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金融英语笔记期末总结Introduction:Financial English is a specialized subset of English language skills that are used in the finance industry. It encompasses a wide range of topics and skills, including financial vocabulary, reading financial statements, conducting financial analysis, and communicating effectively with clients and colleagues. As the finance industry continues to grow and become increasingly globalized, proficiency in financial English is becoming more important for professionals in this field. This summary highlights the key topics and skills covered throughout the course.Financial Vocabulary:One of the first and most important areas covered in the course was financial vocabulary. This included learning the definitions and usage of various financial terms and phrases. Essential financial vocabulary covered included terms related to financial statements, such as balance sheet, income statement, and cash flow statement. Other important terms included asset, liability, equity, revenue, cost, profit, and loss. It is crucial for professionals in the finance industry to have a solid understanding of these terms in order to effectively communicate and analyze financial information.Financial Statements:Reading and understanding financial statements is a fundamental skill in finance. The course provided a comprehensive overview of the three main financial statements: the balance sheet, the income statement, and the cash flow statement. We learned how to analyze these statements to gather information about a company's financial health and performance. Students were also taught how to calculate ratios and metrics to assess the company's liquidity, profitability, and solvency. By the end of the course, students were able to analyze financial statements and make informed decisions based on the information presented.Financial Analysis:Financial analysis is a crucial skill for professionals in the finance industry. Throughout the course, we learned various methods and techniques for analyzing financial data. This included trend analysis, ratio analysis, and comparative analysis. We also discussed the importance of benchmarking and how it can be used to compare a company's financial performance to its competitors or industry standards. Through practical exercises and case studies, students developed their skills in financial analysis and gained confidence in interpreting financial data.Investment and Portfolio Management:Another important aspect covered in the course was investment and portfolio management. We learned how to evaluate different investment options and develop investment strategies based on an individual's financial goals and risk tolerance. The course discussed various asset classes such as stocks, bonds, and mutual funds, and explored the different risks associated with each. Students were also introduced to the concept of portfolio diversification and learned how to construct and manage a diversified investment portfolio. This part of the course provided valuable insights into the world of investing and enabled students to make informed investment decisions.Financial Communication:Effective communication is essential in the finance industry, and the course emphasized the importance of clear and professional communication skills. We learned how to write financial reports, memos, and emails in a concise and professional manner. The course also covered presentation skills, and we practiced delivering presentations on various financial topics. These skills are crucial for professionals in the finance industry who often need to convey complex financial information to clients, colleagues, and stakeholders.Conclusion:Overall, the financial English course provided a comprehensive overview of essential skills and knowledge required in the finance industry. From developing financial vocabulary to analyzing financial statements and communicating effectively, students gained valuable insights into the world of finance. The course equipped students with the necessary skills to analyze financial data, make informed investment decisions, and communicate financial information effectively. As the finance industry continues to thrive and develop, proficiency in financial English is becoming increasingly important for professionals in this field.。
proof of sufficient financial provisionsProof of Sufficient Financial ProvisionsIn today's globalized and interconnected world, the importance of proving sufficient financial provisions cannot be overstated. Whether it is a visa application, college enrollment, or even an employment opportunity, individuals are often required to provide evidence of their financial stability. This article aims to provide a comprehensive guide on how to present a compelling proof of sufficient financial provisions, ensuring a smooth and successful outcome.Step 1: Understand the RequirementsThe first step in presenting a robust proof of sufficient financial provisions is to thoroughly understand the requirements of the institution or organization requesting the documentation. Each entity may have its specific guidelines and expectations, which must be met to ensure compliance. Review any provided documentation or consult with the respective authority to gain a clear understanding of the necessary information and supporting documents.Step 2: Gather Relevant Financial StatementsOnce familiar with the requirements, it is essential to gather all relevant financial statements and paperwork. Thesemay include bank statements, tax returns, salary slips, investment statements, property deeds or rental agreements, declarations of assets, and any other relevant financial documents. Collecting a comprehensive range of financial statements will help demonstrate consistent financial stability and abundance.Step 3: Analyze Cash Flow and AssetsAfter gathering the necessary financial statements, it is crucial to analyze and understand the individual's overall cash flow and assets. This step involves evaluating income sources, regular expenses, debts, and liabilities. A detailed analysis will allow individuals to present a comprehensive picture of their financial situation, demonstrating not only stable income but also prudent financial management.Step 4: Demonstrate Available FundsOne of the key elements in proving sufficient financial provisions is to showcase available funds that can cover expenses under consideration. Whether it is tuition fees, living costs, or investments, it is vital to demonstrate that there are ample funds readily available. This can be shown through bank statements with a consistent balance, investment portfolios, or any other evidence of financial reserves such as fixed depositsor savings. It is essential to ensure that these funds meet or exceed the required financial thresholds.Step 5: Show Steady Income and EmploymentIn addition to available funds, demonstrating a steady income and employment is critical in proving financial stability. This can be accomplished through payslips or employment contracts, highlighting a consistent income stream. Forself-employed individuals, providing documentation of business ownership, income statements, and client contracts can demonstrate a predictable source of income. Stable employment or business income not only reassures the requesting party but also showcases the ability to continue supporting oneself financially in the long run.Step 6: Consider Additional Financial SupportIn some cases, individuals may not possess sufficient personal financial resources to meet the requirements. In such situations, it is essential to consider additional financial support from family members, sponsors, or scholarships that may be available. Including letters of support or sponsorship agreements from the respective individuals or organizations can strengthen the proof of sufficient financial provisions.Step 7: Seek Professional Assistance, if NecessaryWhile the aforementioned steps provide a comprehensive approach to proving sufficient financial provisions, it is worth noting that complex cases or unfamiliar requirements may benefit from professional assistance. Financial advisors or immigration lawyers can offer expertise and guidance throughout the process, ensuring compliance and increasing the chances of a favorable outcome.In conclusion, presenting a robust proof of sufficient financial provisions requires thorough preparation and an organized approach. By understanding the requirements, gathering relevant financial statements, analyzing cash flow and assets, demonstrating available funds, showcasing steady income and employment, considering additional financial support, and seeking professional assistance when necessary, individuals can effectively prove their financial stability and enhance their chances of success in various applications and opportunities. Remember, a well-prepared proof of sufficient financial provisions not only instills confidence in the requesting party but also reflects an individual's soundfinancial standing.。
