The Fundamentals of Dissertation Service Revealed

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Conservation of Marine Biodiversity within the Framework...

Conservation of Marine Biodiversity within the Framework of Impure Public Goods Since the early days when Adam Smith coined the term â€Å"invisible hand of the market† in his magnum opus, The Wealth of Nations, it was typically believed among the general population that all goods can be distributed without any interference from the government. Contrary to the popular belief, however, this applies specifically to private goods, i.e. a type of good that is both rivalrous and excludable. It may seem that marine biodiversity is a type of public good, since they are in the vast ocean and everyone is entitled to their ownership. However, many marine biodiversity have tremendous economic values, and one person using it may constitute as another†¦show more content†¦Impure public goods also create asymmetric externality, which its â€Å"economic agents who generate this externality are distinct from those who experience them.† (Squires, Environmental Externalities and Market Failure, 26) In the case of marine biodiversity such as dolphins, one ca n see that it is affected by technological externalities because people do not buy dolphins, hence dolphins do not have a market price tag to them; however, they are extremely useful in catching tuna, therefore people use them to catch tuna, and in the process, dolphins can get caught in the net and drown. In this example, the external effect is not through market price, but through the number of dolphins caught in the net and drown. There are three types of technology of public good supplies: additive, best-shot and weakest-link. First, ‘additive’ public goods are the ones that â€Å"the socially available amount of a public good is nothing but the ‘simple sum’ of the separate amounts produced by each of the participating countries.† (Arriagada and Perrings, 799) In the case of ‘best-shot’ public goods, â€Å"the benefit to all countries is determined by the most effective provider.† (Arriagada and Perrings, 799) Last but not least, ‘weakest-link’ public goods are ones that that â€Å"benefits to all countries are limited to the benefits offered by the least effective provider.† (Arriagada and Perrings, 799) In the case of marine biodiversity

Principles of Business free essay sample

ROLE OF THE ENTREPRENEUR An entrepreneur is a person who launches, or help launches a new venture or enterprise and accept full responsibility for a company’s output. M. J. S. Boutique has three (3) entrepreneurs. Each entrepreneur has to identify what resources will be needed to establish and run the business. Each entrepreneur has to create an initial outline study to determine whether the concept looks like a practical idea. Each entrepreneur has to acquire the necessary funds for the business. Each entrepreneur has a specific part to play in M. J. S. Boutique though. Two (2) of the entrepreneurs design the clothes and choose colour schemes while the third entrepreneur handles all the finances of the business. GOVERNMENT REGULATIONS The entrepreneurs will have to register the company. Registration will take place at Registrar General, Ministry of Legal Affairs. Registration is important in order to gain legal access to operate and transfer any transaction in and out. 11. Establish guidelines for the conduct of good management and staff relations in the workplace; Guidelines for establishing good relations between managers and employees. 12. Evaluate the role of teamwork in the success of an organization; The value of teamwork within an organization: (a) definition; (b) advantages; (c) disadvantages. 13. Outline strategies for effective communication within an organization; The communication process and strategies for effective communication within an organization. 14. Explain the concept of a Management Information System (MIS); The concept of MIS in an organization (to manage information for decision-making for example, manual and automated). 15. Outline the benefits and challenges of a Management Information System in business; (a) Benefits of an MIS system, for example: (i) savings in time, money and labour; (ii) improvement in production; (iii) increased competitiveness. (b) Challenges of an MIS system, for example: (i) cost of setting up and maintaining (establishment, maintenance and security); (ii) cost of training (human resource development) (iii) Human error. 16. Discuss the personal needs that are satisfied through employment. Economic, social, psychological and physiological needs. CXC CSEC Principles of Business Exam Guide Profile 1: Organizational Principles Section 1: The Nature of Business SPECIFIC OBJECTIVES The students should be able to: CONTENT 1. Explain terms and concepts related to business; Definition and explanation of the following terms and concepts: (a) enterprise (b) entrepreneurship (c) barter (d) profit (e) loss (f) trade (g) organization (h) economy (i) producer (j) consumer (k) exchange (l) goods (m) services (n) market (o) commodity (p) capital (q) labour (r) specialization 2. Trace the development of instruments of exchange; Brief history of trading instruments from subsistence economy to money economy, including the use of the following: (a) bills of exchange (b) credit cards (c) electronic transfer (d) tele-banking and e-commerce 3. State reasons why an individual may want to establish a business; Reasons for establishing a business 4. Describe the various forms of business organizations and arrangements; Forms of business organizations and arrangements: definition, formation and management of: (a) sole trader (b) partnerships (c) co-operatives (d) companies (including conglomerates and multi-nationals) (e) franchises (f) state corporations and nationalized industries (g) local and municipal authorities (h)government departments (j) concept of private and public sectors 5. Differentiate among the different economic systems; Types of economic systems: (a) traditional (subsistence) (b) command or planned (socialist) (c) free or capitalist (d) mixed (public and private) 6. Identify the stakeholders involved in business activities; Owners, employees, customers and all other members of society 7. Discuss the role of the stakeholders involved in business activities; Role of employers, employees, consumers and government. 8. Outline the functions of a business; Functions of a business in satisfying needs and wants through the provision of goods and services. 