How risky is your investment portfolio? Answer quickly? Would it be : Very risky? Sort of risky? Not very risky? One can freely say that this is one of the most important personal finance questions someone could ask a person. No matter what kind of investor one might be, it’s likely he/she won’t be able to answer this absolutely critical question with any degree of accuracy. It doesn’t matter whether the people in question are conservative investors, wild speculators, or something in between, when it comes to analyzing risk, most need to admit that they do not know the answers. Contents
1. Preface. 2 2. What is risk?. 3 2.1 Classification of risks. 4 3. How Does Financial Risk Arise?. 5 4. Financial risk management 6 4.1. What is financial risk management?. 6 4.2. Risk Management Process. 7 4.3. Diversification. 8 4.4. Instruments often used to manage financial risks. 11 4.5. Challenges in risk management 12 5. Risk Management Framework: Policy and Hedging. 13 5.1. Tolerance for Risk. 14 5.2. Board and Management 14 5.3. Risk Management Policy. 15 5.4. Hedging Policy. 16 5.4.1. Hedging Strategy Selection. 16 6. Financial risk measurement 17 6.1. Process of Estimating Risk. 17 6.2. How to measure financial risk?. 18 6.2.1. Valueatrisk. 18 6.2.2. Methods to Calculate ValueatRisk. 19 6.2.3. The examples of Historical, Monte Carlo and Parametric Approaches. 20 6.3. Quantification of financial risk. 24 6.3.1. Investment returns. 24 6.3.2. Probability and its distribution. 25 7. Conclusion. 29 8. Literature. 30 1. Preface How risky is your investment portfolio? Answer quickly? Would it be : Very risky? Sort of risky? Not very risky? As one can notice, the person questioned might have trouble answering quickly. One can freely say that this is one of the most important personal finance questions someone could ask a person. No matter what kind of investor one might be, it’s likely he/she won’t be able to answer this absolutely critical question with any degree of accuracy. It doesn’t matter whether the people in question are conservative investors, wild speculators, or something in between, when it comes to analyzing risk, most need to admit that they do not know the answers. This term paper seeks to provide in a readable and perhaps useful manner, the basic elements of financial risk management and measurement. Since the subject of financial risk management is both wide and deep, this paper is necessarily selective. Financial risk is covered only partially, in order to foster an understanding of the risks and the methods often used to manage those risks. After reading this paper one should know basis of risk, recognize different types of risk, and be introduced to process of managing financial risks. The paper will, further on, explain different ways of measuring financial risk starting with the definition of ValueatRisk and its three basic approaches of measuring financial risk. The approach we shall use is informal, however, emphasizing a study of models’ implications at the expense of formality. 2. What is risk? Let's say you have a room full of people, and you ask them to define what is risk. More than a few unique responses are likely to be given. That's just because risk is a concept that is hard to comprehend. Generally speaking risk is the uncertainty of the future value of financial assets. It usually refers to the danger of loss and is a result of exposure. One can find subtle differences in the meaning of the terms risk and exposure and conclude that risk refers to the probability of loss, while exposure is the possibility of loss. For example: exposure to financial markets can affect most organizations, directly or indirectly. If one organization has exposure to financial market, there is always a possibility of loss and in the same time an opportunity for gain or profit (it may provide strategic or competitive benefits). If one has an exposure to a risk, it means that some circumstances exist under which one can lose money, some hypothetical future loss. Therefore, the very concept of risk assumes that one knows how much one’s possessions are worth. The greater the risk, the greater the potential range of one’s future wealth, on both the upside and the downside, and therefore the greater the uncertainty about meeting one’s financial goals. Perhaps the best description of risk comes from the Chinese characters denoting the term (Fig. 1[1]). Figure 1 This Chinese symbol, which represents risk, is a mixture of danger and opportunity, where the first character is the symbol for danger, and the second is the symbol for opportunity. This is a perfect illustration of what is the thought process of every investor  deciding between the higher rewards that potentially come with the opportunity and the higher risk that the investor has to deal with as a consequence of the danger. Although the „equation“: Risk = Danger + Opportunity, can help one capture the essence of risk, it still can't be practically applicable in the financial world because it is too abstract as a definition. By translating risk from a descriptive concept into something more tangible, such as putting it into a framework that can be measured on both a relative and an absolute scale, one is able to show risk in a meaningful light. In this sense, risk is a numbers game. Whatever the preferred definition might be, one thing is certain: most people view risk as a negative concept. 