The understanding of the financial managementThis team I learnt the Financial Management, which is a n important subject and a basic tool of management. The Financial Management is the management of how to deal with Capital Budgeting, Capital Structure and the Working Capital in certain principles as a whole, and financial management is an integral part of the enterprise management, according to the financial legal system, and the principle of financial management, it organizes the enterprise financial activities, deal with financial relationship of an economic management.The goals of Financial ManagementThe enterprise is an organization, which is built for pursuing profit, and its starting point and destination is profit, so Financial Management first should consider the company’s profit, and there are some basic goal s related with the profit.The first goal is to maximize the profit. Its basic point is that profit represented the enterprise’s new wealth, more profit then explaining the wealth of enterprises increases, and the more approximates to corporate goal. But this kind of goal has its drawbacks that it does not consider profit obtained the time value factors, it would be difficult to make right decision with the same amount of money in differen t time point. What’ more it does not consider the relationship between the profit and its invested capital, and finally it doesn’t consider the relationship between the profit and the risk it will take. While, the second goal is to maximize the current value per share of the existing stock. It means that the company's profit should related closely with the shareholder capital, and uses earnings per share to generalize the enterprise financial management goal, thus to avoid defects in the "profit-maximising gaol". But this goal still doesn’t consider earnings per share are obtained the time value of factors, in addition, It still does not consider risks. There’s a third goal that is enterprise wealth (value) maximization, and it means add shareholder’s wealth is the financial management’s goal. But it’s hard to measure. And the final goal is make the stakeholders’ profit maximum. And it means not only considers the creditor, the shareholders and related party interests, but also consider enterprise employees, customers and social responsibility of the enterprise factors, and strive to make the interests of all parties to maximize.Financial Management decisionsSo, when we make some financial decisions we should care all about the parts of the financial goal. And what’s more, we should understand the basictypes of financial management decisions. There are three types of financial management decisions: Capital budgeting, Capital structure, and Working capital management.The first decision concerns the firm’s long-term investments. the process of planning and managing a firm’s long-term investments is called Capital budgeting. In capital budgeting, the manager tries to identify investment opportunities that are worth more to the firm than they cost to acquire, this means that the value of the cash flow generated by an asset exceeds the cost of asset. The types of investment opportunities that would typically be considered depend in part on the nature of the firm’s business. Regardless of the specific nature of an opportunity under consideration, financial managers must be concerned nor only with how much cash they expect to receive, but also with when they expect to receive it and how likely they are to receive it. Evaluating the size, timing, and risk of f uture cash flows is the essence of capital budgeting.While the second decision called Capital Structure refers to the specific mixture of long-term debt and equity the firm uses to finance its operations. There are two main questions when looking at the capital structure - 1) How much $ do we need to borrow to buy this long-term asset? 2) What are the least expensive sources of funds for the firm? For example, since we are thinking of buying this new crusher, we need to decide how we are going to afford this new machine. In this example, we determined that if we cut back a little bit on labor and in other areas, we would be able to afford the new machine. In regards to where the money will come from, we do not take out loans to buy long-term assets. We borrow from our company, and repay overtime.The third decision concerns working capital management. The term working capital refers to a firm’s short-term assets, such as inventory, and its short-term liabilities, such as money owed to suppliers. Managing th e firm’s working capital is a day-to-day activity that ensures that the firm has sufficient resources to continue its operations and avoid costly interruptions. This involves a number of activities related to the firm’s receipt and disbursement of cash.The core element in financial managementThe three areas of corporate financial management are very broad and we should deal these decisions well to make profit for the company. And we should also care about the core element in finance management__ cash flow. Cash flow is the movement of cash into or out of a business, project, or financial product. It is usually measured during a specified, finite period of time. Measurement of cash flow can be used for calculating other parameters that give information on the companies' value and situation. Cash flow is very important because it determines a project's rate of return or value. The time of cash flows into and out of projects are used as inputs in financial models such as internal rate of return, and net prese nt value. What’s more it determines problems with a business's liquidity. Being profitable does not necessarily mean being liquid. A company can fail because of a shortage of cash, evenwhile profitable. As an alternate measure of a business's profits when it is believed that accrual accounting concepts do not represent economic realities. For example, a company may be notionally profitable but generating little operational cash (as may be the case for a company that barters its products rather than selling for cash). In such a case, the company may be deriving additional operating cash by issuing shares, or raising additional debt finance. The impressions of the Financial ManagementFirstly, financial management is a comprehensive management work. The development of social economy requires financial management making use of business activities value form implementation management. Control all the material conditions to achieve enterprise efficiency enhances unceasingly, wealth increasing purpose. Therefore, financial management is an independent enterprise management, and is a kind of comprehensive management work.Secondly, Financial management haves a large connection with various aspects in the Enterprise. In the enterprise, the capital of all involved with payment activities related to financial management. In fact, it is very rare that the departments in the internal enterprise do not deal with money. Therefore, financial management, often reaches each corners of the enterprise management. Each department would have relationship with the financial department through using the money. Each department will also in the proper use of the money, and economize on expenditure by accepting the financial department guidance, and subject to the control of the financial system to ensure that improve the economic benefits of the enterprises.Finally, financial management can reflect the production and the operation condition of the enterprise quickly. In enterprise management, the financial index can reflect rapidly about whether or not the decision is proper, the business is reasonable, production technology is advanced or not. For example, if the production of enterprise is marketable and the good quality reliable, it can drive the production development and realize the production and marketing of two flourishing, thus the capital turnover will be accelerated, and the profit ability will be strengthened, so all these can be reflected by financial index quickly.In the end, the financial management is very important, and it is not only a science, but also an art, only we grasp the knowledge of this subject can we have the ability to manage the company well.下面红色为工作计划模板，不需要的下载后可以编辑删除！谢谢工作计划一、近期今年是在新的工作岗位工作的年，是熟悉工作，履职，方法，积累经验的一年，年中“转变，”，即转变工作角色，工作职责。
