Financial Risk Mitigation Essay Example

Financial Risk Mitigation Essay Discussion Paper Financial Risk Mitigation in Insurance Time for Change The Chief Risk Officer Forum Risk Mitigation Working Group Copyright  © 2006 Chief Risk Officer Forum 1 Discussion Paper Preface The Chief Risk Officer Forum is delighted to be presenting the study â€Å"Financial Risk Mitigation in Insurance – Time for Change†. The Chief Risk Officer Forum comprises risk officers of the major European insurance companies and financial conglomerates, and was formed to address the key relevant risk issues for its industry. It is a technical group focused on developing and promoting industry best practices in risk management. The membership comprises: Aegon NV Allianz AG Aviva PLC AXA Group Converium Fortis Generali ING Group Munich Re Prudential plc Swiss Re Winterthur Zurich Fin’l Services Tom Grondin Raj Singh Sue Kean Francois Robinet Peter Boller Luc Henrard Paul Caprez John Hele Charlie Shamieh Andrew Crossley Christian Mumenthaler Joachim Oechslin Andreas Grunbichler tom. [emailprotected] com raj. [emailprotected] de [emailprotected] com francois. [emailprotected] com peter. [emailprotected] com luc. [emailprotected] com [emailprotected] com john. [emailprotected] com [emailprotected] com andrew. [emailprotected] co. uk [emailprotected] com joachim. [emailprotected] ch andreas. [emailprotected] com We will write a custom essay sample on Financial Risk Mitigation specifically for you for only $16.38 $13.9/page Order now We will write a custom essay sample on Financial Risk Mitigation specifically for you FOR ONLY $16.38 $13.9/page Hire Writer We will write a custom essay sample on Financial Risk Mitigation specifically for you FOR ONLY $16.38 $13.9/page Hire Writer Chief Risk Officer Forum Contact Details: Via E-mail: [emailprotected] org [emailprotected] rg The report demonstrates that the use of derivatives offers insurance companies a more robust and efficient way to hedge market risk exposures, but there are definitive regulatory/accounting obstacles to the full deployment of these strategies, perversely discouraging state of the art risk management practices. With this report the Chief Risk Officer Forum is proposing a set of principles and policies for insurers and their regulators which would encourage financial risk mitigation activities in the sector. The working group which wrote the report comprised representatives of Munich Re (chair), Winterthur and Zurich Financial Services. Special thanks are expressed to the following delegates of the CROs who assisted in compiling the report: Jan Willing (Munich Re), Robert Lempertseder (Munich Re), Daniel Bronnimann (Winterthur), Doug Niemann (Zurich Financial Services), Markus Spillmann (Zurich Financial Services) and Saeid Samiei (Zurich Financial Services). We hope that this study will provide guidance for best practices in risk management, helping to improve risk management culture and facilitate the greater deployment of sound financial risk mitigation strategies in the insurance sector. Chief Risk Officer Forum Copyright  © 2006 Chief Risk Officer Forum 2 Discussion Paper Contents 1. Introduction. 7 1. 1. Purpose of this paper .. 7 1. 2. Example to support motivation: interest rate risk in life insurance . 7 2. Case for change. 8 2. . Life insurance policy: Guarantee plus option for more†¦ 8 2. 2. Dynamic duration strategy required 9 2. 3. Hedging strategies using derivative instruments evolved.. 10 2. 4. Some regulators give partial incentives for insurers to make use of hedging strategies 12 2. 5. Adequate accounting treatment for hedging strategies achievable 13 2. 6. Some considerations on market capacities for financial risk mitigation transactions. 15 2. 7. Many regulatory regimes still hinder deployment of optimal hedging strategies .. 16 3. Recommended principles.. 17 3. 1. Introduction 7 3. 2. Incentives for sound risk mitigation strategies 18 3. 3. Sound risk management framework as a precondition 19 3. 4. Permission to use financial instruments (e. g. derivatives) for risk mitigation purposes . 19 3. 5. Unrestricted capital credit for financial instruments in a risk mitigation context . 20 3. 6. Economic view should supersede legacy rules 21 3. 7. Valuation consistency of risk mitigation instruments with risk mitigation context . 21 4. Suggested policies. 23 4. 1. Policies giving effect to Principle 1 (Provide the right incentives) .. 23 4. 2. Policies giving effect to Principle 2 (Sound risk management framework) . 23 4. 3. Policies giving effect to Principle 3 (Permission to use financial instruments for risk mitigation purposes) .. 24 4. 4. Policies giving effect to Principle 4 (Equal yardsticks for qualifying financial instruments) 24 4. 5. Policies giving effect to Principle 5 (Supersede legacy rules). 26 4. 6. Policies giving effect to Principle 6 (Consistent treatment under statutory accounting) . 6 5. Conclusion 28 Appendix A. Primer on financial risk concepts 29 A. 1. Duration and convexity 29 A. 2. Swaps and options on swaps. 30 Appendix B. Many regulatory regimes still hinder deployment of optimal hedging strategies 32 Appendix C. Essential components of a sound risk management framework.. 38 C. 1. Policy 2A (I): Appropriate supervisory/management oversight. 38 Copyright  © 2006 Chief Risk Officer Forum 3 Discussion Paper C. 2. Policy 2A (II): Comprehensive and documented policies and procedures 39 C. 3. Policy 2A (III): Sound risk/valuation systems. 0 C. 4. Policy 2A (IV): Independent effective risk management function.. 40 Copyright  © 2006 Chief Risk Officer Forum 4 Discussion Paper Executive summary In many regulatory regimes risk mitigation activities of insurers are not adequately incentivised, or not even allowed; sometimes even perverse incentives are given to insurers. Along the example of life insurance we will describe how research in Asset/Liability Management (A/LM) evolved in the last years and what hurdles (regulatory and other) insurers encounter in the implementation of risk mitigation strate gies. A particular focus is set on the measurement of interest rate risk and how insurers came to the conclusion that the mere linear approximation (duration) of A/L value changes for interest rate changes (i. e. ignoring convexity) was flawed and often led to inappropriate policies for managing those risks. More generally, more and more insurers realise the true financial nature of their core business. Given this development it is but a small step to the consideration of the necessary tools for interest rate risk management, e. . swaps and swaptions. Starting