2.1 Classification of risks Risks can be classified in many ways. However, differences still exist, and depending on one’s needs, the following classification is taken as the most appropriate: • Business risk: appears as a consequence of result variability of the organization’s business. It depends in great part on fixed and variable costs relationship. Greater participation of fixed costs in the total costs leads to the increase of business risk. Capital intensive business activities have greater business risk comparing to those business activities that are less capital intensive. • Financial risk: is defined by the level of engagement, or by the degree of use of the financial leverage. It is important to emphasize that financial risk is an umbrella term for any risk associated with any form of financing. [2] • Project risk: reflects in variations of money income that are expected in future, as a result of project exploitation. Sources of this risk are: market, technology and costs. • Portfolio risk: reflects in variations of income from securities or other components of the portfolio. 3. How Does Financial Risk Arise? Financial risk arises through countless financial transactions, including sales and purchases, investments and loans, and various other business activities. It can arise as a result of legal transactions, new projects, mergers and acquisitions, debt financing, the energy component of costs, or through the activities of management, stakeholders, competitors, foreign governments, or even weather. When financial prices change dramatically, it can increase costs, reduce revenues, or otherwise adversely impact the profitability of an organization. Financial fluctuations may make it more difficult to plan and budget, price goods and services, and allocate capital. Major market risks arise out of changes to financial market prices such as exchange rates, interest rates, and commodity prices. There are three main sources of financial risk: 1. Organization’s exposure to changes in market prices, such as interest rates, exchange rates and commodity prices 2. Organization’s actions, and transactions with, other organizations such as vendors, customers and counterparties in derivatives transactions 3. Organization’s internal actions or failures, particularly people, processes and systems. 4. Financial risk management 4.1. What is financial risk management? Financial risk management can be defined as a process that deals with financial market's uncertainties. It should involve addressing the financial risks that one organization might be faced with and developing management strategies that are not confronting internal priorities and policies. If an organization successfully addresses financial risks in a proactive manner, it could provide a competitive advantage of that organization. Financial risk management makes organizational decisions such as those concerning risks that are acceptable versus those that are not a vital necessity. On the contrary, the acceptance of all risks by default is a characteristic of the passive strategy, the strategy of taking no action whatsoever. A variety of strategies and products can be used in managing financial risk and understanding how they work is crucial in reducing risk within the context of the organization’s risk tolerance and objectives. Derivatives are often involved in strategies for managing risk and are widely traded between financial institutions and on exchanges that are professionally organized. One can trade derivatives on different rates such as on interest rates or on exchange rates, on securities such as fixed income securities and equity, on commodities, credit and also on weather. Speculators use different varieties of products and strategies to increase leverage and risk, the same products and strategies are used by the market participants who attempt to manage financial risk. It is highly desirable to have the possibility to estimate the likelihood of a financial loss. However, failure of analyzing financial markets by standard theories of probability is very high. This is understandable, considering the fact that risks do not exist in isolation and in developing an understanding of how financial risk arises, interactions of several exposures have to be considered. These interactions can be difficult to forecast since they depend on human behavior. Good risk management requires[3]: • An understanding of the risks being take • A comprehensive definition of the firm’s risk appetite • Allowing opportunities to be exploited within the risk appetite • Ensuring that risks outside it are not taken 4.2. Risk Management Process The process of financial risk management is an ongoing one. Since the market and the requirements change, organizations need to implement and refine strategies according to these changes. Therefore, risk management can be seen as a process that should be able to ensure the absence of undesirable events. In general, the process can be summarized as[4]: • Identify and prioritize key financial risks that face the organization • Determine an appropriate level of risk tolerance • Implement risk management strategy in accordance with policy • Measure, report, monitor, and refine as needed Financial risk management process contains strategies whose function is to ensure that an organization is capable to manage financial risks that arise from financial market fluctuations. Risk management is an everchanging process that should develop simultaneously with an organization and the business that the organization in question runs. It includes and affects significant parts of an organization such as: sales, marketing, treasury, tax, commodity, and corporate finance. Both internal and external analyses have to be involved in the risk management process. The first part of the process is oriented on identifying and prioritizing the financial risks that an organization faces and on realizing their relevance. It involves examining the organization and its products, management, customers, suppliers, competitors, pricing, industry trends, balance sheet structure, and position in the industry, taking in consideration the stakeholders and their objectives and tolerance for risk. Once a clear understanding of the risks emerges, appropriate strategies can be implemented in conjunction with risk management policy. For example, it might be possible to change where and how the business is done, thereby reducing the organization’s exposure and risk. Alternatively, existing exposures may be managed with derivatives. Another strategy for managing risk is to accept all risks and the possibility of losses. There are three broad alternatives for managing risk[5]: 1. Do nothing and actively, or passively by default, accept all risks 2. Hedge a portion of exposures by determining which exposure can and should be hedged. 