财经英语试题及答案一、选择题（每题2分，共20分）1. Which of the following is not a financial instrument?A. StockB. BondC. CommodityD. Insurance policyAnswer: D2. In financial markets, what is the term for the difference between the buying and selling prices of a security?A. SpreadB. DividendC. YieldD. Interest rateAnswer: A3. What is the term used to describe the risk of a security's value changing due to market fluctuations?A. Credit riskB. Market riskC. Liquidity riskD. Operational riskAnswer: B4. Which of the following is not a type of financial statement?A. Balance sheetB. Income statementC. Cash flow statementD. Profit and loss statementAnswer: D5. What is the term for the process of evaluating an investment based on various factors to determine its potential return and risk?A. Due diligenceB. Portfolio managementC. Financial analysisD. Risk assessmentAnswer: C6. What does GDP stand for in economics?A. Gross Domestic ProductB. Gross Domestic ProfitC. Gross Domestic PerformanceD. Gross Domestic PriceAnswer: A7. In the context of finance, what does the acronym "IPO" stand for?A. Initial Public OfferingB. International Profit OrganizationC. International Portfolio OrganizationD. International Product OfferingAnswer: A8. What is the term for a financial contract that gives the buyer the right, but not the obligation, to buy or sell anunderlying asset at a specified price on or before a certain date?A. Call optionB. Put optionC. Forward contractD. Futures contractAnswer: A9. Which of the following is not a component of the financial system?A. BanksB. Securities exchangesC. Insurance companiesD. Manufacturing companiesAnswer: D10. What is the term used to describe the process of determining a company's value based on its financial performance and potential for future growth?A. ValuationB. ForecastingC. BudgetingD. AuditingAnswer: A二、填空题（每题2分，共20分）1. The process of converting cash into other assets is known as ____________.Answer: investing2. A __________ is a financial institution that acceptsdeposits, offers loans, and provides other financial services. Answer: bank3. The __________ is a document that outlines the terms and conditions of a loan, including the interest rate and repayment schedule.Answer: loan agreement4. __________ is the risk that a borrower may default ontheir loan payments.Answer: credit risk5. A __________ is a financial statement that shows acompany's financial position at a specific point in time. Answer: balance sheet6. __________ is the process of evaluating a company'sfinancial health by analyzing its financial statements. Answer: financial analysis7. The __________ is a financial statement that shows a company's revenues, expenses, and net income over a specific period.Answer: income statement8. __________ is the risk that a security's value maydecrease due to a decline in the overall market.Answer: market risk9. A __________ is a financial instrument that represents an ownership interest in a company.Answer: stock10. __________ is the risk that a security may be difficult to sell at a desired price.Answer: liquidity risk三、简答题（每题10分，共20分）1. Explain the difference between a stock and a bond. Answer: A stock represents ownership in a company and typically offers the potential for capital appreciation and dividends. A bond, on the other hand, is a debt instrument issued by a company or government, promising to pay periodic interest and return the principal at maturity.2. What are the main factors that influence a company'scredit rating?Answer: The main factors that influence a company's credit rating include its financial stability, debt levels, profitability, management quality, industry position, and economic conditions. Credit rating agencies assess these factors to determine the likelihood of the company meetingits financial obligations.四、论述题（每题15分，共30分）1. Discuss the importance of diversification in an investment portfolio.Answer: Diversification is crucial in an investment portfolio as it helps to spread risk across a variety of investments, reducing the impact of a poor-performing asset on the overall portfolio. By investing in different asset classes, sectors, and geographical regions, investors can potentially achievebetter returns and lower volatility. Diversification also allows for the exploitation of different market opportunities and can protect against unforeseen events that may affect specific investments.2. Explain the role of financial statements in business decision-making.Answer: Financial statements play a vital role in business decision。
财务进阶笔记Financial advancement is a goal that many individuals aspire to achieve in their careers. It represents an opportunity for growth, stability, and security in an ever-changing economic landscape. To successfully advance in the field of finance, one must possess a combination of knowledge, skills, and experience.财务进阶是许多人职业生涯中渴望实现的目标，它代表着在不断变化的经济环境中发展、稳定和安全的机会。
为了在财务领域成功进阶，一个人必须具备知识、技能和经验的结合。
One crucial aspect of advancing in finance is continuous learning and skill development. This includes staying updated on industry trends, regulations, and best practices. By actively seeking out opportunities for professional development, individuals can enhance their expertise and stay competitive in the field.财务进阶的一个关键方面是持续学习和技能发展。
这包括及时了解行业趋势、法规和最佳实践。
通过积极寻找专业发展机会，个人可以提升自己的专业知识，并在该领域保持竞争力。
Networking is another essential component of advancing in finance. Building relationships with colleagues, mentors, and industry professionals can provide valuable insights, opportunities for collaboration, and career advancement. By actively engaging in networking events, conferences, and online communities, individuals can expand their professional connections and support system.人际网络是财务进阶的另一个重要组成部分。
Financial Institutions Management Seventh Edition 课后练习题含答案Chapter 1Multiple Choice Questions1.Which of the following is not one of the primary economicfunctions of financial institutions?a.Channeling funds between savers and investorsb.Creating and selling financial instrumentsc.Managing riskd.Providing investment adviceAnswer: d2.Which of the following is not a significant trend in thefinancial services industry?a.Disintermediationb.Deregulationc.Globalizationd.Increased government interventionAnswer: d3.Which of the following is not one of the three broadcategories of financial institutions?a.Depository institutionsb.Contractual savings institutionsc.Investment intermediariesd.Insurance companiesAnswer: dShort Answer Questions1.What is financial intermediation?Financial intermediation is the process of channeling funds between savers and investors. Financial intermediaries take in funds from savers and lend or invest those funds to borrowers or investors.2.What is disintermediation?Disintermediation is the process of savers investing directly in financial markets rather than through financialintermediaries. It typically occurs when interest rates are high, making alternative investments such as certificates of deposit more attractive.3.What is globalization?Globalization is the process of increased interconnectedness and interdependence among individuals, companies, and countries around the world. In the financial services industry,globalization has led to increased competition, new markets, and new financial products.Chapter 2Multiple Choice Questions1.Which of the following is not a typical function of acommercial bank?a.Accepting depositsb.Making loansc.Issuing corporate bondsd.Providing checking accountsAnswer: c2.Which of the following is not a typical function of a thriftinstitution?a.Making mortgage loansb.Accepting depositsc.Providing checking accountsd.Issuing bondsAnswer: d3.Which of the following is not a characteristic of a creditunion?a.Owned by its membersb.Insured by the FDICc.Provides savings and checking accountsd.Specializes in consumer loansAnswer: bShort Answer Questions1.What is a commercial bank?A commercial bank is a financial institution that acceptsdeposits, makes loans, provides checking accounts, and offers other financial services to customers. Commercial banks aretypically chartered by the state or federal government and are regulated by banking authorities.2.What is a savings and loan association?A savings and loan association, also known as a thriftinstitution, is a type of financial institution that specializes in making mortgage loans. These institutions also accept deposits and typically offer savings and checking accounts.3.What is a credit union?A credit union is a member-owned financial cooperative thatprovides financial services to its members. Credit unions are typically organized around a specific group or community, such as employees of a particular company or residents of a particular city or town.。
一、英汉单词、词组互译（1.5X20=30）Financial Institutions 金融机构securities 有价证券Portfolio 投资组合financial assets 金融资产credit union 信用合作社pension funds 养老基金mutual funds 互助基金Universal credit card 万能信用卡annual fee 年度费用capital market 资本市场short-term securities 短期证券monetary policy 货币政策New York Stock Exchange 纽约证券交易所Federal Reserve（Bank）联邦储蓄银行commercial paper 商业票据equity market 股票市场Mortgage Markets 抵押品市场real property 不动产letter of credit 信用证draft 汇票sight draft 即期汇票time draft 远期汇票acceptance 承兑document of title 物权凭证policyholder 投保人insurance premium 保险费insurance policy 保险单investment return 投资回报junk bond 垃圾债券National Debt 国债Bonds and Shares 债券和股票maturity （票据的）期限inflation 通货膨胀interest return 利息收入yield rate 收益率二、选词填空（2X10=20）1、Now I’m clear about how the bank deals with the saver’s deposited money.2、Our company acquired that piece of land by purchase.3、Theory is based on practice and in turn serves practice.4、Adam Smith’s concept of ”invisible hand” can be applied to modern economy.5、The primary function of money is to facilitate exchange.6、U.S Treasury bills are central to money market transactions.7、Money and banks play dominant roles in our economic life.8、In the money market, the purpose of a dealer is distinct from that of a broker.9、Many finance companies in our country specialize in consumer finance, particularly in small loans.10、The sales contract specifies container shipment for the goods.11、Those goods have to be inspected prior to shipment.12、The economist sets out his ideas clearly in his article that the central bank should carry out a loose monetary policy,13、A letter of credit always indicates the exact documents which the beneficiary must submit.14、Insurance claims statistics reveal that drivers under 30 are involved in far more accidents than are older drivers.15、The marine insurance is associated with the risks such as fire, storm, collision, pilferage, leakage and explosions, etc.16、Many health insurance policies list the dollar value for specific medical procedures.三、英汉句子互译（4X10=40）1、Lower-then-expected returns on one issue may be offset by higher-then-expected returns on another,一项低于预期的证券收益可以通过另一项高于预期收益的证券发行来抵消。