from these observations a series of principles is developed in this paper designed to allow the insurance industry to properly develop financial risk mitigation strategies as follows: Principle 1: Provide the right incentives Solvency II should provide incentives for sound risk mitigation strategies. Principle 2: Sound risk management framework is a precondition A precondition for the use of financial instruments for risk mitigation is a sound risk management framework for the company. Principle 3: Focus on the process, not the instrument The admissibility of financial instruments for risk mitigation should be based upon the soundness of the risk hedging process. Restrictions on the use of financial instruments for risk mitigation cannot follow a â€Å"one size fits all† approach (e. g. a list of admissible and inadmissible financial instruments). Principle 4: Equal yardsticks for qualifying financial instruments Qualifying financial instruments used for risk mitigation purposes should receive full and unrestricted capital credit under Pillar I of Solvency II. The credit given for financial instruments used for risk mitigation under Pillar I, should be based on the documented and evaluated economic effect on both the valuation of assets and liabilities and the determination of the MCR and SCR. Principle 5: Supersede legacy rules Determination of capital requirements for solvency purposes under Pillar I of Solvency II or under Solvency I should be based entirely on economic principles if the insurance company can demonstrate that it has a sound risk management framework (Principle 2) and that it is using financial instruments for risk mitigation satisfying the requirements of Principles 3 and 4. Principle 6: Consistent treatment in statutory accounting Under the statutory accounting regime, the asset valuation rules in respect of financial instruments used for risk mitigation purposes must be consistent with the valuation rules in respect of the liabilities they are designed to hedge. Copyright  © 2006 Chief Risk Officer Forum 5 Discussion Paper In section 6 policies are developed, which are designed to give effect to these principles and result in sound risk mitigation practices in the insurance industry. Copyright  © 2006 Chief Risk Officer Forum 6 Discussion Paper 1. Introduction 1. 1. Purpose of this paper Regulatory and accounting rules in many European countries posed and often still pose a real hindrance to sound risk management practices in insurance companies. This hindrance usually comes in the following two forms: Inconsistent valuation of assets and liabilities and Restricted admissibility of risk mitigating instruments. The scope of this paper is to encourage regulators to overcome these obstacles by introducing consistent valuation techniques for assets and liabilities and by fostering the admissibility and usage of any financial instrument for isk mitigation purposes in insurance companies. In its full generality, this could apply to all financial instruments (inflation linked securities, commodities, derivatives etc. ) and to all sorts of insurance companies (life and non-life, primary and reinsurance). Nonetheless, our paper is inspired by the management of interest rate risk in life insurance and the usage of swaps and swaptions in this area. The usage of swap derivatives in life insurance, will serve as a case study, which accompanies the paper to motivate our principles and policies and to make the paper less theoretical. Hence, we often refer to derivatives or even swaps and swaptions instead of the more general term financial instruments. Since interest rate risk is one of the biggest sources of risk in insurance, we also think that this example per se has most relevance to risk officers. 1. 2. Example to support motivation: interest rate risk in life insurance The typical financial risk, which one encounters in a life insurance company is a duration gap between assets and liabilities, i. e. assets will typically have a significantly shorter duration than liabilities. This duration gap exposes the insurer (and hence its share holders, other investors and policy holders) to falling interest rates, but the net A/L position gains in value if interest rates rise. Although unintended, this A/L mismatch was (and often still is) favoured by many regulatory and accounting regimes in Europe as liabilities are valued at a statutory interest rate, which does not flex with market interest rates. Fixed income assets on the other hand have to be valued at the lower of market value and acquisition cost. This method of asset valuation does give preference to shorter duration assets, which exhibit less price volatility if interest rates change. In addition, many regulatory environments prohibited or discouraged the use of certain financial instruments (e. g. derivatives) that are often vital for affecting a proper hedge. Hence the regulatory and accounting rules in many European countries hindered the introduction of sound interest rate risk management in life insurance. Other reasons for this A/L mismatch reside in the historically scarce availability of longer duration assets in some jurisdictions and in the presumed policy holder expectation to participate in rising bonus rates if interest rates rise. Copyright  © 2006 Chief Risk Officer Forum 7 Discussion Paper 2. Case for change In 2001 and 2002 the financial markets underwent a serious revaluation, characterised by falling equity markets and interest rates and rising volatilities and credit spreads. These market disruptions led to significant losses in the European life insurance industry. In addition to that, as was mentioned in the previous section, most regulatory and accounting frameworks aggravated the problem by incentivising A/L mismatches. The need to improve A/LM capabilities became obvious after this turmoil. As a consequence, considerable improvements have been made in the area of A/LM throughout the European life insurance industry in the past 3 years, with a central focus on managing guaranteed benefits. Driven by ever declining interest rates, many insurers had a closer look at the liabilities and learnt about the long duration of the guaranteed benefits. Also at around this time, the capital markets were undergoing rapid evolution offering liquid and targeted instruments for hedging certain risks (e. g. development of the derivative markets). Matching of guaranteed policyholder benefits with corresponding assets evolved as a credo in many insurance companies. As a result, considerable lengthening of fixed income portfolio durations took place in times of low interest rates. (For the reader not familiar with the subject matter, Appendix A provides a primer on financial risk concepts including duration and convexity and describes the structure of important risk mitigation instruments such as swaps and swaptions). 