3. Hedge all exposures possible Measuring and reporting risks provides decision makers with information to execute decisions and monitor outcomes, both before and after the strategies are taken to mitigate them. Since the risk management process is ongoing, reporting and feedback can be used to refine the system by modifying or improving strategies. An active decisionmaking process is an important component of risk management. Decisions about potential loss and risk reduction provide a forum for discussion of important issues and the varying perspectives of stakeholders. 4.3. Diversification Unlike many of the physical ailments one regularly experiences on a day to day basis, a risk is much more difficult to diagnose and treat. Often, one does not realize anything is wrong until trouble strikes. Along the way, one might misinterpret the signals that should warn against impending risks. Diversification is an important tool in managing financial risks. Counterparties diversification may reduce the risk that unexpected events adversely impact the organization through defaults. Diversification among investment assets reduces the magnitude of loss if one issuer fails. Diversification of suppliers, customers, and financing sources reduces the possibility that an organization will have its business adversely affected by changes outside management’s control. Although the risk of loss still exists, diversification may reduce the opportunity for large adverse outcomes. Smart investors do not try to forecast the future movements of the markets. Instead, they rely on firm rules of portfolio management and diversify. Dispersing money in a reasonable manner over many investments will help avoid excessive exposure to a single source of risk. A mutual fund investor can invest in index funds that track the broader market or purchase a bond fund to offset equity growth funds. Since market cycles oscillate, a properly diversified portfolio allows investors to offset losses in one sector or investment type with gains in another. Though the impulsive side in one may argue: “Diversification never appears that smart, because investors always have at least some exposure to the market’s most lackluster sectors”, one’s sensible instinct argues: “Over the long haul, it is a much surer way to build wealth” as emphasized in Jonathan Clemens’s article on market losses in the Wall Street Journal.[6] That is the aim of diversification—capturing the market’s overall returns while moderating volatility, thereby making it easier for investors to stay on the course. Looking at the charts in Figures 2. and 3., the importance of diversification becomes remarkably apparent. Both illustrate just how dramatically market performance in the equity markets changes from year to year. Not only do different segments of the stock market behave differently, but leadership among these different segments changes drastically, too. For this reason, it is critical that investors maintain their longterm focus and refrain from reacting to shortterm leadership changes in the market. Jack Sherry, president of the Phoenix Investment Partners’ Private Client Group, strongly cautions investors against switching among the various equity styles in a vain attempt to time the shifts in leadership. This behavior has historically led to higher portfolio volatility and poor results. For evidence, one can refer to the besttoworst performances turned in by the largecap growth sector in 1999 and 2000 (Figures 2. and 3). Figure 2[7] Figure 3[8] 4.4. Instruments often used to manage financial risks • Forwards – a commitment for one party to sell and another to buy a specific asset at a set price on a given future date. • Options – the right to buy (a call option) or the right to sell (a put option) a financial instrument or commodity during a given period in return for a payment in advance of a premium. The option is exercised at the discretion of the buyer of the call or put option. • Swaps – the exchange of one entitlement for another, for example, a borrower with a fixed interest rate obligation may swap this for a floating interest rate. • Futures – an agreement to buy or sell specified financial instruments or commodities on an agreed date at a price determined when the contract is entered into on a futures exchange. These financial instruments can be used separately or together to produce complex derivative products that may have leverage built in. Swaps and options would normally be negotiated with a dealer (transactions known as OTC or overthecounter). However, certain options and futures contracts are available through a recognized futures exchange or stock exchange. In each case, the first question to be asked is whether the organization has a written boardapproved policy for the management of the financial risk and the use of the financial instrument. Where a derivative instrument is used directly or indirectly to minimize or offset a financial risk arising in the course of an organization’s business, the process is known as ‘hedging’ and is a fundamental tool of risk management. 