Quantitative Risk Analysis in Investment - Essay Example

Quantitative Risk Analysis in Investment Introduction It is commonly understood that risk is present in all our decisions. However, the degree of risk varies from decision to decision depending upon the type, length of period that the decision covers etc. Risk simply is the possibility of incurring an event, which is different from one's expectations. Therefore, risk occurs when there is variability between the expected outcome and the actual outcome. The incurrence of risk in investment is quite common and risk analysis in investment is a necessity. Since investment is putting one's hard earned money in some assets for a certain period of time, the investor looks at the risk which he/she is going to incur from the investment. Risk analysis is common now-a-days in all types of investment as the modern risk management literature has grown significantly. Many theories and models have been developed in the area of risk management by eminent thinkers. This paper takes a look at the classical risk analysis framework, namely mean-variance framework. The essay takes a descriptive approach wherein the mean variance model is discussed in the context of single as well as portfolio investment. An attempt is also made to incorporate the application of the model in pricing of insurance policies. Meaning and Significance of Risk Analysis Risk analysis in the context of investment is the process of quantifying the possibility of incurring loss to the return from the investment. The return from an investment is prone to risk when the actual return varies from expected return. Since risk measures the possibility of incurring an outcome, it can be measured with the help of probability and other statistical measures. As defined by T. V Bedford, risk analysis is the process of identification and quantification of scenarios, probabilities and consequences (Bedford 2001 p. 11). It is notable here that risk analysis cannot be possible without measuring return from the investment as risk and return are correlated and risk measures how actual return varies from expected return. Therefore, statistical measures are extensively used in quantifying risk and return. Among the various models the classical measure of risk analysis is mean variance model. Risk analysis can be discussed from two dimensions, namely risks in individual security investment and that in portfolio investment. Risk analysis of individual security investment is relatively easy as compared to that of portfolio. Risk Analysis in Portfolio Investment Portfolio is the collection of securities selected for investment. The logic behind investors' preference for portfolio rather than individual security is that the risks in portfolio can be reduced more easily than that of individual security. In other words, portfolio facilitates the risk diversification through spreading risks across all securities in the portfolio. The loss in one security can be nullified by the profit from another security/ securities in a portfolio. Calculation of Expected Return The analysis of risk in a portfolio is possible only after measuring return there from. The level of return expected from an investment is calculated by using the expected value of the distribution, and the probability distribution of expected returns for a portfolio. Then, risk is measured by the degree of variability around the expected value of the probability distribution of returns. The most accepted measures of this variability are the variance and standard deviation (Frank 2002 p. 21). The expected return from a portfolio can be estimated with the following model: (Source: Frank 2002 p. 21) Where, = 1.0; n = the number of securities; = the proportion of the funds invested in security i; = the return on i th security and portfolio p; and = The expectation of the variable in the parentheses (Source: Frank 2002 p. 21) Calculation of Portfolio Risk Risk is the chance that actual return will differ from their expected values. The expected value of return can be obtained from probability estimates for expected return. One must know the expected distribution of returns to estimate the risk. Portfolio risk is calculated by the standard deviation (or variance) of the portfolio's return. Thought the expected return from a portfolio is the weighted average of the expected return of the individual securities in the portfolio, risk of a portfolio is not the weighted average of the risk of the individual securities in the portfolio. The portfolio risk depends not only on the risk of the individual securities in the portfolio, but also on the correlations or covariance between the return on the securities of the portfolio. It can be defined as the function of each individual security's risk and the covariance between the returns on the individual securities (Steven 2003 p.352). The model can be developed as below: (Source: Steven 2003 p.352) Covariance can also be expressed in terms of the correlation coefficient as follows: (Source: Steven 2003 p.352) Where, = correlation coefficient between the rates of return on security i,, and the rates of return on security j,, and, and represent standard deviations ofandrespectively. Therefore: (Source: Steven 2003 p.353) Efficient Portfolio The asset in the portfolio should be selected in such a manner that the risk return paradigm for the investor gets maximised. While constructing a portfolio, the time horizon and the objectives of the investment should always b at the back of the investor's mind so as to derive the maximum benefit out of it. Usually an efficient portfolio is composed of any number of asset combinations. For example, a two risky asset portfolio can constructed as below: Two-Asset Portfolio The first thing to be noticed when two risky assets are used to construct a portfolio is that how the uncertainties of asset returns interact with each other should be understood first. This decides the degree of portfolio risk and the extent to which the return from the assets tend to vary each other. For example, there are two assets, namely A and B. The proportion of the asset A in the portfolio is denoted by and that of asset B () is indicated by . The expected rate of return, as already mentioned, is the weighted average of the expected returns on individual assets, in which portfolio proportions is taken as weights. It can be represented as below: (Source: Jae 1997, p. 175) The variance (standard deviation) of the above two asset portfolio can be expressed as, (Source: Jae 1997, p. 175) Where, = the correlation coefficient between the returns of asset A and asset B. This can be diagrammatically represented with the help of the following figure: (Source: Jae 1997, p. 182) Insurance Risks Risks in business are of many kinds. However, the meaning and significance of risks varies with change in the type of business. For example, the risk of a trading concern may be totally different from that of a manufacturing firm, even though all risks share some common features. Financial institutions are confronted with the problem of certain risks. Insurance industry, one of the major segments of the financial system of a country faces the following types of risks: Market Risk Underwriting Risk Claims Reserving Risk Credit Risk Market Risk It is the most common and simplest of the various risks. It is the change in the market price of an asset from the purchase of the asset between two different dates. In other words, market risk arises when the market price of an asset is different from purchase price ad it causes loss to the holder. It can be ascertained by observing the asset price in the marker, which changes every time. Underwriting Risk This is an unavoidable loss to an insurer as it arises because of the nature of the business. It comes in to effect when a new policy is sold by an insurer on the undertaking that the insure amount shall be paid to the policy holder on the occurrence of a certain event. In terms of volume, underwriting cost is the first and foremost risk attached to insurance business. Claims Reserving Risk This risk is associated with the timing of payment of claims by insurer to the insured. Therefore, this risk occurs when there is underwriting risk. When the payment to be made lasts for a long time, it means the insurer needs to accumulate a huge amount to be equivalent to the value of the payment to be made in the future. This occurs as a result of the difference between the date of occurrence of an event and the date of claim becoming due. In fact, it is uncertain for the company to decide how much amount should be set aside to pay off a certain liability. Credit Risk This type of risk in an insurance company occurs when one insurance company reinsure a part of the business to another insurance company and the latter makes default when the claim becomes due. This risk can be avoided to a certain extent as it is decided by the extent to which reinsurance business is undertaken. When the counter party makes a default, it becomes a liability for the former to bear the total claim independently. It is known that credit risk is harder to measure and quantify than market risk and thus its modelling is still less developed. References Bedford T., Roger M. Cooke 2001, Probabilistic Risk Analysis: Foundations and Methods, illustrated, Cambridge University Press Frank J. Fabozzi, Harry M. Markowitz 2002, The theory and practice of investment management, illustrated, John Wiley and Sons Allen, Steven 2003, Financial risk management: a practitioner's guide to managing market and credit risk, illustrated, John Wiley and Sons Jae K. Shim, Joel G. Siegel 1997, Schaum's outline of theory and problems of financial management, 2, illustrated, McGraw-Hill Professional Read More