CHAPTER 13THE CAPITAL ASSET PRICING MODELObjectives•Explain the theory behind the CAPM.•Explain how to use the CAPM to establish benchmarks for measuring the performance of investment portfolios. •Explain how to infer from the CAPM the correct risk-adjusted discount rate to use in discounted-cash-flow valuation models.•Explain the APT and its relationship to the CAPM.Outline13.1 The Capital Asset Pricing Model in Brief13.2 Determinants of the Risk Premium on the Market Portfolio13.3 Beta and Risk Premiums on Individual Securities13.4 Using the CAPM in Portfolio Selection13.5 Valuation and Regulating Rates of Return13.6 Extensions, Modifications, and Alternatives to the CAPMSummary•The CAPM has three main implications:•In equilibrium, ev eryone’s relative holding of risky assets are the same as in the market portfolio.•The size of the risk-premium of the market portfolio is determined by the risk-aversion of investors.•The risk premium on any asset is equal to its beta times the risk premium on the market portfolio. •Whether or not the CAPM is strictly true, it provides a rationale for a very simple passive portfolio strategy: •Diversify your holdings of risky assets in the proportions of the market portfolio, and•Mix this portfolio with the risk-free asset to achieve a desired risk-reward combination.•The CAPM is used in portfolio management primarily in two ways:•To establish a logical and convenient starting point in asset allocation and security selection•To establish a benchmark for evaluating portfolio management ability on a risk-adjusted basis.•In corporate finance the CAPM is used to determine the appropriate risk-adjusted discount rate in valuation models of the firm and in capital budgeting decisions. The CAPM is also used to establish a “fair” rate of return on invested capital for regulated firms and in cost-plus pricing.•Today few financial scholars consider the CAPM in its simplest form to be an accurate model for explaining or predicting risk premiums on risky assets. However, modified versions of the model are still a central feature of the theory and practice of finance.•The APT gives a rationale for the expected return-beta relationship that relies on the condition that there be no arbitrage profit opportunities; the CAPM requires that investors be portfolio optimizers. The APT and CAPM are not incompatible; rather, they complement each other.Solutions to Problems at End of ChapterComposition of the Market Portfolio1. Capital markets in Flatland exhibit trade in four securities, the stocks X, Y and Z, and a risklessgovernment security. Evaluated at current prices in US dollars, the total market values of these assets are, respectively, $24 billion, $36 billion, $24 billion and $16 billion.a. Determine the relative proportions of each asset in the market portfolio.b. If one trader with a $100,000 portfolio holds $40,000 in the riskless security, $15,000 in X, $12,000 in Y, and$33,000 in Z, determine the holdings of the three risky assets of a second trader who invests $20, 000 of a $200, 000 portfolio in the riskless security.SOLUTION:The total value of all assets in the economy is 100 billion dollars. a. The proportions of each asset relative to the value of all assets are, respectively, .24 (X), .36 (Y),b. .24 (Z) and .16 (riskless bond.) The proportions of each risky asset to the total value of all risky assets are,respectively, (2/7) (X), (3/7) (Y) and (2/7) (Z). c. . Ignore the question as it appears in the First Edition of the textbook. Instead, the question should be: If aninvestor has $100,000 with $30,000 invested in the riskless asset, how much is invested in securities X, Y, and Z? The answer to this question is $20,000 in X and Z, and $30,000 in Y.Implications of CAPM2. The riskless rate of interest is .06 per year, and the expected rate of return on the market portfolio is .15 per year.a. According to the CAPM , what is the efficient way for an investor to achieve an expected rate of returnof .10 per year?b. If the standard deviation of the rate of return on the market portfolio is .20, what is the standarddeviation on the above portfolio?c. Draw the CML and locate the foregoing portfolio on the same graph.d. Draw the SML and locate the foregoing portfolio on the same graph.e. Estimate the value of a stock with an expected dividend per share of $5 this coming year, an expecteddividend growth rate of 4% per year forever, and a beta of .8. If its market price is less than the value you have estimated, i.e., if it is under-priced, what is true of its mean rate of return?SOLUTION: a.So one would hold a portfolio that is 4/9 invested in the market portfolio and 5/9 in the riskless asset. b.c. The formula for the CML is9415.)1(06.10.)()1()(=+-=⨯+-⨯=x xx x r E x r r E M f 08889.)20(.94==⨯=M x σσσσσ45.06.)()(+=-+=MfM f r r E r r Ed. The formula for the SML ise. Use constant growth rate DDM and find r using the SML relationIf the market price of the stock is less than this, then its expected return is higher than the 13.2% required rate.()ββ09.06.)()(+=-+=f M f r r E r r E 35.54$04.132.504.510=-=-=-=r g r D P 132.8.09.06.09.06.=⨯+=+=βr3. If the CAPM is valid, which of the following situations is possible? Explain. Consider each situation independently.a.PortfolioExpected ReturnBeta A 0.20 1.4B 0.25 1.2b.PortfolioExpected ReturnStandard DeviationA 0.300.35B 0.400.25c.Portfolio Expected ReturnStandard DeviationRisk-free 0.100Market 0.180.24A 0.160.12d.Portfolio Expected ReturnStandard DeviationRisk-free 0.100Market 0.180.24A0.200.22SOLUTION:a. Impossible. Since the risk premium on the market portfolio is positive, a security with a higher beta must have ahigher expected return.b. Possible. Since portfolios A & B are not necessarily efficient, A can have a higher standard deviation and alower expected return than B.c. Impossible. Portfolio A lies above the CML, implying that the CML is not efficient. If the standard deviation ofA is .12, then according to the CML its expected return cannot be greater than .14.d. Impossible. Portfolio A has a lower standard deviation and a higher mean return than the market portfolio,implying that the market portfolio is not efficient.4. If the Treasury bill rate is currently 4% and the expected return to the market portfolio over the same period is 12%, determine the risk premium on the market. If the standard deviation of the return on the market is .20, what is the equation of the Capital Market Line?SOLUTION: The risk premium on the market portfolio is .08. The slope of the CML is .08/.2 = .4. Thus, the equation of theCML is:Determinants of the Market Risk Premium5. Consider an economy in which the expected return on the market portfolio over a particular period is .25, the standard deviation of the return to the market portfolio over this same period is .25, and the averagedegree of risk aversion among traders is 3. If the government wishes to issue risk-free zero-coupon bonds with a term to maturity of one period and a face value per bond of $100,000, how much can the government expect to receive per bond?[]σσσ4.04.)