9. Describe the role of business within a community. Economic, financial, social, political and ethical CXC CSEC Principles of Business Exam Guide Profile 1: Organizational Principles Section 3: Establishing a Business SPECIFIC OBJECTIVES The students should be able to: CONTENT 1. Define the term entrepreneur; The concept of entrepreneurship 2. Explain the role of an entrepreneur; The role of the entrepreneur in conceptualizing, planning, accessing funds, organizing, operating and evaluating the performance of a business. Attention should be paid to the bearing of risks and the entitlement to the profits and losses of the business. 3. Identify the characteristics of the the typical entrepreneur; Personal traits and leadership qualities: (a) creative (b) innovative (c) flexible (d) goal-oriented (e) persistent (f) persevering (g) propensity to take calculated risks 4. Outline reasons why persons may want to establish their own business; Reasons for wanting to start a business: (a) desire for financial independence (b) self-fulfillment (c) self-actualization 5. Outline the essential steps that should be taken in establishing a business; Steps for establishing a business: (a) conceptualization (b) research (market probe) (c) identification of resources (d) creation of a business plan (e) acquisition of funds (f) operation of the business 6. Describe the role of key functional areas in the operation of diferent types of business. Role of the production, marketing and finance, legal, Research and Development (R and D) departments in a business. 7. Identify sources of information for conducting research into the establishment of a business; Primary and secondary sources of information for conducting research. 8. Explain the relationship between planning and the operation of a business; The necessity for short-term, medium-term and long-term planning in a business. 9. Identify regulatory practices instituted by governments for the establishment of different types of businesses; Local regional and global rules for conducting business, including local government (municipal, village council, parish council regulations) 10. Outline the advantages and disadvantages of different types of business organizations; Opportunities and challenges encountered by different types of organizations. 11. Identify sources of captial for the setting up of a business; Sources of capital including venture capital. 12. Explain the significance of collateral in accessing capital to establish a business; Collateral: (a) concept; (b) evaluation of different types; (c) the value of collateral. 13. Outline the features of a business plan; Analysis of all the elements of a business plan, including the executive summary and the operational, marketing and financial plans. 14. Explain the purposes of a feasibility study; The purpose of a feasibility study. 15. Identify ethical and legal issues in the establishment and operation of a business; Ethical and legal issues, for example advertising, taxation and environmental issues. 16. Explain the consequences of ethical and illegal practices in business. Consequences of unethical and illegal practices in business: (a) misleading advertisements- unfair and fraudulent practice on the population (b) withholding of tax cheating the government of revenue (c) unethical disposal of waste- pollution (d) money laundering distortions in the national economy CXC CSEC Principles of Business Exam Guide Profile 1: Organizational Principles Section 4: Legal Aspects of Business SPECIFIC OBJECTIVES The students should be able to: CONTENT 1. Explain the concept of contract; Definition and concept of a contract. 2. Describe the characteristics of a simple contract; Offer and acceptance, competence of parties, intention to create legal relations, consideration. 3. Differentiate between a simple contract and a specialty contract; special contracts including mortages, sale of land and insurance 4. Determine the validity of various contracts; Use of case studies to determine the validity of contracts. 5. Distinguish between offer and invitation to treat or bargain; Concepts of offer and invitation to treat. 6. Explain the conditions under which offer and acceptance are communicated; Concepts of offer and acceptance. 7. Outline ways by which contracts may be terminated or discharged; Definitions of discharge, types of discharge methods of discharge. 8. Explain why documentation is necessary in business transactions; The importance of record-keeping in a business, including its value in satisfying requirements for taxation and auditing 9. Prepare business documents for various purposes; preparation of various business documents including pro forma invoices, purchase requisitions, statements of accounts and stock cards. 10. Interpret information on transport documents; Transport documents including import license, bill of lading, and airway bills. 11. Identify instruments of payment; Instruments of payment including cheque, money order, bank draft, debit card, credit card and telegraphic money transfer. 12. Interpret information on various instruments of payment; Interpretation and significance of information on instruments of payment. 13. Explain the use of documentary credit; The concept of documentary credit, 14. Distinguish between insurance and assurance; The concepts of insurance and assurance. . 15. Evaluate the principles upon which insurance is based; The concept of pooling of risks. 16. Explain the various types of insurance policies; Types of insurance policies: life and business insurance. 17. Explain how insurance facilitates trade. The value of insurance coverage in lowering the risks associated with business CXC CSEC Principles of Business Exam Guide Profile 2: Production, Marketing and Finance Section 5: Production SPECIFIC OBJECTIVES The students should be able to: CONTENT 1. Identify factors in the production of goods and services; Factors of production: Land, Labour, Capital, Enterprise. 2. Identify industries developed from the natural resources of Caribbean territories; Caribbean industries developed from agricultural produce and mining. 3. Differentiate between production and productivity; The effects of efficiency in the production of goods and services. 4. Explain the importance of productivity Productivity as it relates to the efficiency of labour, including its value and importance; the factors affecting its supply; human resource development (including education, health, and working conditions). 