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The Fund offers you the option to submit purchase orders through your financial intermediary or send purchase orders by mail, fax or internet and send purchase proceeds by check, wire transfer or ACH to the Fund for accounts opened directly. The Fund typically does not accept third-party checks. Fund management reserves the right to refuse other payment instruments if, in the sole discretion of Fund management, it is deemed to be in the best interest of the Fund.

Retirement contributions will be considered as current year contributions unless otherwise instructed in writing at the time of the contribution. You may buy shares and send your purchase proceeds by any of the following methods:.

IRA and other retirement accounts require additional paperwork. Complete the account application that corresponds to the type of account you are opening. Complete the Guggenheim Investments investment slip included with your quarterly statement or send written purchase instructions that include:. Make your check payable to Guggenheim Investments. Your check must be drawn on a U. Include the name of the Fund s you want to purchase on your check.

If you do not specify the Fund s you want to purchase, your investment generally will be credited to the Rydex U. Government Money Market Fund, which is offered in a separate prospectus. Mail your application and check to:. Mail your written purchase instructions and check to:. Mailing Addresses:. Standard Delivery. Guggenheim Investments. Attn: Ops. Box Topeka, KS Mail Zone One Security Benefit Place.

Client Services phone number:. Complete and submit the account application that corresponds to the type of account you are opening. Contact Client Services at Use the Wire Instructions below to send your wire. You will receive a confirmation number to verify that your purchase order has been accepted. If you do not notify Guggenheim Investments Client Services of the incoming wire, your purchase order may not be processed until the Business Day following the receipt of the wire.

Wire Instructions:. Cincinnati, OH. Routing Number: For Account of: Guggenheim Investments. Account Number: Initial Purchase Class A Shares. Subsequent Purchases. Guggenheim Investments Fax number: Submit a new account application.

All other applications should be mailed. To make a subsequent purchase send written purchase instructions that include:. If you have existing ACH instructions on file, log-in to your account at www. Guggenheim Investments will ordinarily cancel your purchase order under the following circumstances:.

If your purchase order is cancelled for any of these reasons, you will not be entitled to benefit from any increase in NAV that the Fund may have experienced from the time of your order to the time of its cancellation. Selling Fund Shares.

The Fund redeems its shares continuously and investors may sell their shares back to the Fund on any Business Day. The Fund may suspend your right to redeem your shares during times when trading on the NYSE is suspended or restricted, or otherwise as permitted by the SEC. If the Fund redeems your shares in kind, you may bear transaction costs and will bear market risks until such time as such securities are converted to cash.

You will ordinarily submit your transaction order through your financial intermediary or other securities dealers through which you opened your shareholder account or through Guggenheim Investments if you opened your account directly with the Fund. The Fund also offers you the option to send redemption orders to Guggenheim Investments by:. If you send your redemption order by fax, you must call Guggenheim Investments Client Services at Whether you transmit your redemption order by mail, fax or telephone, you must include the following information in your redemption order:.

You may only place a redemption order if you are the registered owner of the account or the registered owner has given Guggenheim Investments written authorization to allow you to make redemptions from the account.

You will receive a confirmation number for your redemption. Please retain it for your records. Shareholders who choose not to use the default cost basis method i. Shareholders using the specific identification method are expected to provide lot selection information along with their redemption or exchange request. For situations where shareholders are unable to or do not provide instructions i.

Shareholders who wish to use the specific identification method for identifying lots of shares sold, however, are not permitted to use the average cost basis method. Unless requested otherwise at the time of the transaction, the Fund will redeem or exchange shares in the following order: undated non-covered shares, non-covered shares, followed by covered shares using the method in effect for the account.

Distributions from your tax-qualified plan or individual retirement account IRA may have adverse tax consequences to you. You should consult your tax adviser before redeeming shares and making distributions from your tax-qualified plan or IRA account.

All requests for distributions of redemption proceeds from tax-qualified plan and IRA accounts must be in writing. All distributions from tax-qualified plans and IRAs are subject to tax withholding rules. Distributions from b accounts may require employer or plan administrator approval. Your redemption proceeds normally will be sent within seven days of the Transfer Agent receiving your request.

For redemption orders that settle on federal bank holidays, your redemption proceeds will be sent on the next Business Day following the holiday. For investments made by check or ACH not wire purchases , purchases will be on hold for up to 10 Business Days before a payment of redemption proceeds may be made. All redemptions will be mailed to your address of record, sent electronically via ACH, or wired to your bank account of record.

You may request overnight mail service for an additional fee. If redemption proceeds are transmitted by ACH or wire and the payee instructions are not valid, the proceeds may be re-invested into shares of the Rydex U. Government Money Market Fund, which are offered in a separate prospectus, as of the date of the redemption. If you request payment of redemption proceeds to a third party or to a location other than your address of record, alternate address on file, or bank account s of record, your redemption request should be in writing and include a Medallion signature guarantee and may not be faxed.

You may not send redemption proceeds to an address of record that was changed within the last 10 business days unless your request is Medallion signature guaranteed. For certain exceptions e. Please contact Guggenheim Investments Client Services at Medallion signature guarantees help protect you and your account against fraud. You can obtain a Medallion signature guarantee at most banks and financial intermediaries.