()(+=++=MfMf r rE r r ESOLUTION:According to the CAPM, E(r M) - r f = Aσ2, so that r f = E(r M) - Aσ2.Substituting into this formula we find: r f = .25 – 3 x .252 = .0625Therefore the revenue raised by the government per bond issued is $100,000 = $94,117.651.06256. . Norma Swanson has invested 40% of her wealth in MGM stock and 60% in Industrial Light and Magic stock. Norma believes the returns to these stocks have a correlation of .06 and that their respective means and standard deviations are:MGM ILMExpected Return (%) 10 15Standard Deviation (%) 15 25a.Determine the expected value and standard deviation of the return on Norma’s portfolio.b.Would a risk-averse investor such as Norma prefer a portfolio composed entirely of only MGM stock? Ofonly ILM stock? Why or why not?SOLUTION:a.The expected return is .13, and the standard deviation is .1649.b. A risk averse investor will not want to hold a portfolio composed entirely of MGM or of ILM stock, becauseone can, in general, achieve the same expected return with a lower standard deviation by combining a portfolio of MGM and ILM with the risk-free asset.7. Consider a portfolio exhibiting an expected return of 20% in an economy in which the riskless interest rate is 8%, the expected return to the market portfolio is thirteen percent, and the standard deviation of the return to the market portfolio is .25. Assuming this portfolio is efficient, determine:a.its beta.b.the standard deviation of its return.c.its correlation with the market return.SOLUTION:e the security market line to infer that the beta of this portfolio is 2.4:.20 = .08 + β(.13 - .08)β = (.20 - .08)/(.13 - .08) = .12/.05 = 2.4e the capital market line to infer that the standard deviation of the yield to this portfolio is .6:.20 = .08+ (.13 - .08) σ = .08+ .2 σ.25σ = .12/.2 = .6c.By definition the following relationships hold:β = cov/σ2Mρ = covσiσMwhere ρ denotes the correlation coefficient. We know that β = 2.4, σM = .25, and σi = .6.So from the definition of β, we get that the cov is 2.4 x .252 = .15. Substituting this into the definition of ρ: ρ = cov = .15 __ = 1σiσM .6 x .25Application of CAPM to Corporate Finance8. . The Suzuki Motor Company is contemplating issuing stock to finance investment in producing a new sports-utility vehicle, the Seppuku. Financial analysts within Suzuki forecast that this investment will have precisely the same risk as the market portfolio, where the annual return to the market portfolio is expected to be 15% and the current risk-free interest rate is 5%. The analysts further believe that the expected return to the Seppuku project will be 20% annually. Derive the maximal beta value that would induce Suzuki to issue the stock.SOLUTION:The project would be on the borderline if its required return were 20% per year. Since the risk-free rate is 5% and the risk premium on the market portfolio is 10%, the required return would be 20% if the beta were 1.5.9. . Roobel and Associates, a firm of financial analysts specializing in Russian financial markets, forecasts that the stock of the Yablonsky Toy Company will be worth 1,000 roubles per share one year from today. If the riskless interest rate on Russian government securities is 10% and the expected return to the market portfolio is 18% determine how much you would pay for a share of Yablonsky stock today if:a.the beta of Yablonsky is 3.b.the beta of Yablonsky is 0.5.SOLUTION:Use the security market line in each case to determine a required rate of return, then infer the current price from the forecasted price of 1,000 roubles and the required rate of return you have determined.a.If beta is 3, the required return is .10+ 3x.08 = .34. You would pay 1,000/1.34 = 746.27 roubles;b.If beta is .5, the required return is .10+ .5x.08 = .14. You would pay 1,000/1.14 = 877.19 roubles.Application of CAPM to Portfolio Management10. Suppose that the stock of the new cologne manufacturer, Eau de Rodman, Inc., has been forecast to havea return with standard deviation .30 and a correlation with the market portfolio of .9. If the standard deviation of the yield on the market is .20, determine the relative holdings of the market portfolio and Eau de Rodman stock to form a portfolio with a beta of 1.8.SOLUTION: By definition:β = cov/σ2Mρ = covσrσMTherefore, β = ρσr/σM. The beta of Rodman stock is therefore .9x.3/.2 = 1.35.The beta of a portfolio is a weighted average of the betas of the component securities. Let A be a fraction of the portfolio invested in Rodman stock to produce a beta of 1.8. Then we have:1.35A + (1-A) = 1.8.35A = .8A = 2.286So the portfolio would have to have 228.6% invested in Rodman stock and a short position in the market portfolio equal to 128.6%.11. The current price of a share of stock in the Vo Giap Clothing Company of Vietnam is 50 dong and its expected yield over the year is 14%. The market risk premium in Vietnam is 8% and the riskless interest rate 6%. What would happen to the stock’s current price if its expected future payout remains co nstant while the covariance of its rate of return with the market portfolio falls by 50%?SOLUTION:Deduce that the expected future price of a share of Vo Giap is 57 dong, so that a reduction in this stock’s beta of 50% implies, by the security market relation, that the required yield on Vo Giap is now 10%, so that its current share price rises by 3.64% to a new value of 51.82 dong.12. Suppose that you believe that the price of a share of IBM stock a year from today will be equal to the sumof the price of a share of General Motors stock plus the price of a share of Exxon, and further you believethat the price of a share of IBM stock in one year will be $100 whereas the price of a share of General Motors today is $30. If the annualized yield on 91-day T-bills (the riskless rate you use) is 5%, the expected yield on the market is 15%, the variance of the market portfolio is 1, and the beta of IBM is 2, what price would you be willing to pay for one share of Exxon stock today?SOLUTION:Expected return = .05 + 2(.15 - .05) = 25%; (100 - x)/x = .25 → x = $80Deduce that the current price of a share of IBM stock is $80, so that the upper bound on the price of a share of Exxon is ($80 - $30 = $50).13. Ascertain whether the following quotation is true or false, and state why:“When arbitrage is absent from financial markets, and investors are each concerned with only the risk and return to their portfolios, then each investor can eliminate all the riskiness of his investments through diversification, and as a consequence the expected yield on each available asset will depend only on the covariance of its yield with the covariance of the yield on the diversified portfolio of risky assets each investor holds.”SOLUTION:False. You cannot eliminate all risk through diversification, only the unsystematic risk.Application of CAPM to Measuring Portfolio Performance14. During the most recent 5-year period, the Pizzaro mutual fund earned an average annualized rate of return of 12% and had an annualized standard deviation of 30%. The average risk-free rate was 5% per year. The average rate of return in the market index over that same period was 10% per year and the standard deviation was 20%. How well did Pizzaro perform on a risk-adjusted basis?SOLUTION:Compute the ratio of average excess return to standard deviation for Pizzaro and compare it to that of the market portfolio:Pizzaro risk-adjusted performance ratio = (.12-.05)/.30 = .233Market portfolio risk-adjusted performance ratio = (.1-.05)/.2 = .250So, on a risk-adjusted basis, Pizzaro did worse than the market index.Challenge ProblemCAPM with only 2 Risky Assets15. There are only two risky assets in the economy: stocks and real estate and their relative supplies are 50% stocks and 50% real estate. Thus, the market portfolio will be half stocks and half real estate. The standard deviations are .20 for stocks, .20 for real estate, and the correlation between them is 0. The coefficient of relative risk aversion of the average market participant (A) is 3. r f is .08 per year.a.According to the CAPM what must be the equilibrium risk premium on the market portfolio, on stocks,and on real estate?b.Draw the Capital Market Line. What is its slope? Where is the point representing stocks located relativeto the CML?c.Draw the SML. What is its formula? Where is the point representing stocks located relative to the SML? SOLUTION:a.The market portfolio consists of half stocks and half real estate. It has a standard deviation of .1414, computedas follows:σ2M = w2σ2s + (1-w)2σ2r+ 2 w(1-w) cov s,rσ2M = 2 x (1/2)2 .22 = .02σM = .1414The equilibrium risk premium on the market portfolio is E(r M)-r f = Aσ2M = 3x.02 = .06.The market portfolio’s expected rate of return is also a weighted average of the expected rates of return on stocks and real estate, where the weights are each 1/2. Stocks and real estate must have the same risk premiumbecause they have the same standard deviation and correlation with the market. Therefore the risk premium on stocks and real estate must be .06, the same as the market portfolio’s risk premium.b.The slope of the CML is .06/.1414 = .424. The point representing stocks is M, it is to the right of the CML.equaling to 1.The formula is: E(r) = r f + (E(r M) –r f).。