5. Outline the effects of migration; Migration and its positive and negative effects on the labour force. 6. Describe the role of the entrepreneur in the decison making process; Importance of entrepreneurial organizational skills. 7. Explain the role of capital in production; Fixed working and venture capital. 8. Differentiate among the various production levels; Production levels: subsistence, domestic consumption, surplus and export. 9. Classify the different types of production; Types of production: (a) extractive; (agriculture, mining, fishing) (b) construction; (building) (c) manufacturing; (assembling, refining) (d) service; (transport, communication, tourism) 10. Describe the characteristics of cottage industry; Cottage industries: (a) home-based; (b) mainly manual; (c) small scale; (d) use of local raw materials; (e) use of family members as labour. 11. Outline the opportunities for and the benefits of developing linkage industries; Linkage industries: (a) backward; (b) forward; 12. Outline the factors that determine the location of a business; Factors affecting location: (a) geographical; (b) availability of raw materials and supplies; (c) infrastructure; (d) power; (e) water; (f) transport; (g) health facilities; (h) labour supply; (i) governmental regulation 13. Outline the functions of a small business; Functions of a small firm 14. Explain the effects of growth on a business; Growth of a business and effects on: (a) organizational structure; (b) capital; (c) labour; (d) scale of production. (economies of scale) (e) use of technology. (f) potential for export. 15. Describe the economic and social implications of technological development. Capital intensive versus labour intensive production in developing countries, mechanization and automation, e. g. computer-aided design (CAD) and computer aided instruction (CAI). CXC CSEC Principles of Business Exam Guide Profile 2: Production, Marketing and Finance Section 6: Marketing SPECIFIC OBJECTIVES The students should be able to: CONTENT 1. Distinguish between the terms market and marketing; Definition of market and marketing 2. Identify marketing activities; Marketing activities: (a) market research (b) pricing (c) packaging (d) branding (e) sales promotion (f) advertising (g) distribution 3. Describe the marketing mix; Marketing mix: (a) product (b) price (c) place (d) promotion 4. Explain the concept of market and market research; Market research: (a) concept; (b) definition; (c) types. 5. Outline the reasons for conducting market research; Reasons for conducting market research. Identification of: (a) consuumer taste; (b) competition; (e) consumer behaviour. 6. Describe the factors that influence consumer behaviour; Factors that influence consumer behaviour: (a) price; (b) price of substitutes (c) quality; (d) taste; (e) tradition; (f) income (affordability) (g) spending patterns; (h) brand loyalty 7. Identify main types of market structures; Market structures: (a) perfect competition; (b) monopoly; (c) monopolistic competition; (d) oligopoly. 8. Explain how price is determined; Pricing: determinants of price: (a) demand and supply; (b) concept of equilibrium price or market clearing price. 9. Identify forms of packaging and presentation of goods; Packaging: (a) presentation; (b) use of brand names. 10. Explain the concept of copyright; Concept of copyright: (a) producers or entrepreneurs: tose who maintain ownership and control over the product they have created and registered by obtaining a patent; (b) consumers: those who may purchase the product but cannot reproduce it for commerical purposes without permission of the producer. 11. Explain the term patent; Concept of patent including the concept of franchisee who is given a patent or official permission to reproduce the product. 12. Describe methods of promoting sales; Methods of promoting sales: (a) advertising: (i) functions and forms (ii) promotion including trading stamps and coupons; (iii) loss leaders. (b) public relations including business entertainment and the offering of special awards and sponsorship; (c) sales promotion; (d) personal selling. 13. Identify the techniques of selling; Selling: (a) salesmen and their approaches (b) merchandising and adjusting of pricing policy; (c) methods of maintaing good customer -firm relationships, for example, after sales services. 14. Explain the various terms of sales; Terms of sale: (a) cash; (b) credit; (c) hire purchase; (d) cash and trade discounts. 15. List the functions of consumer organizations; Functions of consumer organizations: (a) The rights and protection of consumers (private organizations and government); (b) The role of the Bureau of Standards; (c) role of the Ombudsman. 16. Identify the links in the chain of distribution; The distribution chain: (a) manufacturer; (b) wholesaler; (c) retailer; (d) consumer. 17. Identify methods of retailing; Methods of retailing: (a) shops; (b) department stores; (c) mail order; (d) e-commerce; (e) tele-marketing; (f) vending machines. 18. List the various forms of transport; Forms of transport: (a) land; (b) air; (c) sea. 19. Explain the importance of transport in marketing; Importance of transport in domestic regional and foreign trade. 20. Distinguish among the methods used for transporting specific goods; Methods of transporting specific goods: (a) oil and gas- pipelines and tankers; (b) timber rivers and barges; 21. Identify the problems likely to be encountered in distribution; (a) Relationship betwen the availability of airport, harbour and docking facilities and the efficient distribution of goods; (b) Problems of distribtion: delayed shipment, spoilage, misdirection of goods, inadequate wharehousing facilities, lack of proper security measures, industrial unrest, ineffective communication. 22. Outline measures to mitigate problems in distribution. Measures to mitigate problems of distribution. CXC CSEC Principles of Accounts Exam Guide Section 5: THE PREPARATION AND ANALYSIS OF FINANCIAL STATEMENTS OF THE SOLE-TRADER SPECIFIC OBJECTIVES The students should be able to: CONTENT 1. Explain the purpose of preparing financial statements; The purpose of preparing Financial Statements to satisfy the needs of user. 2. List methods of inventory (stock) valuation; Methods of inventory (stock) valuation: First in, First out (FIFO), Last in, First out (LIFO), Average Cost (AVCO) 3. Calculate the values of closing inventory (stock); Calculation of closing inventory (stock) using: FIFO, LIFO, AVCO. 4. Assess the effect of different method of inventory (stock) valuation on profit; The effect on profit of different methods of (inventory) stock valuation. 