). LIBOR market model (LMM) is another pricing model for the derivatives, and it is used for the interest rate derivatives. The model overcomes the limitations of models that prices short term interest rate. LMM takes into account the variations of the entire curves and movements of the interest rates by implying LIBOR forwards. LMM model also ensures that process is arbitrage free  and takes into consideration the multiple factors such as parallel shifts, butterflies, steepening of the curve, etc. (Hagan and Lesniewski, 2008).  Hence, many other models are developed for different derivatives. For instance, Fischer Black and Myron Scholes models (for option pricing) in addition to Binomial option pricing model, etc. are among the widely used model for derivative pricing (Fabozzi, Grant and Collins, 1999).  However, each is faced with certain limitations. Consequently, various models of derivative pricing are used for various derivatives in order to produce the potentially most positive impact on the portfolio.   RELATIONSHIP OF DERIVATIVE PRICING TO PORTFOLIO MANAGEMENT Derivatives are used for the pricing of different securities in order to overcome the underlying factor of uncertainty. Portfolio is a set of securities that are also aimed at the development of the mix with controlled risk with the application of diversification. Hence, directed by the closely related objective of reducing risk and generating higher returns, derivative pricing model has considerable relationship with the portfolio management. Various derivative pricing models have been implied in different portfolios in order to produce the returns from underlying assets in the portfolio. Also, it also enables the portfolio management offered with calculated risk. Consequently, firms are less turbulent to the volatility and the risk associated with the assets in the portfolio. Moreover, the relationship of the derivative pricing models and the portfolio management is emphasized in the various markets. For instance, the under the impact of the liberalized market which has resulted in open market competition for various industries in different countries, the industries are not only faced with the physical problems related to industry such product and price, etc. Instead, liberalization has resulted in the wider impact as the prices of the inputs have become volatile. Consequently, the industries are facing much higher uncertainty than ever. For example, Talley (2012) has discussed the hedging of price risk of ship by using freight derivatives. Hence, various derivative pricing models are also developed in order to control the financial risk in terms of price volatility, etc. for the portfolios. Equity portfolios are one of the most widely developed portfolios. Contrary to this, this domain of portfolio management is faced with the immense number of challenges  such as strict regulation, another constraint such as the need to constant monitor volatility, constant scrutiny, etc. These and other challenges have led to the development of Global Minimum variance portfolios (GMV) by the asset management companies. A case study describes that European companies have used Markov regime-switching model so as to differentiate between the periods of low and high volatility in the equity market of Europe. This model helped the entire market to determine the correlation level in the equity market. Also, using the EURO STOXX 50-index data, companies differentiated between the conditions of low, medium and high volatility (EDHEC-Risk Institute, 2012). In this context, a study has been conducted in the German power exchange and electricity market. The issue was raised about the optimal unit commitment problem which consequently led to results that this can be resolved independently in the existence of a liquid spot market that is without taking into account the entire portfolio. A model based on real option theory is proposed for the unit commitment problem which can consider all the operational constraints of a turbine. In this study, a numerical method, initiated from computational finance, was used to solve the model which merged backward stochastic dynamic programming with forward Monte Carlo simulation. The study has worked out the optimal exercise rule for a single turbine in the form of case and verified how the model can be utilized for calculating the complete profile risk of the turbine. The benefit of this approach lies in its flexibility concerning supplementary constraints and/ or supplementary sources of uncertainty. Its main detriment is that it is extremely demanding with respect to computer time (Hlouskova, Kossmeier, Obersteiner and Schnabl, 2003). Considering the banking sector, the model used for measuring risk is Vasicek one-factor model which uses the