4.5. Challenges in risk management Some of the challenges risk management faces are internally preventable, but some of them arise from the nature of the business or the industry and aren’t preventable. Those challenges are: • Different time zones, language, reporting, regulatory environments • Reporting entities that are geographically dispersed • Level of knowledge, experience, interest, or understanding of issues • Tasks and duties that are inappropriately delegated • Information, reports, or communications that is inadequate or poor • Too complex reports (Psychological constraints) • Lack of independence in board of directors 5. Risk Management Framework: Policy and Hedging In addition to general business risks, other factors include exposure to market prices, tolerance for risk, an organization’s history and its stakeholders. The risk management policy is a framework that allows an organization to grow by building decisionmaking processes instead of treating each decision independently. The policy is a tool for communicating what constitutes an acceptable level of risk to individuals throughout an organization. All organizations should develop risk management policies to identify and manage risks that reflect their business and industry, and that requires an understanding of the organization’s risk profile. The risk profile is unique and it depends, in turn, on attributes such as risk tolerance, financial position within the industry, management culture, stakeholders, and the competitive landscape in which it operates. Once risks and exposures have been identified, they can be assessed and prioritized. In evaluating financial exposures, the first step is to identify the relevant exposures. Since broad risks are often composed of a number of different risks, they should all be considered for their potential impact on the business. For example, it is important to be able to separate market risk from credit risk and liquidity risk. Example: Evaluating Risk in a New Currency A company is considering a sale to a new customer in an emerging market. Evaluation of the potential foreign exchange risk might include qualitative features: · Is it a major industrial or emerging market currency? · What is the underlying legal system? · Can funds be freely moved into or out of the country? · Can the business alternatively be conducted in a major · Currency such as U.S. dollars or Euros? · Does the currency exchange rate operate under a pegged or a target rate regime? 5.1. Tolerance for Risk Risk management involves reducing the probability of loss. Decisions about how much loss can be tolerated are very important. Risk tolerance is the ability or willingness to withstand risk, and it depends on the culture of an organization. The determination of an acceptable level of risk is important, since business and risk are interconnected. In developing a hedging policy, it may be helpful to consider the following issues: · The structure of an organization may provide clues about its risk tolerance. (A majority of shareholders might be management and founders’ families) · The business of the organization may provide guidance in risk tolerance. (Financial institutions, companies with a trading history are typically more conversant with financial risks) · The origins of the business may impact organizational culture for decades (If the founders took great risks in achieving success, risk tolerance may be strongly impacted as a result.) · The characteristics of the stakeholders should be considered (The stakeholders—including employees and shareholders—can walk away if they do not like the risks) 5.2. Board and Management Management typically develops risk management policy, while the board of directors has responsibility for its approval. Given the potential for substantial losses, boards are especially concerned about financial risk management and its implications in these key areas: • Policy • Strategy • Oversight The policy is intended to be used by the management and the staff in their duties. If one does not exist, staff should insist on its development. The board of directors and the management have specific information requirements with differing needs for detail. Both groups require information that is: • Reliable • Timely • Accessible • Accurate • Consistent in format • Suited to different users Members of management and the board must comprehend: financial risks being taken by the organization in the course of the business planned financial instruments and strategies for managing financial risks, risks of any unusual financial instruments or strategies, risk measurement methodologies and their relationship to policy and, finally, the results of the financial risk reporting. 5.3. Risk Management Policy The policy provides and formalizes a framework for making individual decisions and reflects the organization’s perspective on risk. The risk management policy is predicated on setting organizational priorities and it can be as broad as the risks facing an organization and may include disaster planning, investment policy and insurance, the traditional arena of risk management. There are three major reasons for a risk management policy:[9] • To provide a framework for decision making • To mandate a policy for controlling risk • To facilitate measurement and reporting of risk Appropriate risk measurement methodologies and acceptable limits for risk tolerance must be determined. Both the management and the board need enough information to determine whether the responsibilities are being handled appropriately, within specified guidelines or parameters. 5.4. Hedging Policy A subset of the broad risk management policy deals with financial risks. Known as the hedging policy, or financial risk management policy, it provides clear direction on the organization’s approach to managing financial risks. Developing a hedging policy requires knowledgeable input from various groups that are responsible for sources of risk. Hedging strategies are not designed to anticipate the market. The intent is to reduce or eliminate the risks associated with market fluctuations. It is an almost certain observation that the future is unlikely to look like the past. As many organizations have discovered, it is easier, and often cheaper, to preemptively hedge than to successfully forecast markets. The benefits of hedging are:[10] 1) It is not complicated to handle. 