5. Prepare closing journal entries; (a) journal entries to close off accounts in the ledger (b) linkage with Trading and Profit and Loss accounts 6. Identify the components of the Financial Statements; Trading and profit and Loss Account and Balance Sheet. 7. Draw up the Trading and the Profit and Loss account to determine gross profit or loss and net profit or loss; Trading and Profit and Loss Account for sole-traders including: adjustments for return inwards and outwards; closing stock. 8. Show the effect of net profit or loss on capital; Treatment of net profit or loss on the Balance Sheet. 9. Use ratios to determine the performance (profitability) of the business; Trading results: simple ratios such as stock turn, average stock, gross profit percentage, net profit percentage. 10. Prepare classified balance sheet in vertical style; Definition of working capital, Calculation of working capital; Preparation of classified Balance Sheet showing working capital. 11. Explain the significance of the working capital for the operation of a business; Working capital as a basic tool for solvency; Working capital formula. 12. Calculate ratios to demonstrate the financial position of a business; Analysis and interpretation of the financial position of a business using ratio: current ratio; acid test ratio; return on investment. 13. Make recommendations about a business based on ratio analysis. Preparation of simple reports evaluating a business based on ratios and making recommendations. CXC CSEC Principles of Business Exam Guide Profile 3: The Business Environment Section 8: The Role of Government in an Economy SPECIFIC OBJECTIVES The students should be able to: CONTENT 1. Outline the responsibilities of government in an economy; Responsibilities of government in an economy: (a) security of the State; (b) protection and general welfare of citizens; (c) job security and severance benefits to workers; (d) protection of the environment (e) maintenance of a safe environment for investors 2. Identify ways by which business could protect the environment; Adherence by business to laws, including laws governing taxation, labour and the environment. 3. Describe measures used by governments to protect consumers; Consumer protection legislation, including regulations on price controls, food and drug standards, hire purchase legislation. 4. Identify ways by which government regulates business activity; For example, by divising laws related to zoning and the disposal of waste. 5. State the purposes of taxation; The role of taxes in raising revenue, income distribution,and control of spending. 6. Distinguish between direct and indirect taxes; Direct taxes and indirect taxes. 7. Distinguish between progressive, regressive and proportional taxation; Concepts of progressive, regressive and proportional taxation. 8. Outline forms of assistance offered by government to business; Forms of government assistance to business, including institutions for lending capital, training and technical assistance, research and information centres, subsidies and grants. 9. Evaluate the impact on the country with respect to social services provided by government. Impact of socal services provided by government: (a) healthcare a healthy population (b) National Insurance Scheme -provision and security for the elderly; (c) education an informed and literate population; (d) roads and transportation access to goods and services CXC CSEC Principles of Business Exam Guide Profile 3: The Business Environment Section 9: Social Accounting and Global Trade SPECIFIC OBJECTIVES The students should be able to: CONTENT 1. Outline the factors that determine a countrys standard of living; Indicators of a countrys standard of living (factors indicating a countrys wealth): (a) level of consumption of goods and services; (b) average disposable income of the population; (c) level of national ownership of capital equipment; (d) access to modern technology; (e) level of investment in research and technology. 2. Distinguish between a countrys standard of living and its quality of life; Indicators of a countrys quality of life (factors indicating the extent to which a population enjoys the benefits of its wealth): (a) extent of security enjoyed (level of crime); (b) availability of health, educational and recreational facilties; (c) diet and nutrition; (d) life expectancy; (e) rate of infant mortality; (f) access to public utilities, such as electricity and potable water. 3. Explain the concept of national income and its variants; The concept of national income and its variants; 4. Explain the approaches used to measure national income; Approaches to measure: (a) Gross Domestic Product (GDP); (b) Gross National Product (GNP); (c) National Income (NI); (d) Per Capita Iincome; (e) Advantages and disadvantages of different approaches used to measure national income. 5. Distinguish between economic growth and development; Concepts of economic growth, negative growth, growth witout development, the quatitative nature of growth and the qualitative nature of development. 6. Describe the role of education in economic growth and development; The role of human resource development in economic growth and development. 7. Outline the reasons for international trade; Reasons for internatonal trade. 8. Differentiate between balance of trade and balance of payments; Concepts of balance of trade and balance of payments. 9. Outline the measures which a country may adopt to address balance of payment problems. Measures to address balance of payment problems: (a) tariffs; (b) licenses; (c) quotas; (d) exchange control; (e) devaluation (f) borrowing from another country; (g) accepting gidts from other countries; (h) importing on credit; (i) drawing on the resources of the International Monetary Fund or other international financial institutions. CXC CSEC Principles of Business Exam Guide Profile 3: The Business Environment Section 10: Regional and Global Business Environment SPECIFIC OBJECTIVES The students should be able to: CONTENT 1. Explain the functions of major economic institutions and systems; Major economic institutions and systems: (a) Caribbean Community (CARICOM); (b) Caribbean Single Market Economy (CSME); (c) Caribbean Development Bank (CDB); (d) World Bank; (e) Inter-American Development Bank (IADB); (f) Organization of Eastern Caribbean States (OECS); (g) Organizatin of American States (OAS); (h) Economic Commission for Latin American Countries (ECLAC); (i) Association of Caribbean States (ACS); (j) European Union (EU) (k) World Trade Organization (WTO); (l) Caribbean Basin Initiative (CBI); (m) Organization of Petroleum Exporting Countries (OPEC); (n) Eastern Caribbean Common Market (ECCM); (o) North Amerian Free Trade Agreement (NAFTA) (p) Caribbean Canadian Agreement (CARIBCAN) (q) Free Trade Area of the Americas (FTAA) 2. Identify major economic problems in the Caribbean; Major economic problems in the Caribbean: unemployment; population density; migration debt burden; sourcing captial and raw materials; economic dualism in the region. 3. Outline possible solutions to economic problems in the Caribbean. Possible solutions to economic problems: (a) Access to foreign direct investment; (b) development of human resources; (c) development of the manufacturing sector