2. 1. Life insurance policy: Guarantee plus option for more†¦ While these efforts have clearly brought considerable insight to management, it has also left management with open questions. The reason for this is that significant options embedded in life insurance policies, such as policyholder expectations above guaranteed benefits, the surrender option, and a series of other options, were not always given their due attention. The central question is around the impact of these options on the â€Å"right† duration strategy. Let us consider a typical with-profits life insurance policy to understand the impact of the embedded options. The policyholder is guaranteed a minimum rate of return on its paid premiums, and in addition is entitled to at least 90% of the surplus investment returns, i. e. returns exceeding the guaranteed rate. Since this guaranteed rate of return is always out of the money at inception of the policy, the policyholder is expecting surplus returns. Indeed, the surplus distribution is an essential selling point for this product and therefore much of the competition between life insurers centres around surplus (expectations and realisations). The guaranteed interest rate and entitlement to surplus makes the insurance policy an asymmetric product: the policyholder is participating in (and expecting) the upside when markets (or interest rates! ) rise and is protected when markets fall. This asymmetry can be expressed in the language of financial options. The policyholder is entitled to the investment returns of the insurer’s portfolio, and additionally holds a floor (set at the guaranteed interest rate) on these investment returns. Copyright  © 2006 Chief Risk Officer Forum 8 Discussion Paper Hence, the insurer sold an option on its investments to the policyholder, but is free to choose an investment strategy. Clearly, the value of the policyholder’s floor depends on the investment strategy chosen by the insurer. For example, the insurer could choose to: Minimize the value of the policyholder’s floor option: Assume a portfolio of life insurance liabilities in run-off. In this case, management might focus on protecting the share holders’ capital, i. e. reduce the risks arising from the guarantee part of the liabilities. The investment portfolio would then match the guaranteed cash flows as closely as possible. This strategy is clearly also increasing the protection of policy holders’ interests. Maximize the possibility of declaring attractive bonus rates: Assume a portfolio of life insurance liabilities in a well-capitalized company managed on a going-concern basis. The asset/liability position of this insurer will exhibit some financial risks in order to increase the possibility of declaring attractive bonus rates. The typical financial risk which one encounters in this situation is a duration gap between assets and liabilities, i. e. assets will typically have a significantly shorter duration than liabilities. This duration gap exposes the insurer and its shareholders to falling interest rates, but allows the insurer to declare higher bonus rates as interest rates rise. Of course other sources of financial risk (and hence potential upside for policy holders) are present in life insurance portfolios, e. g. real estate or equity investments. The example illustrates that the insurer has to cope with two conflicting targets: securing guarantee risk versus fulfilling policy holder expectations (and hence enhancing the franchise value of the firm), although it is by no means obvious, what surplus (and hence what sort of A/L risk) policy holders do and reasonably can expect. 2. 2. Dynamic duration strategy required The life insurance industry has been increasingly adopting the more advanced technique called market consistent valuation. It has helped the insurance industry to quantify these embedded options in a manner consistent with what it would cost to hedge or insure these risks. The bases for market consistent valuation are risk-neutral valuation concepts commonly used in the capital markets for pricing of financial derivatives. Market consistent valuations have shown that the options embedded in life insurance policies may indeed have a significant impact on the duration strategy. A central implication of the market consistent valuation work is that it is not always advisable to lengthen the duration of the investment portfolio to match the duration of the guaranteed benefits, but instead the duration gap has to be seen in conjunction with the capital base of the firm and the risk appetite of the management (see the last bullet point in the preceding section). The reason for this is the sensitivity (in opposing directions) of the value of the guaranteed benefits and the embedded options with respect to small interest rate changes. The resulting duration of the combined liability (i. e. uaranteed benefits plus embedded options) is thus shorter than the duration of the guaranteed benefits only. In case of a drastic fall in interest rates, however, it is indispensable to lengthen the duration of the investment portfolio to bring it close to the duration of the guaranteed Copyright  © 2006 Chief Risk Officer Forum 9 Discussion Paper benefits. The objective is to protect the guaranteed benefits, while the embedded options (on surplus) have little value. Vice versa, in the case of substantially rising rates, the value of the embedded options is rising steadily, requiring a shortening of the duration (Figure 1). Figure 1 Illustrative duration strategy of a portfolio of life insurance policies (EUR) 12. 0 10. 0 Guarantee Duration strategy considering guarantees plus options Duration 8. 0 6. 0 4. 0 2. 0 0. 0 1. 0% 2. 0% Asset portfolio Today s interest rate level 3. 0% Interest rates 4. 0% 5. 0% Protecting guarantees Providing upside This lengthening of the duration as interest rates decline (and vice versa) is called convexity. The market consistent valuation allows a company to determine the most appropriate duration for every interest rate environment, and with this the convexity of the respective portfolio. The convexity risk has not been actively managed in the past by many life insurers, thus leaving life insurers with substantial interest rate risk. 2. 