2) The risk is minimized for both parties. 3) The traders can take the risk, without actually buying the future stock. 5.4.1. Hedging Strategy Selection Hedging decisions always involve a tradeoff between an appropriate level of risk and opportunities for gain. Every strategy has a price, whether it is the explicit cost of hedging products or the opportunity cost arising from being hedged. The hedging decision should be based on business objectives and tolerance for risk, rather than on market conditions. 6. Financial risk measurement Financial risk measurement is a component of risk management. It involves measuring risk, followed by decisions about how best to manage it. Attempts to measure risk involve estimating the probability of an unfavorable event occurring and its potential impact. Volatility estimates are typically calculated using variance or standard deviation around the mean. Measurement of financial risk may convey a false sense of security among management that financial risks have been measured and that they are therefore being managed appropriately. Many organizations have succeeded in measuring financial risk but failed at managing it. Markets are always capable of unexpected results. As a result, best efforts at measuring risk will never fully capture potential future outcomes, even if estimates are good most of the time. To reduce risk, it is necessary to manage exposure. Measures of exposure are another component of risk management. There are several ways to estimate potential loss. The concept of probability is the central principle of risk. The term risk measurement is an attempt to answer the question: “How much can I lose?”, and to answer it with reasonable certainty. 6.1. Process of Estimating Risk “The key to truly effective risk management lies in the behavior of markets during times of crisis, when investment value is most at risk. Observing markets under stress teaches important lessons about the role and dynamics of markets and the implications for risk management.”[11] The estimation of risk is a twopart process. The first part of the process is estimating the likely gain, or—more importantly in risk management—the likely loss, from changes in market rates or prices. To calculate potential loss, it is necessary to estimate the sensitivity of the instrument or exposure to market changes. Measures such as duration (for interest rates) are useful to estimate sensitivity to market changes. The second part of the process involves estimating the probability of the aforementioned market changes. Given a potential change in the market rates and the size of the underlying position, plus the probability of the change in market rates occurring, the potential loss (or gain) can be estimated. 6.2. How to measure financial risk? The most common way of measuring financial risk is known as ValueatRisk (VaR). In financial mathematics and financial risk management, VaR is a widely used risk measure of the risk of loss on a specific portfolio of financial assets. VaR has five main uses in finance: risk management, risk measurement, financial control, financial reporting and computing regulatory capital. VaR is at times used in nonfinancial applications as well. 6.2.1. Valueatrisk ValueatRisk is a percentilebased risk measure that measures the expected loss of a portfolio over a specified period of time for a set level of probability or confidence. Answering the aforementioned question: “How much money might I lose?”, ValueatRisk is based on probabilities and within parameters set by the risk manager. Valueatrisk calculations are based on one of several methods. It creates a distribution of potential outcomes at a specified confidence interval. The largest loss outcome using the confidence level as the cutoff is the amount reported as valueat risk. Confidence intervals are typically 95, 97.5, or 99 percent. For example, at a 95 percent confidence interval, there is the probability of a loss being greater than $10,000,000 on 5 days out of 100 days. Although valueatrisk is a useful measure because of its ability to distill a great deal of information into a single number, there are strengths and weaknesses associated with it. Clearly, one of the key advantages of valueatrisk is its ability to focus both nonfinancial and financial managers on the issue of measuring risk. Despite its shortcomings, it may encourage a more systematic and multidimensional approach to financial risk. 6.2.2. Methods to Calculate ValueatRisk There are several ways to calculate ValueatRisk. The methods vary in their need for market data, the computing power required, and the ability to model different types of instruments. ValueatRisk calculations are typically obtained using one of the following methods: • Using historical data • Using Monte Carlo Simulation • Using the variance/covariance (parametric) approach 6.2.2.1. ValueatRisk Using Historical Simulation One way to calculate valueatrisk is to use past returns to simulate future returns as a guide to estimating potential loss. The resultant returns, ranked by magnitude from best to worst, provide a snapshot of the portfolio’s value under historical market data with the worst results commonly at the 95 percent level (excluding the worst 5 percent of returns) or the 99 percent level (excluding the worst 1 percent of returns). The worst returns are the ones that most interest the risk manager. The result provides useful information about the risks associated with the current portfolio based on historical market movements. The historical method simply reorganizes actual historical returns, putting them in order from worst to best. It then assumes that history will repeat itself, from a risk perspective. 