The CAPM In Thin Experimental Financial MarketsPeter Bossaerts‡and Charles Plott§This version:28July2000‡California Institute of Technology and CEPR§California Institute of Technology1The CAPM In Thin Experimental Financial MarketsPeter Bossaerts and Charles PlottAbstract:We report on small-scale experiments of simple,repeated asset markets in two risky securities and one risk-free security.As in large-scale experiments,steady convergence towards the CAPM is discovered,but the process is slower and convergence halts before reaching the actual equilibrium.There is evidence that subjects gradually move up in mean-variance space,in accordance with the CAPM.Yet,adjustment stops,presumably because of subjects’hesitance in the face of market thinness.This hesitance can be optimal because of the multidimensional nature of the desired trades.Because of market thinness,subjects have difficulty implementing bundles of trades in a set of parallel markets based on the MUDA trading mechanism,essentially an electronic version of the Chicago futures markets. JEL Classification:G12,C92,D59.Keywords:Capital Asset Pricing Model(CAPM),Experimental Economics,Financial Markets,Equilibrium,Equili-bration.2The CAPM In Thin Experimental Financial Markets¶Peter Bossaerts and Charles Plott1IntroductionThis paper studies the extent to which the Capital Asset Pricing Model(CAPM)of Sharpe(1964)and Lintner(1965) explains pricing and trading in simple,thin experimentalfinancial markets.The CAPM predicts that equilibrium prices will be set such that expected returns in excess of the riskfree rate will be proportional to the covariance with aggregate risk.Aggregate risk is measured by the return on the market portfolio.The CAPM also predicts that investors will attempt to trade up to a mean-variance efficient portfolio.Since in equilibrium the market portfolio is the only mean-variance efficient portfolio that is entirely invested in risky securities,investors will eventually all hold the market portfolio(plus riskfree securities).The focus on the CAPM is motivated by two considerations.First,the CAPM is the prototype of modern asset pricing theory.Its main pricing prediction,that equilibrium expected returns will be proportional to covariance with aggregate risk,is shared with virtually all other asset pricing models that have been taken to the data(e.g.,Merton (1973),Lucas(1978),Breeden(1979)).The meaning of aggregate risk differs across models.In the CAPM,it is the return on the market portfolio.In Lucas’and Breeden’s models,it is aggregate consumption.CAPM’s main allocational prediction,that investors should hold the same portfolio of risky securities,is recovered or extended in these other models.In the CAPM,this portfolio is the market portfolio;in Merton’s model,hedge portfolios are added to the market portfolio.That is,the models all predict the portfolio separation property where investors’holdings can ¶Thefinancial support of the National Science Foundation and the California Institute of Technology Laboratory for Experimental Research in Economics and Political Science is gratefully acknowledged.Address:m/c228-77,California Institute of Technology,Pasadena, CA91125;Phone(626)395-4067;e-mail:pbs@ and cplott@.3be reduced to the same set of basic portfolios.Ross(1978)provides further analysis on portfolio separation.Second,in an experimental setting risk is fairly limited,so that mean-variance approximations to subjects’actual preferences may be sufficiently reliable.Of course,this is ultimately an empirical issue.Under mean-variance prefer-ences,the CAPM holds in equilibrium.Whence our focus on the CAPM.See also Judd and Guu(2000)for theoretical evidence that the CAPM obtains when risk is small.In large-scale(20to60subjects)experimentalfinancial markets,the CAPM explains many facets of pricing and trading.See Bossaerts and Plott(1999),Bossaerts,Plott and Zame(2000).Prices generally fully equilibrate to the CAPM,and,while individual holdings are quite noisy,transaction-by-transaction price changes are clearly driven by a mean-variance optimal aggregate demand.It is not obvious that thesefindings translate to thin markets.In large-scale markets,competitive pressures must reduce the relevance of strategic behavior.When only10-15subjects are present, strategic considerations may keep markets from moving to their full competitive equilibrium.Our experiments are meant to shed light on this.1Wefind that prices do move towards the CAPM,but very slowly.Also,unlike in the large-scale experiments,the convergence process halts before the actual equilibrium is reached.Still,there is evidence that subjects gradually move up in mean-variance space,in accordance with the CAPM.Yet,adjustment stops as if subjects perceive too little time to fully complete their trades.Subjects’hesitance could be rational given market thinness.This is because subjects generally have to trade combinations of securities in order to improve their positions,yet in thin markets, it is difficult to implement combined trades.Partial execution of portfolio rebalancing can lead to inferior positions.Whence the hesitance.1We should mention Levy[1997],who also reported favorable results from a small-scale CAPM experiment.His argument in support of the CAPM is based on his observation that the average return/beta relationship is positive,and that volatility does not provide incremental explanatory power of the cross-section of average returns.We are more demanding,by testing the full prediction of the CAPM,that the average return/beta relationship is proportional,and not only linear.The proportionality is equivalent to the prediction that the reward-to-risk ratio(Sharpe ratio)of the market portfolio be the highest possible.It is the latter that we verify in the experimental data.4The remainder of this paper is organized as follows.The next section describes the experimental design.Section3 summarizes the predictions that the CAPM makes about the likely experimental outcomes.Section4presents the experimental evidence.Section5concludes.2Experimental DesignThe main features of the experiments are summarized in Table1.A total of seven experiments were conducted.They are indexed by the date of the experiment.Subjects were recruited from the Caltech student community.Many were familiar with basic investment theory,including mean-variance analysis and the CAPM,through an investment class on campus.About one-third of the subjects were graduate students from the natural sciences.The remainder of the subjects was undergraduates,mostly in their junior and senior years.Subjects in the later experiments(5/19and6/9) were drawn exclusively from those who participated earlier and were thus experienced with the experimental setting, markets,etc.The number of subjects varied from a low of5(4/30experiment)to a high of13(5/13experiment). With onlyfive subjects,there was insufficient trade in the riskfree security to make reliable inference,as documented below.While the details of the experiments are outlined in the paragraphs that follow,a brief summary of the setting might be useful.Each experiment consisted of multiple replications(periods)of the same set of conditions.Three securities were created,denoted A,B and C.They had a life of one period,at the end of which they paid a single dividend/payoffand after which they were removed from the system.The magnitude of the dividends depended upon a random draw of one of three possible states,X,Y and Z.The state was drawn after the period was closed,so during trading there was no insider or asymmetric information in the markets.The magnitude of dividends for each of the securities and each state are in Table1.As can be seen there,the dividend of A varies dramatically with the state, the dividend of B varies much less,and the dividend of C does not vary at all with the state.5All trading took place in an experimental currency called francs,which had a known conversion rate into U.S. dollars(shown in Table1for each experiment).2Each period traders were endowed with units of A and B(shown in Table1)and no units of security C.In addition each trader was endowed with afixed number of francs.It was not possible for holdings of francs,security A or security B to go negative(no short sales)but it was possible for holdings of C to go negative(up to a limit).Thus,an individual could use francs to buy A and B but the ability to do so was limited by the endowment of francs.If the individual wanted to increase holdings of A and B beyond the implicit holdings of francs it could be done by selling units of C and paying the dividend,which was the same for all states. Thus,a sale of C is like borrowing.The amount of the(known)dividend will be paid by the person who sold the unit of C to the person who bought the unit.Of course,to the buyer the difference between the price paid and the certain dividend is a risk free return since payment is guaranteed by the experimenter.The price of C was determined in the market so the risk-free rate was determined simultaneously with other rates of return.Table1contains the relevant parameters for each experiment.At the beginning of each period,all subjects were endowed with400francs and a number of securities A and/or B.Each experiment consisted of three markets and the dividends were identical and public.These are shown in Table1.The three securities had the same expected value. As can be seen,security A had a higher variance than security B.Security C had no variance at all.The dividends were the same in all experiments,apart from experiment6/9,when the parameters were changed.Except in the6/9 experiment,subjects were always endowed with four units of security A and security B and no units of security C(but they could go short in security C).The probability of the states was1/3in all experiments.The parameters for experiment6/9differed from the other experiments in two ways.First,the endowments differed.Three groups were formed.Each subject in Group I was given8units of security A;each subject