3. Hedging strategies using derivative instruments evolved There are generally two approaches to manage the convexity of life insurance portfolios, dynamic hedging and hedging using financial instruments (Figure 2). Combinations of the two approaches are also feasible. Figure 2 Dynamic duration management 12. 0 10. 0 Guarantee Hedging using interest rate options 12. 0 10. 0 Guarantee Underlying FI pf plus hedge Duration 6. 0 4. 0 2. 0 0. 0 Dynamic strategy Optimal strategy Duration 8. 0 8. 0 6. 0 4. 0 2. 0 0. 0 Underlying fixed income portfolio 1. 0% 2. 0% 3. 0% Interest rates 4. 0% 5. 0% 1. 0% 2. 0% 3. 0% Interest rates 4. 0% 5. 0% 2. 3. 1. Dynamic hedging A dynamic hedging strategy is to adjust the duration of the fixed income portfolio when interest rates reach certain trigger levels. The duration can be adjusted either by sales of Copyright  © 2006 Chief Risk Officer Forum 10 Discussion Paper bonds and subsequent reinvestment in bonds with a different duration, or through the use of interest rate derivatives like swaps. Dynamic hedging strategies require a great deal of management attention, since the fixed income portfolio is constantly rebalanced. Dynamic strategies sometimes require tough trade-offs by management. Imagine interest rates are low and have declined further, and are now next to a trigger point. Management’s view is that interest rates will rise. Do you lengthen the duration in this situation? The A/LM strategy requires lengthening, but intuition tells you to stay shorter versus the benchmark – an unpleasant situation. Dynamic strategies often lead to high transaction costs due to the constant rebalancing. Furthermore, rebalancing usually leads to profit or loss recognition and ultimately, to PL volatility. The management of this volatility is demanding and may result in even higher transaction costs. For these reasons, dynamic interest rate hedging strategies are not widely used by life insurance companies. Generally it can be said, that this dynamic hedging strategy is equivalent to the delta hedging technique, which a bank uses to hedge the linear risks of a short option position. The choice between dynamic hedging strategies and the use of the corresponding financial derivatives will also depend on the price of the latter, i. e. he implied volatility of their underlying. If the implied volatility is considerably higher than the estimated future volatility of the underlying, then a dynamic hedging strategy could look more attractive. There is clearly a risk of misestimating the future volatility and in fact banks also hedge this so-called vega risk in their option books. 2. 3. 2. He dging using financial instruments A better way is to position the duration of the fixed income portfolio shorter than the duration of the guaranteed benefits (to account for the embedded options), and on top of it to enter into a series of interest rate options to hedge against convexity. The purpose of the options is to significantly lengthen the duration of the combined portfolio (fixed income plus options) as interest rates fall. In order to determine this strip of options, the reinvestment risk (taking into account future premiums of the existing book) is considered. By positioning the duration of the fixed income portfolio shorter than the guaranteed benefits, a reinvestment need will arise in the future. The reinvestment risk is the risk of not achieving the technical interest rate at the time of reinvestment. The reinvestment risk can be hedged with a strip of corresponding receiver swaptions. The strip of receiver swaptions hedging the reinvestment risk introduces the precise convexity required to protect the guaranteed benefits in case of a material interest rate decline (Figure 3). Depending on the life insurance portfolio to be hedged, the terms of the required receiver swaptions vary. Usually, the required options are of a long-term nature, just as the corresponding liabilities are. Depending on the currency, such options may be available in liquid markets (e. g. in the EUR swaption market), or may not be (e. g. in the CHF market). In the latter case, a company may choose to hedge the reinvestment risk in a different currency providing the required liquidity in long-term interest rate options, but leaving a certain basis risk. Based on the strong correlations of certain currencies (such as CHF and EUR), it is evident that the basis risk is only a fraction of the reinvestment risk hedged. (See also the case study below). Copyright  © 2006 Chief Risk Officer Forum 11 Discussion Paper Figure 3 100% Reinvestment Volume 80% Assets/ Liabilities 60% 40% 20% 0% 0 Reinvestment 30% 20% 10% 0% 0 5 #6 #4 #1 #5 #2 #3 Reserves Asset Portfolio 5 10 15 20 25 30 35 40 45 10 15 20 25 Year 30 35 40 45 As opposed to the dynamic hedging strategy, this strategy does not require an ongoing rebalancing of the portfolio although it is advisable to monitor the effectiveness of the hedge periodically. 2. 4. Some regulators give partial incentives for insurers to make use of hedging strategies Some European insurance regulators recently introduced new solvency regimes making interest rate risks more transparent and hence provide an incentive for life insurers to hedge these risks. The UK regulator, the FSA, introduced the â€Å"Realistic Valuation Requirement†, a form of market consistent valuation, for With-Profits Funds, as well as an â€Å"Individual Capital Assessment† requirement. These standards have encouraged many insurers to hedge their exposures to guaranteed annuity options (GAO) in recent years. The Danish insurance regulator introduced a reporting regime based on market valuation of assets and liabilities in 2003, as well as a stress test based on the market value of assets and liabilities in 2001 (yellow test/red test). The consequence was a large-scale hedging of interest rate risk (duration matching, hedging of convexity from guarantees and mortgage bonds). The industry entered into Constant Maturity Swap floors, swaptions, and swaps on underlying in excess of EUR 70bn. The Swiss insurance regulator introduced the Swiss Solvency Test in 2006. A field test was performed in 2004 with selected companies, and a second field test was performed in 2005. However, no significant trend towards hedging has yet been observed in Switzerland as yet. 2. 4. 