6.2.2.2. ValueatRisk Using the Parametric Approach The parametric approach to calculating valueatrisk is also known as the variance/ covariance method, the correlation method, or the analytical method. Of the parametric models available, the best known is probably RiskMetrics. The parametric approach to valueatrisk has origins in modern portfolio theory, where the risk of a portfolio of assets is assumed to be a function of the risk or variability of each instrument in the portfolio and the correlations between instruments in the portfolio. The parametric valueatrisk methodology is often combined with another methodology for analyzing the behavior of nonlinear instruments and exposures. The traditional parametric approach is not effective for all types of assets or instruments such as options. 6.2.2.3. ValueatRisk Using Monte Carlo Simulation Monte Carlo simulation involves computing ValueatRisk using tools that automatically generate large numbers of random price or rate changes. These price changes are applied to the portfolio of assets or exposures and the results are measured. The worst results of the resulting distribution are considered to be the ValueatRisk amount, using a specified confidence level. One advantage of Monte Carlo simulation is that it allows a financial manager to use the results of hundreds or thousands of scenarios to calculate ValueatRisk. The resultant frequency distribution can be used to determine ValueatRisk with the desired confidence interval. Monte Carlo simulations are typically accomplished using specialized software. Innovations in technology and simulation have made the calculations using Monte Carlo simulation for large, complex portfolios more accessible and cost effective. 6.2.3. The examples of Historical, Monte Carlo and Parametric Approaches[12] Institutional investors use VAR to evaluate portfolio risk, but in this introduction we will use it to evaluate the risk of a single index that trades like a stock: the Nasdaq 100 Index, which trades under the ticker QQQQ. The QQQQ is a very popular index of the largest nonfinancial stocks that trade on the Nasdaq exchange. 6.2.3.1. Historical method example The QQQQ started trading in Mar 1999, and if one calculates each daily return, one produces a rich data set of almost 1.400 points. For example, at the highest point of the histogram (the highest bar), there were more than 250 days when the daily return was between 0% and 1%. At the far right, the bar located at 13% is hardly visible; it represents a single day (in Jan 2000) within a period of fiveplus years when the daily return for the QQQ was a stunning 12.4%. Figure 5 Concentrating on the red bars that compose the "left tail" of the histogram, one notices that these are the lowest 5% of daily returns (the returns are ordered from left to right, the worst appropriately located on the "left tail"). The red bars run from daily losses of 4% to 8%. Because these are the worst 5% of all daily returns, one can claim with 95% confidence that the worst daily loss will not exceed 4%. In other words, one can expect with 95% confidence that the gain will exceed 4%. This is a simplified explanation of VaR. Reviewing the statistic in terms of both percentage and dollar terms, the aforementioned can be summarized as :
Figure 6 The idea behind the variancecovariance is similar to the ideas behind the historical method  except that the familiar curve is used instead of actual data. The advantage of the normal curve is the instant knowledge of where the worst 5% and 1% lie on the curve. They serve as a function of the desired confidence and the standard deviation (): The blue curve above is based on the actual daily standard deviation of the QQQ, which is 2.64%. The average daily return is close to zero, so one must assume an average return of zero for illustrative purposes. The table below displays the results of plugging the actual standard deviation into the formulas above: 6.2.3.3. Monte Carlo Simulation example The third method involves developing a model for future stock price returns and running multiple hypothetical trials through the model. A Monte Carlo simulation refers to any method that randomly generates trials, but by itself does not tell anything about the underlying methodology. For most users, a Monte Carlo simulation amounts to a "black box" generator of random outcomes. A Monte Carlo simulation on the QQQ based on its historical trading pattern was conducted, where 100 trials were conducted. If conducted again, it would produce different resultsalthough it is highly likely that the differences would be narrow. The result arranged into a histogram is presented below (note: the following histogram displays monthly returns): Figure 7 A hundred hypothetical trials of monthly returns for the QQQ were run. Among them, two outcomes were between 15% and 20%; and three were between 20% and 25%. That means the worst five outcomes (the worst 5%) were less than 15%. The Monte Carlo simulation therefore leads to the following VARtype conclusion: with 95% confidence, a loss more than 15% during any given month is not expected. 