Pnl Explain free essay sample

Why? Because the YTM is defined as the rate which, if used to discount the bond’s cash flows, gives its price. We could picture it like this: Bond Cash Flows on a Time Scale Each fixed coupon of 10% is discounted back to today by the yield to maturity of 12%: 93. 93% = 10 + 10 + 10 + 110 (1. 12)1 (1. 12)2 (1. 12)3 (1. 12)4 All we are doing is observing the yield in the market and solving for the price. Alternatively, we could work out the yield if we have the price from the market. Bond price calculators work by iteratively solving for the yield to maturity. For a bond trading at par, the yield to maturity and coupon will be the same, e. g. a four year bond with a fixed coupon of 10% and a yield of 10% would be trading at 100%. Note that bond prices go down as yields go up and bond prices go up as yields go down. This inverse relationship between bond prices and yields is fairly intuitive. We will write a custom essay sample on Pnl Explain or any similar topic specifically for you Do Not WasteYour Time HIRE WRITER Only 13.90 / page For our par bond above, if four year market yields fall to 9% investors will be willing to pay more than par to buy the above market coupons of 10%. This will force its price up until it, too, yields 9%. If yields rise to, say, 11% investors will only be willing to pay less than par for the bond because its coupon is below the market. For a detailed example of the bond pricing process, see Appendix 3. For now, note that the dirty price of a bond is the sum of the present values of the cash flows in the bond. The price quoted in the market, the so-called â€Å"clean† price or market price, is in fact not the present value of anything. It is only an accountants’ convention. The market price, or clean price, is the present value less accrued interest according to the market convention. . Pamp;L sensitivities of a bond As we saw above, the price of a bond can be determined if we know its cash flows and the discount rate (i. e. YTM) at which to present value them. The yield curve from which are derived the discount factors for a bond can itself be considered as the sum of two curves: 1. the â€Å"underlying† yield curve (normally Libor), and 2. the â€Å"credit† curve i. e. the spread over the underlying curve The sensitivity of the bond price to a change in these two curves is called: i. PV01, and ii. CS01 respectively. In terms of the example above, the discount rate of 12% might be broken down into, say, a Libor rate of 7% together with a credit spread of 5%. (Note, in the following, it is important not to confuse the discount rate, which is an annualised yield, and the discount factor, which is the result of compounding the discount rate over the maturity in question. ) In addition to the sensitivities described above, we can also consider the impact on the price of the bond of a one day reduction in maturity. Such a reduction affects the price for two reasons: ) assuming the yield curve isn’t flat, the discount rates will alter because, in general, the discount rate for time â€Å"t† is not the same as that for time â€Å"t-1† b) since one day has elapsed, whatever the discount rate, we will compound it based on a time interval that is shorter by one day The names given to these two sensitivities are, respectively: iii. Theta, and iv. Carry Note that, of these four sensitivi ties, only the first two, i. e. PV01 and CS01, are â€Å"market sensitivities† in the sense that they correspond to sensitivities to changes in market parameters. Theta and Carry are independent of any change in the market and reflect different aspects of the sensitivity to the passage of time. i)PV01 Definition The PV01 of a bond is defined as the present value impact of a 1 basis point (0. 01%) increase (or â€Å"bump†) in the yield curve. In the derivation below, we will refer to a generic â€Å"discount curve†. As noted earlier, this discount curve, from which are derived the discount factors for the bond pricing calculation, can itself be considered as the sum of two curves: the â€Å"underlying† yield curve (normally Libor), and a credit curve (reflecting the risk over and above the interbank risk ncorporated in the Libor curve). The PV01 calculates the impact on the price of bumping the underlying yield curve. Calculation For simplicity, consider the case of a zero coupon bond i. e. where there is only one cash flow, equal to the face value, and occurring at maturity in n years. Note, though, that the principles of the following analysis will equally apply to a coupon paying bond. We start by defining: P = price or present value today R(t) = discount rate, today, for maturity t FV = face value of the bond Then, from the above, we know: P = FV/(1+r(t))^n Now consider the impact a 1bp bump to this curve. The discount rate becomes: R(t) = R(t) + 0. 0001 The new price of the bond, Pb(t), will be: Pb = FV/(1+[r(t)+. 0001])^n Therefore, the sensitivity of this bond to a 1bp increase to the discount curve will be: Pb – P = FV/(1+[r(t)+. 0001])^n FV/(1+r(t))^n Eqn. 1 The first term is always smaller than the second term, therefore: * if we hold the bond (long posn), the PV01 is negative * if we have short sold the bond (short posn), the PV01 is positive We can also see that: the higher the yield (discount rate), the smaller the PV01. This is because a move in the discount rate from, for example, 8. 00% to 8. 01% represents a smaller relative change than from 3. 00% to 3. 