1. Case study: The hedging activities in Denmark In the second quarter of 2001 the Danish regulator introduced a market stress test on assets and liabilities to ensure that life and pension companies had sufficient reserves to withstand substantial declines in interest rate and equity markets. The test consists of two parts: Copyright  © 2006 Chief Risk Officer Forum 12 Discussion Paper Red test: Equities down 30%, interest rates up/down 100bps Yellow test: Equities down 12%, interest rates up/down 70bps In October 2001, it was announced that all Danish life and pension companies had to account for assets and liabilities on a market basis starting from 1 January 2003. It is worthwhile noting that the Danish regulator sets the accounting regime for the life and pensions industry and it could therefore introduce a â€Å"fair value† accounting regime and a â€Å"fair value† solvency regime at the same time. Under this â€Å"mark-to-market† solvency/accounting regime, insurers’ solvency would be hurt as interest rates fall due to the existence of minimum guarantees. It is instructive to look at how the costs of derivatives changed during the hedging activities in Denmark. The Danes used the â‚ ¬-market for hedging because the DKKmarket is way too small and illiquid to absorb the hedging volumes. The currency risk between â‚ ¬ and DKK can be regarded as limited. Two numbers characterize the costs of a swaption very well: the forward rate and the normalized volatility. The following graph shows the development for 5 in 10 year forward rates and 5Yx10Y normalized swaption volatilities for the â‚ ¬. Figure 4 7. 00 0. 80% 6. 50 0. 75% 6. 00 0. 70% 5. 50 0. 65% 5. 00 0. 60% 4. 50 0. 55% 4. 00 3. 50 Danish hedging Danish hedging activities activities 30/11/2000 08/09/2001 18/4/2002 26/12/2002 09/04/2003 13/5/2004 20/1/2005 0. 50% 0. 45% 3. 00 23/3/2000 0. 40% 5 in 10 forward rate (lhs) x10 normalised swaption volatility (rhs) As can be seen in the chart, the Danish hedging activities had a huge impact on the European interest rate markets and hedges quickly became more expensive. 2. 5. Adequate accounting treatment for hedging strategies achievable The principles laid out in this paper do not require or presuppose a move to fair value accounting. Under specific circumstances, hedge accounting can be achieved for these receiver swaptions under both US-GAAP and IFRS and under some national accounting principles, avoiding substantial PL volatility. It should be noted, however, that achieving hedge accounting for this type of strategy is a privilege rather than a right. It requires substantial documentation work and limits managements flexibility in trading the hedging instruments for a very long period of time. Copyright  © 2006 Chief Risk Officer Forum 13 Discussion Paper The following review of local/international accounting standards is not intended to be exhaustive, but rather illustrates the range of treatments of risk mitigation strategies and the accounting hurdles that need to be considered. 2. 5. . US-GAAP and IFRS Under both US-GAAP and IFRS, derivatives are generally carried at fair value in the balance sheet, and fair value changes are recognized in

Writing Algebraic Expressions

Writing Algebraic Expressions Algebraic expressions are the phrases used in algebra to combine one or more variables (represented by letters), constants, and the operational ( - x / ) symbols.  Algebraic expressions, however, dont have an equals () sign. When working in algebra, you will need to change words and phrases into some form of mathematical language. For instance, think about the word sum. What comes to your mind? Usually, when we hear the word sum, we think of addition or the total of adding numbers. When you have gone grocery shopping, you get a receipt with the sum of your grocery bill. The prices have been added together to give you the sum. In algebra, when you hear the sum of 35 and n we know it refers to addition and we think 35 n. Lets try a few phrases and turn them into algebraic expressions for addition. Testing Knowledge of Mathematical Phrasing for Addition Use the following questions and answers to help your student learn the correct way to formulate Algebraic expressions based on mathematical phrasing: Question: Write seven plus n as an Algebraic expression.Answer: 7 nQuestion: What Algebraic expression is used to mean add seven and n.Answer: 7 nQuestion: What expression is used to mean a number increased by eight.Answer: n 8 or 8 nQuestion: Write an expression for the sum of a number and 22.  Answer: n 22 or 22 n As you can tell, all of the questions above deal with Algebraic expressions that deal with the addition  of numbers - remember to think addition when you hear or read the words add, plus, increase or sum, as the resulting Algebraic expression will require the addition sign (). Understanding Algebraic Expressions with Subtraction Unlike with  addition  expressions, when we hear words that refer to subtraction, the order of numbers cannot be changed. Remember 47 and 74 will result in the same answer but 4-7 and 7-4 in subtraction do not have the same results. Lets try a few phrases and turn them into algebraic expressions for subtraction: Question: Write seven less n as an Algebraic expression.Answer: 7 - nQuestion: What expression can be used to represent eight minus n?Answer: 8 - nQuestion: Write a number decreased by 11 as an Algebraic expression.Answer: n - 11 (You cant change the order.)Question: How can you express the expression two times the difference between n and five?Answer: 2 (n-5) Remember to think subtraction when you hear or read the following: minus, less, decrease, diminished by or difference. Subtraction tends to  cause students greater difficulty than addition, so its important to be sure to refer these terms of subtraction to ensure students understand. Other Forms of Algebraic Expressions Multiplication, division, exponentials, and parentheticals are all part of the ways in which Algebraic expressions function, all of which follow an order of operations when presented together. This order then defines the manner in which students solve the equation to get variables to one side of the equals sign and only real numbers on the other side. Like with addition and subtraction, each of these other forms of value manipulation come with their own terms that help identify which type of operation their Algebraic expression is performing - words like times and multiplied by trigger multiplication while words like over, divided by, and split into equal groups denote division expressions. Once students learn these four basic forms of Algebraic expressions, they can then begin to form expressions that contain exponentials (a number multiplied by itself a designated number of times) and parentheticals (Algebraic phrases which must be solved before performing the next function in the phrase). An example of an exponential expression with parentheticals would be 2x​2 2(x-2).