6.3. Quantification of financial risk 6.3.1. Investment returns An individual or a business spends money today because they expect to gain even more money in the future. The concept of return provides investors with a convenient way of expressing the financial performance of an investment. To illustrate, suppose an investor buys 15 shares of a stock for $1,000. The stock pays no dividends, but at the end of one year, the investor sells the stock for $1,100. What is the return on your $1,000 investment? [13] One way of expressing an investment return is in dollar terms. The dollar return is simply the total dollars received from the investment less the amount invested: Dollar return = Amount received  Amount invested = $1,100 $1,000 = $100 If at the end of the year the stock is sold for only $900, the dollar return would have been $100. Although expressing returns in dollars is considered to be easy, two problems arise: 1) Making a meaningful judgment about the return requires knowing the scale (size) of the investment; a $100 return on a $100 investment is a good return (assuming the investment is held for one year), but a $100 return on a $10,000 investment would be a poor return 2) Knowing the timing of the return; a $100 return on a $100 investment is a very good return if it occurs after one year, but the same dollar return after 20 years would not be very good The solution to the scale and timing problems is to express investment results as rates of return, or percentage returns. For example, the rate of return on the one year stock investment, when $1,100 is received after one year, is 10 percent: The rate of return calculation “standardizes” the return by considering the return per unit of investment. In this example, the return of 0.10, or 10 percent, indicates that each dollar invested will earn 0.10 ($1.00) = $0.10. If the rate of return had been negative, this would indicate that the original investment was not even recovered. For example, selling the stock for only $900 results in a 10 percent rate of return, which means that each dollar invested lost 10 cents. A $10 return on a $100 investment produces a 10 percent rate of return, while a $10 return on a $1,000 investment results in a rate of return of only 1 percent. Thus, the percentage return takes account of the size of the investment. Expressing rates of return on an annual basis, which is typically done in practice, solves the timing problem. A $10 return after one year on a $100 investment results in a 10% annual rate of return, while a $10 return after five years yields only a 1.9% annual rate of return. The rate of return solves the two major problems associated with dollar returns, size and timing. Therefore, the rate of return is the most common measure of investment performance. 6.3.2. Probability and its distribution Probability modeling in finance and economics provides a means to rationalize the unknown by imbedding it into a coherent framework, clearly distinguishing what one knows and does not know. However, modeling uncertainty is not merely a collection of techniques but an art in blending the relevant aspects of a situation and its unforeseen consequences with a descriptive, yet theoretically justifiable and tractable, economic and mathematical methodology. Of course, probabilities to describe quantitatively the set of possible events that may unfold over time are conveniently used. Specification of these probabilities and their associated distributions are important and based on an understanding of the process and the evidence applied in order to estimate these probabilities. Any model is rationally bounded and also has its own sources of imperfections that one may, or may not, be aware of. However, probabilities and their quantitative assessment, remain essential and necessary to provide a systematic approach to constructing a model of uncertainty. An event’s probability is defined as the chance that the event will occur. If all possible events, or outcomes, are listed, and if a probability is assigned to each event, the listing is called a probability distribution. Probabilities can also be assigned to the possible outcomes, or returns, from an investment. If one buys a bond, one expects to receive interest on the bond plus a return of your original investment, and those payments will provide the buyer with a rate of return on your investment. The possible outcomes from this investment are: 1. that the issuer will make the required payments or 2. that the issuer will default on the payments If the probability of default is higher, the bond is riskier, and if the risk is higher, the required rate of return is also higher. If you invest in a stock instead of buying a bond, you will again expect to earn a return on your money. A stock’s return will come from dividends plus capital gains. Again, the riskier the stock—which means the higher the probability that the firm will fail to perform as expected—the higher the expected return must be to induce the buyer to invest in the stock. With this in mind, considering the possible rates of return that one might earn next year on a $10,000 investment in the stock of either Martin Products Inc. or U.S. Water Company, the following table is produced[14]: Figure 8 Martin manufactures and distributes computer terminals and equipment for the rapidly growing data transmission industry. Because it faces intense competition, its new products may or may not be competitive in the marketplace, so its future earnings cannot be predicted as one might wish. Indeed, some new company could develop better products and literally bankrupt Martin. U.S. Water, on the other hand, supplies an essential service, and because it has city franchises that protect it from competition, its sales and profits are relatively stable and predictable. There is a 30% chance of strong demand, in which case both companies will have high earnings, pay high dividends, and enjoy capital gains. There is a 40% probability of normal demand and moderate returns, and there is a 30% probability of weak demand, which will mean low earnings and dividends as well as capital losses. Martin Products’ rate of return could vary far more widely than that of U.S. Water. There is a fairly high probability that the value of Martin’s stock will drop substantially, resulting in a 70% loss, while there is no chance of a loss for U.S. Water. 