01%. In other words, the higher the yield, the less sensitive is the bond price to an absolute change in the yield * the longer the maturity, the bigger the PV01. This is more obvious the longer the maturity, the bigger the compounding factor that is applied to the changed discount rate, therefore the bigger the impact it will have. To extend this method to a coupon paying bond, we simply note that any bond can be considered as a series of individual cash flows. The PV01 of each cash flow is calculated as above, by bumping the underlying yield curve at the corresponding maturity. In practice, where a portfolio contains many bonds, it would not be practical, nor provide useful information, to have a PV01 for every single cash flow. Therefore the cash flows across all the positions are bucketed into different maturities. The PV01 is calculated on a bucketed basis i. e. by calculating the impact of a 1bp bump to the yield curve on each bucket individually. This is an approximation but enables the trader to manage his risk position by having a feel for his overall exposure at each of a series of maturities. Typical bucketing might be: o/n, 1wk, 1m, 2m, 3m, 6m, 9m, 1y, 2y, 3y, 5y, 10y, 15y, 20y, 30y. Worked example: Assume we hold $10m notional of a zero-coupon bond maturing in 7 years and the yield to maturity is 8%. Note that, for a zero coupon bond, the YTM is, by definition, the same as the discount rate to be applied to the (bullet) payment at maturity. We have: Price, P = $10m / (1. 08)^7 = $5. 834m Bumping the curve by 1bp, the â€Å"bumped price† becomes: Pb = $10m / (1. 0801)^7 = $5. 831m Therefore, the PV01 is: Pb – P = $5. 831m $5. 835m = -$0. 004m (or -$4k) Meaning In the example above, we have calculated the PV01 of the bond to be -$4k. This means that, if the underlying yield curve were to increase from its current level of 8% to 8. 01%, the position would reduce in value by $4k. If we assume the rate of change in value of the bond with respect to the yield is constant, then we can calculate the impact of, for example, a 5bp bump to the yield curve to be 5 x -$4k = -$20k. Note, this is only an approximation; if we were to graph the bond price against its yield, we wouldn’t see a straight line but a curve. This non-linear effect is called convexity. In practice, while for small changes in the yield the approximation is valid, for bigger changes, convexity cannot be ignored. For example, if the yield were to increase to 9%, the impact on the price would be -$365k, not -(8%-9%)x$4k = -$400k. Use The concept of PV01 is of vital day to day importance to the trader. In practice, he manages his trading portfolio by monitoring the bucketed yield curve exposure as expressed by PV01. Where he feels the PV01 is too large, he will perform a transaction designed to either flatten or reduce the risk. Similarly, when he has a view as to future yield curve movements, he will position his PV01 exposure to take advantage of them. In this case, he is taking a trading position. ii)CS01 The basis of the CS01 calculation is identical to that of the PV01, only this time we bump the credit spread rather than the underlying yield curve. The above example was based on a generic discount rate. In practice, for any bond other than a risk free one, this rate will be combination of the yield curve together with the credit curve. At first glance therefore, we would expect that, whether we bump the yield curve or the credit spread by 1bp, the impact on the price should be similar, and described by Eqn. 1 above. What we can also say is that, bumping the yield curve, the overall discount rate will increase and therefore, as for PV01: * if we hold the bond (long posn), the CS01 is negative * if we have short sold the bond (short posn), the CS01 is positive From the same considerations as for PV01, we can see that: * the higher the credit spread, the smaller the CS01 * the longer the maturity, the bigger the CS01 In practice, when we look at multiple cash flows, the impact of a 1bp bump in the yield curve is not identical to a 1bp bump in the credit spread. This is because, inter alia: * the curves are not the same shape and therefore interpolations will differ * bumping the credit spread affects default probability assumptions that will, in turn, impact the bond price In general though, PV01 and CS01 for a fixed coupon bond will be similar. The exception is where the bond pays a floating rate coupon. In this case, the sensitivity to yield curve changes is close to zero so, although the PV01 will be very small, the CS01 will be â€Å"normal†. Worked example: A worked example would follow the same steps as for PV01 above, only this time we would bump the credit spread by 1bp rather than the underlying yield curve. Theta and Carry We now look at the two sensitivities arising from the passage of time (â€Å"1 day decay†, to use option pricing terminology). First, let’s calculate what the total impact on the value of a position would be if the only change were that one day had passed. In particular, we assume that the yield and credit curves are unchanged. Again, for simplicity, consider the case of a zero coupon bond i. . where there is only one cash flow, equal to the face value, and occurring at maturity in n years. Again, we note that the principles of the following analysis will equally apply to a coupon paying bond. Following the previous notation, the value (or price) today will be: P(today) = FV/(1+r(t))^n The value tomorrow will be: P(tomorrow) = FV/(1+r(t-1))^(n-1/365)Eqn. 2 There are two differences b etween the formula for the value today and that for tomorrow. Firstly, the discount rate has moved from r(t) to r(t-1). Here, r(t-1) is the discount rate for maturity (t-1) today. We have assumed that the discount curve does not move day on day, therefore the rate at which the cash flow will be discounted tomorrow is the rate corresponding to a one day shorter maturity, today. Secondly, the period over which we discount the cash flows has reduced by one day, from n to n-1/365 (we divide by 365 because n is specified in years). Theta and Carry capture these two factors. P(tomorrow) – P(today) gives the full impact on the price due to the passing of one day. This impact can be approximated by breaking down the above formula into its two component parts i. e. he change in discount rate and the change in maturity, as explained below. iii)Theta As before, we define: P = price or present value today r(t) = discount rate, today, for maturity t FV = face value of the bond In addition, we define: r(t-1) = discount rate, today, for maturity t-1 (e. g. for a bond with 240 days to maturity, if the 240 day discount rate today is 8. 