The impact of consumption and Investment on the GDP in Qatar (1990- Statistics Project

The impact of consumption and Investment on the GDP in Qatar (1990- 2012) - Statistics Project Example The reason for selecting this period of data was the incomplete data for all three variables that could have extended the analysis for the longer period. Moreover, it is important to provide definition of three variables included in the analysis. Net FDI = â€Å"The net inflows of investment to acquire a lasting management interest (10 percent or more of voting stock) in an enterprise operating in an economy other than that of the investor.† (â€Å"Indicator Queries†). The table indicated the country’s GDP increased significantly from 1994 to 2011 as the lowest value was recorded in 1994 and the maximum value was achieved in 2011. A sharp decline in the country’s GDP was recorded in 2009. Similar trends were observed in other two variables. The country’s exports increased significantly in the year 2011. The third variable ‘net inflows’ also showed a steady growth in the selected period. However, in 2011 a major decline was recorded. The results indicated that the value of adjusted R2 was 0.9871, which implies that the regression model implemented explained 98.71% of the total variations observed in 18 data entries. The regression equation obtained from the analysis indicated that the coefficient of constant, ÃŽ ²0 was 664545798.4126. A high value of constant coefficient suggested that there are other factors that affect the country’s GDP. Referring back to the equation of GDP provided, it could be noted that there are other variables included in the calculation of GDP. The coefficient of slopes obtained from the regression analysis were ÃŽ ²1 = 1.4160 (exports) and ÃŽ ²2 = 3.7452 (FDI net inflow). These values indicated that there is a positive relationship between GDP and exports and GDP and FDI net inflows. The findings reassert that to calculate a country’s GDP the values of investment and exports are added. The results imply that for every $1 increase or decrease in exports the country’s GDP would increase or decrease by $1.4160 respectively.

The Politics of a New Industrial Order Essay Example | Topics and Well Written Essays - 250 words

The Politics of a New Industrial Order - Essay Example elieved that every individual is equal and no one should be treated unequally in the society so they struggled to remove corruption and influence of rich people on the society. They also aimed to increase the government-public relationship so that there will be no communication gaps between and the problems of people could be solved. (Ideas and movements, 19th Century) To carry on with their motives and beliefs the progressives used different tactics. Many intellectuals wrote about the horrors of poverty, urban slums, dangerous factory conditions, and child labor to inform the people and get their support which was needed for the movement to succeed. The next major thing in the early reform period was abolitionism that is the force to remove slavery from the society. It also prohibited the intake of intoxicants as it pollutes the mind. After that was the struggle for the rights of women and the decreasing value of rural areas. After that it was the turn of social Darwinism to be removed from the society. This step was taken to loosen the grip of wealthy people on the society. The movement benefitted the people by loosening the power of their bosses on them. It helped them in getting rid of the gentry. The steps to stop labor exploitation gave safer work environment to the workers and this dropped the death rate. Different acts that were passed helped the investors (Sherman Antitrust Act 1890). Apart from benefits, the movement had some drawbacks. It triggered long work hours as the economy was expanding and the labor worked for very long hours. The next flaw was that by increasing the public-government relationship, the movement increased the chances of corruption and bribery. The movement encouraged schooling but at that time the industry had a great influence due to which the intellectual became reluctant to teach and thus the students became reluctant to study.

Transformational Leadership Essay Example | Topics and Well Written Essays - 2000 words - 3

Transformational Leadership - Essay Example According to the study  transformational leadership style is the kind of a leader the author ams. This is a kind of leadership style that believes in building relationships as well as motivating his fellow collogues at work. The motivation works well because they have a vision and mission that we all want to achieve together as a team. Naturally, the reporter is charismatic; he believes that communication is the basis of every relationship that works well. Most of the times he works confidently so that he can inspire his staff, command respect from them in addition to loyalty.  From this paper it is clear that  one vivid memory of a time the author was able to implement transformational leadership style is when the hospital had inadequate equipment. Such a situation hinders a conducive working environment for nurses. He wrote to the board of the hospital on the issue and ensured that the equipment was purchased.  His staffs were very happy and were able to perform well at wor k. There was also a time when they had an emergency case, and they had more than thirty patients being brought to the hospital. The author was able to coordinate the situation beforehand by assigning each and every nurse their role. It was a difficult job, but they managed thanks to his loyal team who gave their best shot.  As a student nurse, the author worked under the strict supervision of a nurse who was an authoritarian. He always dreaded the days he made a mistake or any of other students for that matter.