in Group II 2In the4/30experiment,a new member of the experimental team changed the exchange rate ex post,from0.02to0.005dollar per franc.A high number of occurrences of state X led him to believe that the(five)subjects would have been paid too generously under the original exchange rate.At the beginning of subsequent experiments,it was explicitly announced that such ex-post changes in the terms of payment would not be made.6was endowed with8units of security B;and the(single)subject in Group III was endowed with the market portfolio (4of A and4of B).Groups I and II had an equal number of subjects.This way,the market portfolio consisted of an equal number of securities A and B,as in all other experiments.Second,the dividends were changed.While the skewness of the A security was positive in the other experiments,it was negative in6/9.The distribution of security B was left unchanged,as were the expected values.The changes were made in an attempt to increase the liquidity of the markets and to check the robustness of results from the previous experiments.Each period,earnings were determined as(i)the total payoff(unit dividend times number of units,including the possibility of negative holdings of C)on the securities in inventory at the end of the period,plus(ii)the change in cash position of the period(i.e.,end-of-period cash holdings minus the beginning-of-period cash holdings of F400),minus (iii)a pre-determined payment for the endowments given at the beginning of the period,namely1500francs.At the end of the experiment,subjects calculated their earnings and were paid in cash.Any subject that lost money was required to work it off.3This requirement was especially necessary because of the ability of subjects to borrow(sell C).It was thus possible for a subject to borrow money,buy securities and then suffer losses due to unfortunate draws of the state.In order to prevent the possibility that such bankruptcies would destroy the integrity of the incentive system,the subjects signed an agreement to work offlosses.Subjects were informed that the experiments could last approximately three hours.Once assembled at the Cal-tech Laboratory for Experimental Economics and Political Science,instructions,were read to them.Markets were organized as a computerized,continuous double auction,employing the MUDA technology(Plott and Gray(1990)). The experiment started with a trial period in which subjects could familiarize themselves with the technology and procedures by buying and selling with no monetary payoffattached.When the actual experiment started the length of each period was pre-announced andfixed(8minutes in all experiments,except4/30,where it was6minutes). The number of periods in the entire experiment was not pre-announced but it was determined by the duration of the 3Subjects signed an agreement to cover any losses by working in the laboratory at the rate of seven dollars per hour.7experiment,from two to three hours.3CAPM’s Predictions About The Experimental ResultsModern asset pricing theory was developed with the aim of predicting the cross-sectional properties of returns in financial markets such as the ones described in the previous section.It derives necessary properties for returns using a particular logical argument in which equilibrium plays a prominent role.According to the theory,the nature of financial instruments,financial markets and investor preferences impose special conditions on market equilibrium. The essence can be summarized as follows.Investors demand portfolios that are optimal in a decision-theoretic sense. Prices,and,hence the distributional properties of returns,adjust until a given supply of securities and investors’demands are in equilibrium.Therefore,equilibrium prices and returns will reflect the origin of investors’demands, namely,the portfolio-theoretic optimality.This generally implies that average returns on individual securities will increase with covariation with aggregate risk.The CAPM illustrates this in a simple way.Investors demand portfolios that are optimal in the mean-variance sense, i.e.,they minimize variance for a given mean return.At the core of the derivation of the CAPM is the mathematical property that the set of mean-variance efficient portfolios is convex:any weighted average of optimal portfolios is optimal as well.This result facilitates the analysis of equilibrium,as follows.Investors demand mean-variance optimal portfolios.Since the combined(aggregate)demand is a convex linear combination of the individual demands,the aggregate demand is an optimal portfolio as well.In equilibrium,demand must meet supply.Consequently,the portfolio that is supplied to the market must be mean-variance optimal for equilibrium to hold.Thefixed total supply (sum of initial endowments)has become known as the market portfolio.Therefore,the CAPM essentially states that the market portfolio will be mean-variance efficient in equilibrium. Mathematically,mean-variance efficient portfolios are identified with the property that the expected returns(in excess8of the riskfree rate)will be proportional to the covariance with the return on the portfolio.Hence,in the CAPMequilibrium,mean excess returns are proportional to covariance with the return on the market portfolio.Empiricists have either focused directly on the mean-variance optimality of the market portfolio,or on the pro-portional relationship between average excess returns and covariances that mean-variance optimality implies.The former have essentially tested whether the reward-to-risk ratio of the market portfolio is the highest one can get in the marketplace.The reward-to-risk ratio must be the highest possible,otherwise the market portfolio would not be mean-variance optimal.The reward-to-risk ratio is commonly referred to as the Sharpe ratio.Let R F t denote the return on a risk-free security in period t(we will assume throughout that a risk-free asset exists);let R mt be the return on the market portfolio;letσmt denote its volatility(standard deviation).The Sharpe ratio of the market portfolio isdefined to beE[R mt−R F t].(1)σmtA test of the mean-variance optimality of the market portfolio,and,hence,the CAPM,can simply be based on verifying whether the difference between the actual maximum Sharpe ratio and the Sharpe ratio of the market is zero.So,provided markets converge to equilibrium,the main pricing prediction that the CAPM makes about pricing is the following.Prediction1The difference between the maximum possible Sharpe ratio and the Sharpe ratio of the market ratio should converge to zero.Security C was riskfree and in zero net supply.Its price was not set,but was to be determined by equilibrating demand and supply.Along with the riskfree security there was cash(used in trading),which earned nothing.Hence, the theoretical equilibrium riskfree rate is zero.Most often,however,we observed a positive interest rate.That in itself would lead one to reject equilibrium outright.However,it appeared that subjects felt cash constrained,and, hence,started to borrow money in order to execute their buy orders,without waiting for any sell orders to befilled.9(As a matter of fact,an understanding of this coordination effort is important to explain the experimental results.) After that,interest rates gradually declined.Far cleaner evidence for the cyclical effect of this“cash in advance”constraint on the interest rate could be found in the large-scale experiments,though.See Bossaerts and Plott(1999).As far as allocations is concerned,the CAPM predicts that investors should all trade up to mean-variance optimal portfolios.In equilibrium,the market portfolio will be the component of any mean-variance optimal portfolio that is only invested in risky securities.Away from equilibrium,investors may demand a different portfolio of risky securities. Since markets may spend quite a bit of time offequilibrium(asset pricing theory makes no prediction about how fast a market equilibrates),we do not take CAPM’s equilibrium prediction(that investors’holdings should be mean-variance optimal).Instead,we limit our prediction to“tendency toward mean-variance optimality:”Prediction2The trade-offbetween mean and variance of subjects’holdings(combinations of securities)should grad-ually improve.Further discussion of the CAPM and its relationship with experimentalfinancial markets can be found in Bossaerts, Kleiman and Plott(2000).Let us turn to the experimental results and determine whether these predictions match the data.3.1The Experimental Results3.2PricingIt is standard practice in the experimentalfinance literature to provide plots of the evolution of the prices of the different securities,in order to gauge evidence of convergence.Figure1provides an example.It depicts the evolution of the prices in the5/13experiment.As is typical in experimentalfinancial markets,one observes within-period convergence patterns.Across periods,however,there are clear trends(e.g.,the price of security B drifts upwards), despite the fact that the environment remained identical across periods.10In contrast with classical experiments with