temporary rate as a single factor for modeling interest rates and bond prices. This model is declared as the first model which is based on the structure of rates. The main advantage of this model is that it presents rates and bond prices as closed-form formulas. In addition to this, model is termed as equilibrium model as it supports the process of short rates r(t) in the risk-neutral market where investors receive small rates within a short period. This model is different from other models as it uses diverse type of process driving interest rates. The models which intent to perform modelling of fixed derivatives and income assets or arbitrage models also work on entirely different phenomenon than Vasicek model. The major idea behind this model is to develop a risk-free portfolio which is based on two rates of various maturities. It is convenient to develop a portfolio whose rates are correlated. Seeing the complications in the banking industry, it provides best and convenient model to perform challenging risk related tasks (Bessis, 2011). As of the investment property industry, it can be seen that there are numerous issues that are associated with the management of investment in a property portfolio. These issues are owing to particular features of the property as an investment. The main issue is a comparative liquidity. Contrasting to equity and gilt portfolio managers, it is difficult for investment portfolio managers to respond to new information quickly and create projections about potential growth. Thus, due to this concern, the implementation of strategies regarding portfolio management will get delay as well. The study depicts that financial derivatives can resolve many issues regarding portfolio investment management that deals with direct property investment. As of the high-liquidity rate in overall industry, managers can purchase or sell property in a short period comparatively that enable managers actively to manage portfolio. Today, the use of derivative is at the initial stage in this industry; however, the researchers have stepped ahead to introduce a number of products in the industry. CONCLUSION: Asset markets are increasingly unreliable as they encounter occasional short periods of favorable outcomes and rest with the unfavorable outcomes which results in high increments in prices and the consequent breakdowns in prices. As the intensity of price fluctuations is known as bubbles, and it is the point where asset prices are high variable and thus have strong NPV relationship. The greater the variability of asset prices, the higher will be the NPV relationship. In this context, the derivatives are used in the markets to hedge the market risk. Various industries have used models such as Markov regime-switching model, Vasicek model or models based on real option theory. These models consequently aid companies positively and undoubtedly allow them to diversify risks. References Bailey, R. E. (2005). The economics of financial markets. Cambridge University Press. Barsky, R. B., and J. B. De Long. (1993). Why does the stock market fluctuate?. Quarterly Journal of Economics, vol. 108, no 2. pp. 291–311. Berk, J., and Van Binsbergen, J. H. (2013). Assessing Asset Pricing Models Using Revealed Preference. Available at SSRN 2340784. Bessis, J. (2011). Risk management in banking. John Wiley & Sons. Copeland, T. E., Weston, J. F., & Shastri, K. (1983). Financial theory and corporate policy. Massachusetts: Addison-Wesley. EDHEC-Risk Institute. (2012). The Benefits of Volatility Derivatives in Equity Portfolio Management. Available from: http://www.edhec-risk.com/edhec_publications/all_publications/RISKReview.2012-06-06.1741/attachments/EDHEC_Publication_The_Benefits_of_Volatility_Derivatives_F.pdf [Accessed 19 July 2014]. Fabozzi, F. J., Grant, J. L., & Collins, B. M. (1999). Equity Portfolio Management. John Wiley & Sons. Hagan, P., & Lesniewski, A. (2008). LIBOR market model with SABR style stochastic volatility. JP Morgan Chase and Ellington Management Group, 32. Hlouskova, J., Kossmeier, S., Obersteiner, M., & Schnabl, A. (2003). Real option models and electricity portfolio management. na. Hordahl, P., & Packer, F. (2007). Understanding asset prices: an overview: Bank for International Settlements, Monetary and Economic Department. Available from: http://www.bis.org/publ/bppdf/bispap34.pdf [Accessed 19 July 2014] Kolb, R., & Overdahl, J. A. (Eds.). (2009). Financial derivatives: pricing and risk management. John Wiley & Sons. Talley, W. K. (Ed.). (2012). The Blackwell companion to maritime economics, Vol. 11. John Wiley & Sons. Tankov, P. (2011). Pricing and hedging in exponential Lévy models: review of recent results. In Paris-Princeton Lectures on Mathematical Finance 2010. Springer Berlin Heidelberg. Read More