00% and the 239 day discount rate today is 7. 96% then: r(t) = 8. 00% and r(t-1) = 7. 96%) We now define Theta as: FV/(1+r(t-1))^n – FV/(1+r(t))^n We can see that, compared to the formula for the full price impact above (Eqn. ), this sensitivity reflects the change in the discount rate but ignores the reduction by 1 day of the maturity. In other words, Theta represents the price impact due purely to the change in discount rate resulting from a 1 day shorter maturity but ignores the impact on the compounding factor of the discount rate resulting from the shorter maturity. Note that the sign of Theta, in contrast to PV01 and CS01, can be both positive and negative. This is because r(t-1) can be higher or lower than r(t), depending on the shape of the yield curve. That said, in practice, given that yield curves are normally upward sloping, we would expect r(t) to be higher than r(t-1). Therefore Theta will normally be positive. In the same way, if the yield curve is flat, then Theta will be zero. iv)Carry Using the standard notation, we define Carry as: FV/(1+r(t))^(n-1) – FV/(1+r(t))^n Comparing to the formula for the full price impact above (Eqn. 2), we see that this sensitivity reflects the change in maturity on the compounding factor to be applied to the discount rate but ignores the impact on the discount rate itself of moving one day down the curve. In other words, Carry represents the price impact due purely to the change in discount factor resulting from a 1 day shorter compounding period but ignores the impact on the discount rate resulting from the shorter maturity. Where discount rates are positive (r(t) gt; 0), Carry will always be positive since the first term will be larger than the second. Using the Taylor expansion, we can obtain a simplified approximate value for Carry. Remembering that: 1/(1+x)^n = 1 – n. x + (1/2). n. (n-1). x^2 †¦ we have: Carry = FV. 1-(n-1/365). r(t)) – FV. (1-n. r(t)) = FV. r(t). 1/365 Note that r(t). 1/365 would represent one day’s â€Å"interest† calculated on an accruals basis since, in the case, the yield equals the coupon rate. (Note, where a position is accounted for on an accruals basis, and therefore valued at par, the yield will always equal the coupon. ) In other words, this definition ties in to the intuitive idea of carry that we have from, say, a de posit where the carry would be equal to one day’s interest, based on its coupon. We can also see that Carry is directly proportional to the yield. We have now seen that, between them, Theta and Carry attempt to capture the two components affecting the price move arising from the passing of 1 day, all other factors being kept constant. There will be certain â€Å"cross† effects of the two that will not be captured when performing this decomposition. In other words, Theta + Carry will not exactly equal the full impact (as per Eqn. 2). The difference, however, will not normally be material. In general, for a long bond position, both Theta and Carry will be positive as, with the passing of one day, not only will the annualised discount rate be less (reflecting the lower yield normally required for shorter dated instruments) but the compounding factor will be smaller (reflecting the shorter maturity). Worked example: Assume we hold $10m notional of a zero-coupon bond maturing in 240 days and the yield to maturity today is 8%. Also, the yield today for the 239 day maturity is 7. 96%. Theta = $10m/(1. 0796)^(240/365) $10m/(1. 08)^(240/365) = $23,159 Carry = $10m/(1. 8)^(239/365) $10m/(1. 08)^(240/365) $20,047 Theta + Carry = $43,205 To compare, the full price impact of a 1 day â€Å"decay† is: $10m/(1. 076)^(239/365) $10m/(1. 08)^(240/365) = $43,113 Summary We have now analysed the key sensitivities that explain the 1 day move in a bond’s mark to market value. To summarise some of the main features; for a long bond position: PV01 / CS01: * negative * for a fixed coupon or zero coupon bond, PV01 and CS01 will be similar * the higher the yield/credit spread, the smaller the PV01/CS01 * the longer the maturity, the bigger the PV01/CS01 for a floating rate coupon (with a Libor benchmark), PV01 will be very small but the CS01 will be â€Å"normal† Theta * positive * the flatter the curve, the smaller the Theta Carry * positive * proportional to the yield 3. Extension to interest rate swaps In essence, all the above applies equally to interest rate swaps (IRSs) when calculating/explaining daily Pamp;L. We start by noting that an IRS is simply the exchange of two cash flows, one fixed and one floating. Extending the analysis we made for bonds, we can say: a) The PV01 of the floating rate leg will be close to zero. This is as noted for a floating rate bond. In both cases, as the yield curve changes so do the expected future cash flows but, at the same time, so will the discount rates at which they are PV’d. The two effects will broadly cancel out. (The PV01 will not be exactly zero because, once the Libor fixing occurs, the next cash flow becomes fixed and therefore effectively becomes a zero coupon bond, on which there will be PV01. ) b) The fixed leg is similar to the fixed coupon stream on a bond and can be considered as a series of zero coupon bonds. Therefore the exact same analysis as applied to bonds above will apply to the fixed leg. An IRS that ays floating and receives fixed will have a PV01 sensitivity similar to that of a long bond position. c) IRSs are normally interbank trades where it is assumed that there is no credit risk over and above Libor. Therefore, the CS01 will be zero. d) Theta and Carry may be either positive or negative. Appendix 1 : Date Conventions There are several methods for computing the interest payable in a period and the accrued interest for a period. A particular method applied to a transaction can affect the yield of that transaction and also the payment for a transaction. Counting the Number of Days The conventions used to determine the interest payments depend on two factors: 1) The number of days in a period and 2) The number of days in a year. The conventions are: 0 Actual/360 1 Actual/365 : sometimes referred as Actual/365F (seldom used now) 2 Actual/Actual 3 30/360 European: sometimes referred to as ISMA method (30E/360) 4 30/360 US (30U/360) The first three methods (Actual/360, Actual/365 and Actual/Actual) calculate the number of days in a period by counting the actual number of days. For each method the number of days in a year is different. Actual/365 and Actual/Actual are similar except: 1. Periods which include February 29th (leap year) count the number of days in a year as 365 under Act/365 and 366 under Act/Act; 2. Semi-annual periods are assumed to have 182. 