Development of Architecture During the Industrial Revolution

Development of Architecture During the Industrial Revolution Introduction The industrial revolution is one of the Great changes in human history. It starts in the middle of 18 century in Britain and continuing until now. Before the Revolution, there were no cities only villages. To get from one village to another people used galloping horse, which was the main and fastest transportation of that time. For majority of people the agriculture was dominant. When industrial revolution begins, agriculture and hand-made been stopped. Things that describes the period of Industrial revolution are inventions of steam engine, coal and iron. Everything is changed when James Watt created a â€Å"steam engine† in 1769. Invention of steam engine provided Britain with an industrial power. Factories, fabrics and railroads could be anywhere. (Louis Auguste Blanqui, historical channel.com.au). Invention of iron by Derby Family could not happen without steam engine. Smelting of iron by charcoal was expensive process. Abraham Derby discovered, that instead of using coal, can replace it with coke. The resulted product is cast iron. â€Å"Human of the Industrial Revolution†, www,hystoryworld.net Besides iron industry, there was a development of textile production, because textile is the basic requirements. Food and cotton products were light and easier to transport to different cities. Location of Britain was good for water transports. We know, that Britain is not from sea from any parts. This was the thing that makes the transportation of goods easier. . There was already existing of networks of canals. â€Å"Human of the Industrial Revolution†, www,hystoryworld.net During this time changes the production of goods. Now instead of using hand-made products, machines started replacing people. For example in fabrics and manufactures, machine could replace 5-6 people. This is main disadvantage of the Industrial Revolution, when government starts quitting unnecessary workers. Inventions of Industrial revolution period influenced to the economy growth. It is creation of different machine tools, using of Iron in manufacture. Industrial revolution changed everything and including architecture as well. Industrial revolution really affected on architecture. There was no need of fancy architecture anymore. People started design more industrial type, which is more useful rather than Gothic buildings. Beautiful Gothic buildings were designed to impress people. In that period some people was already on industrial side, started designing simple structure. At the same time some people went back to the old architectural style and brought them back. Therefore there were movements as Gothic revival and Art Nouveau. When people started designing with industrial mind they had many choice of design their house. (The importance of Industrial Revolution in Archietcture). (http://www.fablablima.com) Producing of iron influenced on architecture. One of great examples of architecture of industrial period is Crystal Palace by Joseph Paxton (1850-1851). Joseph Paxton studied and experienced iron and glass, about of joining these components together to design a large building. Body The movement of Gothic style architecture was not accidently. Those movements were against industrial revolution. They wanted to bring back the traditional style of architecture. The Crystal Palace in compare to Gothic Revival and arts and craft movements in architecture is new mode of design of that time. Gothic revival is architectural movement, which was based in England. It’s been a remaking of traditional building style of â€Å"Middle Ages†. Gothic style buildings are very heavy and decorative. Structure made of stone and brick. â€Å"Art Nouveau† movement has same features as Gothic movement, such as: symmetrical shapes and forms, use of arches and heavy structural system. (Jackie Craven, Art Noveau Architecture. architecture.about.com) The Crystal Palace is on of the Great buildings of Industrial period, which represent new direction in architecture. One of building that represent revolutionized architecture. When architecture moved from traditional mode to the new step. This structure is example of how people started experiencing different types of materials, instead of constructing the buildings by masonry and stone and maximizing the indoor spaces. It is a design of lightweight and low-cost buildings. This was the step when architecture of industrial period marked the beginning of new kind of architecture. It plays a big role in a history of architecture. The Crystal Palace was a glass and cast iron structure. The structure was built in London, for the Great Exhibition of 1851. In 1850 the committee were going to choose a design for the structure, which will exhibit the latest technology and innovation from around the world: â€Å" Great Exhibition of the works of industry of all Nations†. The committee requirements was: Economy and maximizing the exhibition space Spaces for circulation Spaces for reception, classification and placement of goods. View from the interior. In three weeks committee received more 250 works from Australia, Belgium, Netherlands, Hanover, Hamburg, France. But the committee rejected all the works. Mostly all the work was brick and masonry structural designs. But there was iron and glass design by Hector Horeau. The committee rejected it as well, because of the cost of the project. (The Crystal palace, p12) Already known architect and gardener Joseph Paxton presented his idea and concept to the committee. Before Joseph already had an experience with combination of cast iron, glass and laminated wood in his â€Å" Chatsworthhouse† building, which was made of glass. The larges glass house of that period. He experienced the idea â€Å"Ridge –and- furrow† roof system in Charsworthhouse, later he apllied this system in Crystal Palace’s design. Joseph’s design was based on module with the sizes 10inch x 49 inches, which is size of larges glass available that time. The structure consisted of right-angled triangles, which were supported by iron beams and pillars. The length of right-angled triangles was for 564 m. These basic components of the structure were light, strong and easy to build. After Joseph submitted his drawings and calculations, the committee approved the low cost design. The concept of ridge-and-roof house was lily flowers. Paxton’s reputation as gardener was high, he wanted to lily flower to be grown in England. He takes care of flowers. Later it became a concept for the roof system in Crystal Palace. In construction of the glass house, there was an issue with ridge-and furrow roof. Glass structure required more light, but because of structural members of roof (trusses, purlins) building does not get morning and evening rays. To avoid this problem he created the methods of glass roofing, which calls â€Å"ridge and furrow†. The principle and concepts of the roof was to get morning and evening light without any restriction. Therefore the glasses were placed in specific position. He tested this idea in his â€Å"Green house†. After it was applied to the Crystal Palace. (The Crystal palace, p29) The roof of transept is semicircular from exterior. In construction of this roof the support was made arched timbers. Columns supported on each arched timber. The transept roof also following the concept of ridge-and-furrow roof. It was constructed in a flat manner, but following the shape of arched timber. The range of the arches had louvered framed opening which allow passive ventilation for the building. Hollow columns of the structure support the roof. The roof itself looks flat. It has ridges and furrows, because of rise and fall of them is small, roof looks flat. Truss span of the roof 24 feet from each other and this spanning were supported by light beams or rafters. These rafters call â€Å"Paxton’s gutter†, because he created the system of using the rafter as a gutter. The advantages are when it rains, water running from the surface of the roof to â€Å"Paxton’s gutter†. From