6.3.2.1. Characteristics of probability distribution: a) Mean Mean presents a simplified mathematical average of the set of two or more numbers. The mean for a given set of numbers can be computed in more than one way, including the arithmetic mean method, which uses the sum of the numbers in the series, and the geometric mean method. However, all of the primary methods for computing a simple average of a normal number series produce the same approximate result most of the time. If stock XYZ closed at $50, $51 and $54 over the past three days, the arithmetic mean would be the sum of those numbers divided by three, which is $51.67. b) Variance and standard deviation Variance is a mathematical expectation of the average squared deviations from the mean. A measure of the dispersion of a set of data points around their mean value. Variance measures the variability (volatility) from an average. Volatility is a measure of risk, so this statistic can help determine the risk an investor might take on when purchasing a specific security. Variance of sample The sample variance, abbreviated s2, is a commonly used measure of variability. It is approximately the mean of the squares of the deviations. Standard deviation Standard deviation for population Standard deviation of sample Standard deviation is the measure of the dispersion of a set of data from its mean. The more spread apart the data, the higher the deviation. Standard deviation is calculated as the square root of variance. In finance, standard deviation is applied to the annual rate of return of an investment to measure the investment's volatility. Standard deviation is also known as historical volatility and is used by investors as a gauge for the amount of expected volatility. c) Covariance Covariance presents the measure of the degree to which returns on two risky assets move in tandem. A positive covariance means that asset returns move together. A negative covariance means returns move inversely. d) Coefficient of Correlation Coefficient of correlation represents a statistical measure of how two securities move in relation to each other. Correlation coefficient ranges between 1 (perfect negative correlation) and +1 (perfect positive correlation). 7. Conclusion World events such as terrorism, natural disasters and the global financial crisis have raised the profile of risk. Now more than ever, organizations must plan, respond and recognize all forms of risks that they face. That’s why financial risk management has become an extremely important discipline for corporations, financial institutions and many government enterprises. Risk management is a core business skill and understanding and dealing with risks effectively can both increase success and reduce the likelihood of failure. Understanding the sources and different forms of risk is important not only in terms of efficiency of investments and the possibilities of protection but also because the techniques of quantifying risk. Measuring and monitoring risk at a firmwide level has increased the focus on quantification and the need for a consistent firmwide approach. Our conclusions are: • Risk assessment is feasible and practical, but must be implemented only after one fully understands the meaning of the word risk and the technical challenges • Also control assessment is feasible and practical, but must only be implemented after one understands the how to make a subjective process more objective. • Integrated risk and control assessment or measurement promotes educated decision making, which in turn facilitates prudent risk management and can contribute to the creation of a good risk culture. 8. Literature 1. Horcher K.A., „Essentials of Financial Risk Management“; John Wiley & Sons, Inc., Hoboken, New Jersey, 2005. 2. Brigham and Houston; „Fundamentals of Financial Management“, SouthWestern College Pub; 10 edition, 2004. 3. Demoderon A., “Applied Corporate Finance: A User's Manual”, John Wiley and Sons, New York, 1999. 4. Tapiero C. „Risk and Financial Management, Mathematical and Computational Methods“, John Wiley and Sons Ltd, West Sussex, England, 2004. 5. Murphy D.; “Understanding Risk; The Theory and Practice of Financial Risk Management”; Chapman & Hall/CRC Financial Mathematics Series, 2008. 6. Elmiger G. and Kim S.; „RiskGrade Your Investments: Measure Your Risk and Create Wealth“; John Wiley & Sons, Inc., Hoboken, New Jersey, 2003. 7. Shirreff D. „Dealing with financial risk“; Profile Books Ltd ; Hatton Garden, London; 2004 8. Jonathan Clemens, “Learning Lessons from Market Losses,” The Wall Street Journal,2000. 9. Bookstaber R.M; “Risk Management, Principles, and Practices”, AIMR Conference Proceeding, 1999. Copyright 1999, CFA Institute 10. www.wikipedia.com http://www.investopedia.com [1] Figure 1. Source: Aswath Demoderon, Applied Corporate Finance: A User's Manual, John Wiley and Sons, New York, 1999, p.35 [2] Definition taken from: http://en.wikipedia.org/wiki/Financial_risk [3] David Murphy, „Basic ideas in risk management“ in Understanding Risk: The Theory and Practice of Financial Risk Management, page 46 [4] Karen A. Horcher, „Essentials of Financial Risk Management“, page 5. [5] Karen A. Horcher, „Essentials of Financial Risk Management“, page 7. [6] Jonathan Clemens, “Learning Lessons from Market Losses,” The Wall Street Journal, December 5, 2000, p. C1. [7] Source: Phoenix Investment Partners, research conducted by Financial Research Corporation (FRC). [8] Source: Phoenix Investment Partners, research conducted by Financial Research Corporation(FRC). [9] Karen A. Horcher, „Essentials of Financial Risk Management“, page 189. [10] Taken from: http://investspec.com/funds/financialderivativesaninstrumentofmoney/ [11] Source: Richard M. Bookstaber, “A Framework for Understanding Market Crisis,” Risk Management, Principles, and Practices, AIMR Conference Proceeding, no. 3, 1999. Copyright 1999, CFA Institute. [12] Taken from : http://www.investopedia.com/articles/04/092904.asp [13] Example taken in full from Brigham and Housto ;„Risk and rates of return“; Fundamentals of Financial Management, page 233. [14] Example taken in full from Brigham and Houston; „Probability distributions“; Fundamentals of Financial Management, page 233
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