5 days under Act/365 and however many actual days under Act/Act. Eurobond markets use the 30E/360 basis. This calculation assumes every month has 30 days. This means that the 31st of a month is always counted as if it were the 30th of the month. For 30E/360 basis, February is also assumed to have 30 days. If the beginning or end of a period falls on a weekend the coupon is not adjusted to a good business day. This means that there are always exactly 360 days in a year for all coupons. For example a coupon from 08-November-1997 to 08-November-1998 of 5% is a coupon of 5%, even though 08-November-1998 is a Sunday. There is no adjustment to the actual coupon payment. The various European government bond markets are described below: Country| Accrual| Coupon Frequency| Austria| Act/Act| Annual| Belgium| Act/Act| Annual| Denmark| Act/Act| Annual| Finland| Act/Act| Annual| France| Act/Act| Annual| Germany| Act/Act| Annual| Ireland| Act/ActAct/Act (Earlier Issues)| AnnualSemi-Annual| Italy| Act/Act| Semi-Annual| Luxembourg| Act/Act| Annual| Netherlands| Act/Act| Annual| Norway| Act/Act| Annual or Semi-Annual| Portugal| Act/Act| Annual| Spain| Act/Act| Annual| Sweden| Act/Act| Annual| Switzerland| Act/Act| Annual| United Kingdom| Act/Act | Semi-Annual| Appendix 2 : Calculating Accrued Interest Even though Eurobond coupons are not adjusted for weekends and holidays, the accrual of a coupon for any part of the year has to use the correct number of days. The difference between European and US 30/360 method is how the end of the month is treated. For US basis the 31st of a month is treated as the 1st of the next month, unless the period is from 30th or 31st of the previous month. In this case the period is counted as number of months: | 30/360 European| 30/360 US| Beginning DateEnding Date| M1/D1/ Y1M2/D2/Y 2| M1/D1/Y1M2/D2/Y 2| If D1 = 31| D1 = 30| D1 = 30| If D2 = 31| D2 = 30| If D1 = 31 or 30Then: D2 = 30Else: D2 = 31| The difference occurs when the accrual period starts and ends at the end or beginning of a calendar month: European and US 30/360 Examples Start| End| European| US| Actual| 31-Jul-01| 31-Oct-01| 90| 90| 92| 30-Jul-01| 30-Oct-01| 90| 90| 92| 30-Jul-01| 01-Nov-01| 91| 91| 94| 29-Jul-01| 31-Oct-01| 91| 92| 94| 01-Aug-01| 31-Oct-01| 89| 90| 91| Euro money markets: 0 Day count basis: actual/360 1 Settlement basis: spot (two day) standard 2 Fixing period for derivatives contracts: two day rate fixing convention Euro FX markets 3 Settlement timing: spot convention, with interest accrual beginning on the second day after the deal has been struck 4 Quotation: ‘Certain for uncertain’ (ie 1 Euro = x foreign currency units) U. S. Conventions Product| Day Count Convention| USD LIBOR| Act/360| USD Swap Fixed Rate in U. S. | Act/Act s. a. | USD Swap Fixed Rate in London| Act/360 p. a. | T-Bills| Act/360 discount rate| Government Bonds| Act/Act s. a. | Agency and Corporate Bonds| 30/360 s. a. | Appendix 3 : Detailed worked example of bond price calculation We can check the pricing of bonds in a more complicated example by using the following German government bond (or Bund) : German Government Bund (in Euros) Coupon:| 5. 00%| Maturity:| 04-Feb-06| Price (Clean):| 102. 2651%| Yield:| 4. 43%| We are pricing this bond on 27/July 2001. It matures on 4 Feb 2006 and has a coupon of 5%. The table below shows that the bond price (the ‘dirty price’ or invoice price) is simply the sum of the present value of all of the coupons discounted at the yield to maturity. Pricing the German Euro Denominated Bund Dates| AA Days| Periods| Cash Flow| Cashflow PV| 04-Feb-01| | | | | 27-Jul-01| | | | 104. 6350%| 04-Feb-02| 192| 0. 5260| 5. 00%| 4. 8873%| 04-Feb-03| 557| 1. 5260| 5. 00%| 4. 6800%| 04-Feb-04| 922| 2. 5260| 5. 00%| 4. 4814%| 04-Feb-05| 1288| 3. 5260| 5. 00%| 4. 2913%| 04-Feb-06| 1653| 4. 5260| 105. 00%| 86. 2950%| The market convention uses the yield to maturity as the discount rate, and discounts each cash flow back over the number of periods as calculated using the accrued interest day-count convention. In the case of Bunds, the day-count convention is the Act/Act convention. Appendix 1 contains more details of date conventions it is recommended that you read this at the end of the module. The part of a year between the settlement date (27 July 2001) and the next coupon (4 February 2002) is: Day Count 192/365 (ie Actual days/Actual days) = 0. 5260 The price of the first coupon can therefore be calculated in the following way: PV of First Coupon = 4. 8873% All of the other cash flow present values are calculated in the same manner. Adding them up gives us the price of the bond. Accrued interest is calculated from 04 February 2001 to 27 July 2001 (173 days) : Accrued Interest Accrued = 5% x 0. 47397 = 2. 3699% There is more detail on Accrued interest in Appendix 2. It is recommended that you read it at the end of this module. Notice that the quoted price of the bond (the ‘clean price’) is 102. 2651% not 104. 6350% (which is the ‘dirty price’ or invoice price ie the price actually paid for the bond). The dirty price is the sum of the present values of the cash flows in the bond. The price quoted in the market, the so-called â€Å"clean† price or market price, is in fact not the present value of anything. It is only an accountants’ convention. The market price, or clean price, is the present value less accrued interest according to the market convention. Practitioners find it easier to quote the clean price because it abstracts from the changing daily accrued interest (i. e. it avoids a â€Å"saw-toothed† price profile). This publication is for internal use only by Deutsche Bank Global Markets employees. The material (including formulae and spreadsheets) is provided for education purposes only and should under no circumstances be used for client pricing. Examples, case studies, exercises and solutions may use simplifying assumptions that do not apply in practice, and may differ from Deutsche Bank proprietary models actually used. The publication is provided to you solely for information purposes and is not intended as an offer or solicitation for the purchase or sale of any financial instrument or product. The information contained herein has been obtained from sources believed to be reliable, but is not necessarily complete and its accuracy cannot be guaranteed.