there water goes to the main gutter, which is connected to the hollow columns and passes down to drainage. (The Crystal Palace, p.36) But later on roofing system gets a problem, because of not availability of good quality construction materials. On of the disadvantages was leaking mostly from all of the part of the big building. This problem could not be solved. In terms of maximizing the space cast columns had advantages compare to masonry columns of traditional architecture, because it could carry the same load as masonry columns. Cast Columns much slimmer than masonry columns and can provide more open indoor space. When the constriction was complete the interior exhibition space was enormous. Because there were no solid walls, only the slender columns supporting the self weight. On of the important advantage of the structural frame works, that cast iron was low in price compare to traditional carved stone. The columns of the Crystal Palace consist of reservoir, where the all the drain water collects from the roof. This drain water is usable in situation of fire or for agriculture. (The Crystal Palace, p18). The great height of the building was divided into 3 stories. Where are the cast iron columns in each stories have different height. In lower floor columns height is 19 feet and for first and second floor is 17 feet. Between the columns the girders have same depth and sizes. They look similar and give an impression of latticework. Therefore construction does not look heavy. â€Å"This showing how great strength may be combined with elegance and lightness† (The Crystal Palace, p35-36). Joseph Paxton designed his â€Å"Victorian house† in such a way, so the building retains moisture and gets bright natural lighting every season of the year. But the mechanical and natural products, which were in the building, were destroyed because of moisture. After this experiment with â€Å"Victorian House†, it was experience for him to create new design to avoid those issues for Crystal Palace. (The Crystal Palace, p 32). An important advantage in construction of Crystal Palace takes machinery. Paxton used different types of cut machines (Punching machine, Iron drilling machine, Adzing and planning machine). Al the machines powered by steam engine. Painting machine reservoir filling with the paint, then it runs on surface of the frame. It constructed in a way so unnecessary part could be cleaned. One of the machines he used for framed wall. The frames being cut in machinery with the exactly same dimensions, after this glass was put into the frame. The glass sashes been designed in way so in summer can be removed. Since the work is done by machine, people did not worry that part might not match with each other. (The Crystal Palace, p51) In pre-industrialized period building been by human crafts without machines. Therefore it is harder and construction takes long time to be completed. The society of Art awarded Paxton’s sash-bar machines in 1841 with medal. These types sash-bar machines started u sing in other part of the country. In present time sash-bar design was taken from Paxton’s machine. The big challenge of The Crystal Palace was to maintain the normal temperature inside. Because the function was exhibition, there would be thousands of people. Heat producing by people and the heat coming from outside was the main issue. Already in that time Joseph Paxton cleverly designed the external shading devices. Direct sun light does not get, light is filtered and it becomes very soft. Another way of solution of heat transfer was to make ventilation system. He designed ventilation system for wall and flooring. Placing prefabricated lovers on the wall provides hot air escape. For flooring system board were placed 1 cm apart from each other. It was cleverly designed passive design. Air could travel inside. (Wikipedia). This is the one of the great example when people started thinking of climatic response. Design the space, which will cleverly work, rather than designing it for decoration. In terms of spatial planning, Paxton provided refreshments spaces for people during the exhibition. There are spaces with open courts and trees. There was no necessity of making solid enclosures, so the structure does not lose the lightness. The trees of the north entrance were also for refreshment purpose. Spaces were enclosed by sash-glazed partitions almost similar as exterior glass panels. Rooms of the building was designed that can get more natural lighting and ventilation. Partitions that separate the rooms give the building very light effect. (The Crystal palace, p.36) In 1936 on 30th November Crystal Palace was set on fire. In one hour the building was destroyed. North Transept was burned. Government not insured to cover the rebuilding. Because the cost was around 2 million pounds. That time Welby Pugin founder of Gothic Architecture called this building â€Å"Glass Monster†. He told Paxton â€Å" You had better keep to building green houses, and I will keep mu churches and cathedrals†. Many other architects started criticizes Crystal Palace. Many books and articles was written after the demolition. Thomas Carlyle called it â€Å"Big glass soup buble†. But in these letter days Crystal Palace benn called â€Å"Proto Modern Architecture† and became a precedent for many buildings such as commercial buildings in Europe and America. Crystal Palace became a symbol of industrial revolution, strength and economic- industrial power of England that time. (Manpret Singh, â€Å"The demolition Of Crystal Palace 1926-1941†. ww w.digital.lib.umb.edu.com ) Conclusion The main idea of this essay was to show the effectiveness of industrialized methods of construction of Crystal Palace in opposition to Gothic revival style and Art Noveau, which represents traditional architecture. The main points are: The main difference is that Crystal Palace represents new modes of design, where buildings do not have to be so heavy. The purpose is economical use of space. For example: slender columns allow having big indoor space compare to masonry columns. Using of different types of machines. Building can be completed in short period of time. Low cost and availability of cast iron. Smart designed structure in response to climatic aspects. As was already mentioned above, Paxton’s gutter system, which collects the rain water in specific reservoir. Drain water is usable in case of fire or for agriculture. Less using of artificial lighting, because of glass material. Passive ventilation design. Louvered wall system and flooring system, where the block’s spacing is 1 cm., which allows the space, breathe. The Crystal Palace was the great example of new style of architecture. It was a step forward from the traditional architecture. The structural system of Crystal Palace we can still use in our time. It was a precedent for future buildings. Already experienced cast iron and glass. After the demolition, people know how to avoid those problems. Test it and make it work better, but the main concept is based on Crystal Palace skeletal system. Therefore nowadays we have improved skeletal structures. My opinion is that this type of architecture is more useful, compare to traditional. In terms of spaces, how could it be better and lighter by using the different types of materials? But at the same time it can carry the similar load. It was the time when people started thinking of different design, shapes and form. When people started thinking of low cost structures and experiencing of different materials except brick and stone. When people started thinking of opportunities engaging with surrounding and climate aspects of those kinds of structures. Which is did not exist for traditional type of architecture. Gothic and arts and crafts buildings are more concentrating to show the importance of it. Even the decorations, which are not useful. There might be disadvantages of Industrial Revolution, but the main advantage is step for the future with industrial mind.

Philosophy of Teaching Essay -- Teachers Education Essays

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