induced demand,however,the dynamics of transaction prices cannot be plotted against clearly defined price levels that equilibrium theory predicts.Indeed,the CAPM equilibrium does not translate into specific equilibrium price levels,absent knowledge of subjects’preferences.That is,we cannot easily interpret the evidence from plots such as Figure1.Therefore,we should focus on a metric that unequivocally characterize the CAPM equilibrium,namely,the difference between the maximum Sharpe ratio and the Sharpe ratio of the market portfolio.However,experiments have made clear in the past that price discovery is a very apparent and distinct phenomenon.One must not expect initial prices to be such that the Sharpe ratio of the market is economically an insignificant distance below the maximum Sharpe ratio.Rather,evidence of convergence must be looked for.The emphasis is on dynamics,i.e.,on tendencies.See Prediction1.To obtain the evolution of the Sharpe ratio difference,we proceeded as follows.At the beginning of each period within an experiment,we waited until all three securities traded at least ing the most recent transaction prices,we computed the maximum Sharpe ratio,as well as the market’s Sharpe ratio.Subsequently,Sharpe ratio differences were re-computed whenever a new transaction took place.When repeated across periods and experiments, such computations produced a plot of the evolution of the difference between the maximum Sharpe ratio and the Sharpe ratio of the market.This metric could not be obtained in the few experimental periods that one of the securities did not trade.For instance,during several periods in the4/30experiment,the riskfree security(asset C) did not trade.So,no transaction prices were recorded,and,hence,the Sharpe ratios could not be calculated.Figure2displays the dynamics of the difference between the two Sharpe ratios.Experiments are delineated with vertical lines and labeled with the date when they took place.The horizontal axis measures time in experimental periods.In other words,each period within an experiment covers one unit of time.Zero is the minimum difference between the two Sharpe ratios.If the difference reaches zero,prices correspond to the prediction of the CAPM.Most often,however,the market’s Sharpe ratio is below the maximum,as suggested by the negative Sharpe ratio differences, suggesting that markets had not equilibrated yet.Figure2exposes a pronounced tendency for the difference between11the Sharpe ratios to diminish over time.This is apparent within experiments,but the trend is most manifest across the seven experiments(which were arranged in chronological order).Because of the scale,within-period convergence is less visible.In fact,Sharpe ratio differences often moved erratically within periods,with no clear sign of convergence. Hence,the trend towards the CAPM is most evident over longer time horizons.As the experience of the subjects grows,by the5/19experiment,the market appears to have reached the CAPM equilibrium.To evaluate the robustness of thisfinding,we altered the payoffstructure(reversing the skewness of the payoffof one of the risky securities),as well as individual endowments(allocating only one of the two risky securities to each subject,instead of the market portfolio),as explained in Section3.Figure2clearly suggests that this has no impact on the results:the market’s Sharpe ratio is as close to the maximum Sharpe ratio in the6/9experiment as it was in the5/19experiment.Still,closer inspection of Figure2reveals that even when the Sharpe ratio of the market is close to the maxi-mal value,the difference may remain nonzero.This is clearest in the5/19experiment:during virtually the entire experiment,markets were close to what the CAPM predicts but remained afinite distance away.In summary:Result1The evidence from Figure2partly supports Prediction1:there is evidence of convergence to the CAPM, but full convergence is often not achieved.There are two major differences in terms of pricing between the large-scale experiments discussed in Bossaerts and Plott(1999)and the small-scale experiments reported on here.First,convergence in large-scale experiments is much faster.Whereas it takes almost an entire experiment,or even a couple of experiments(experience)for markets to come close to the CAPM in the thin markets studied here,convergence in large-scale experiments is a matter of a few periods,or even one period.Second,the convergence process in large-scale experiments never halts.The CAPM ultimately obtains:the difference between the maximum Sharpe ratio and that of the market is eventually (economically)indistinguishable from zero.12We now turn to the dynamics of individual allocations,where we mayfind some clues for the causes of the slow and often halted convergence process.3.3Individual Allocations And Interpreting Halted ConvergenceThe evolution of the Sharpe ratios in Figure2provides evidence that the allocational forces of the CAPM are at work:prices are driven by a mean-variance optimal aggregate demand,for otherwise the market portfolio(aggregate supply)would not move up in mean-variance space.Still,we would like to see more direct evidence that subjects’positions improve in mean-variance terms.Prediction2states that the trade-offbetween mean and variance of subjects’portfolios should gradually improve over time.Wefirst focus on the one experiment where prices where close to the CAPM yet never fully reached the CAPM,the5/19experiment.Figure4displays the evolution of the potential gain for each subject in this experiment.The potential gain is expressed as the difference in expected return between the subject’s actual position and the mean-variance efficient portfolio with the same volatility.In other words,it is the vertical distance between a subject’s position and the frontier in plots like Figure3.Because individual holdings are quite noisy,Figure4also displays the evolution of the average potential gain.Figure4was generated like Figure2: after each transaction,the mean-variance frontier is re-computed,and subjects’positions are re-evaluated.Thefirst observation in each period does not reflect thefirst transaction;at least one transaction in each security is needed. Unlike in Figure2,however,time is measured in number of transactions.Figure4depicts how subjects gradually move in mean-variance space.The picture is very noisy,confirming the findings in large-scale experiments(see Bossaerts,Plott and Zame(2000)).There is weak tendency for individuals to decrease their potential gain as time progresses.Perhaps the clearest evidence is the fact that in the second half of each period,some subjects manage to move onto the frontier of optimal portfolios(where their gain is zero).4The 4The simplest way to do this is to move out of risky securities and cash,investing solely in riskfree securities,which generally traded at a discount to its payoff.13convergence is not always monotone.For instance,in periods1,3and6,subjects’positions become worse before improving.Apparently,subjects did not all attempt to reverse the situation.Some of the noise is eliminated by looking at the average(solid line).The tendency for improvement is clearer.Overall,therefore,Figure4provides some support for Prediction2.An investigation of the evolution of potential gains in other experiments confirmed thesefindings.Instead of presenting further visual evidence,Table2provides statistical evidence for the5experiments where there were more than200transactions.It displays estimates of the intercept,slope and R2in OLS regressions of the change in the average potential gain(defined as in Figure4)onto its level.If the CAPM does not have any predictive power,prices and holdings move randomly,which means that the average potential gain should not display any tendency to revert when high.If the forces of the CAPM are at work,one expects reversion in the average potential gain.That is,the slope should be significantly negative.In all experiments,the slope is highly significant(and the R2s are high as well), confirming the influence of the CAPM on allocations.The significantly positive intercepts in Table2confirm that the CAPM process does not fully converge.For CAPM allocations to really obtain,the average potential gain should revert back to zero,which means that the intercepts reported in Table2should be insignificant.At the same time,Table2does indicate that the distance from CAPM decreases as experience increases:the intercepts are smaller in the later experiments.We conclude:Result2While noisy,subjects’portfolios gradually improve after adverse movements,confirming Prediction2,but they do not tend to full optimum.As an aside,it should be emphasized that the evidence that the average potential gain has the tendency to diminish but does not fully converge to zero is not necessarily a mathematical restatement of thefinding that the Sharpe ratio of the market portfolio tends,but does not fully converge,to the maximum Sharpe ratio.There is no simple, monotonic mathematical relation between the two.Bossaerts,Kleiman and Plott(2000;Appendix)illustrate how the14。