A notary public cannot provide a Medallion signature guarantee. You may not use fax to transmit a Medallion signature guarantee to the Fund. Any dividend, capital gain or partial redemption check that has remained outstanding for a period of 90 days from the issuance date will be canceled and re-issued.

For dividend and capital gain checks, the proceeds will be reinvested into the appropriate share class of the Fund from which such distribution was paid, or if the Fund position has subsequently been redeemed in full, the distribution will be reinvested into shares of the Rydex U. Government Money Market Fund, which are offered in a separate prospectus. The account also will have the distribution payout option adjusted so that all future distributions are reinvested into the appropriate share class of the Fund from which the distribution would have been paid.

For partial redemption checks, the proceeds will be deposited into shares of the Rydex U. Government Money Market Fund. Any redemption check from a retirement account IRA, Roth, SEP, for example that has remained outstanding for a period of 90 days from the issuance date will be cancelled and re-issued one time.

For checks returned in the mail, the Fund will attempt to contact the client. If no contact is made, the check will be processed according to the procedures mentioned above. Classes other than the Institutional Class shares. The Fund may redeem your shares if the value of your account falls below the required minimum account balance. Exchanging Fund Shares. An exchange is when you sell shares of one Fund and use the proceeds from that sale to purchase shares of another Fund.

Investors may make exchanges on any Business Day of shares of the Fund for corresponding shares of any other Fund within the Family of Funds on the basis of the respective NAVs of the shares involved. Exchange requests, like any other share transaction, will be processed at the NAV next determined after your exchange order is received in good order. Exchanges involving other Funds not included in this Prospectus may be subject to different transaction cut-off times. The exchange privilege may be modified or discontinued at any time.

You will ordinarily submit your transaction order through your financial intermediary or other securities dealers through which you opened your shareholder account or through Guggenheim Investments directly. The Fund also offers you the option to send exchange requests to Guggenheim Investments by:.

If you send your exchange request by fax, you must call Guggenheim Investments Client Services at Whether you transmit your exchange request by mail, fax, telephone or internet, you must include the following information in your exchange request:. You may only place exchange orders if you are the registered owner of the account or the registered owner has given Guggenheim Investments written authorization to allow you to trade the account.

You will receive a confirmation number for your exchange. Shareholders may elect to engage in dollar-cost averaging, which allows shareholders to make periodic exchanges of shares from one fund to one or more other funds at regular intervals. With dollar-cost averaging, the cost of the securities is averaged over time and possibly over various market cycles. Dollar-cost averaging does not guarantee profits, nor does it assure that a shareholder will not have losses.

Shareholders should contact Guggenheim Investments Client Services to enroll in dollar-cost averaging. Shareholders will need to choose whether amounts are to be exchanged on the basis of a specific dollar amount or a specific number of shares. Guggenheim Investments will exchange shares as requested on the date of your choosing.

If the date selected falls on a weekend or holiday, your request will be processed on the previous Business Day. Dollar-cost averaging may be terminated at any time by a shareholder by written request or by phone. Account Policies. Federal regulations may require the Fund to obtain your name, your date of birth for a natural person , your residential street address or principal place of business and your Social Security Number, Employer Identification Number or other government issued identification when you open an account.

Additional information may be required in certain circumstances or to open accounts for corporations or other entities. The Fund may use this information to attempt to verify your identity. The Fund may not be able to establish an account if the necessary information is not received. The Fund may also place limits on account transactions while it is in the process of attempting to verify your identity. Additionally, if the Fund is unable to verify your identity after your account is established, the Fund may be required to redeem your shares and close your account.

If your account is closed for this reason, your shares will be redeemed at the NAV next calculated on the date your account is closed, and you bear the risk of loss. Guggenheim Investments provides accounts for U. We will not open a new account for any non-resident aliens natural person or entity. If you are unsure of your status please consult your tax adviser. The Fund has adopted an anti-money laundering compliance program designed to prevent the Fund from being used for money laundering or the financing of terrorist activities.

These actions will be taken when, in the sole discretion of Fund management, they are deemed to be in the best interest of the Fund or in cases when the Fund is requested or compelled to do so by governmental or law enforcement authority.

If your account is closed at the request of governmental or law enforcement authority, you may not receive proceeds of the redemption if the Fund is required to withhold such proceeds. Internet and telephone transactions are extremely convenient, but are not risk free.

To ensure that your internet and telephone transactions are safe, secure, and as risk-free as possible, the Fund has instituted certain safeguards and procedures for determining the identity of web site users including the use of secure passwords and bit encryption technology and telephone callers and authenticity of instructions.

As a result, neither the Fund nor its Transfer Agent will be responsible for any loss, liability, cost, or expense for following internet, telephone or wire instructions they reasonably believe to be genuine.

If you or your intermediaries make exchange requests by telephone or internet, you will generally bear the risk of any loss. Neither the Fund nor its Transfer Agent is responsible for internet transactions that are not received. During periods of unusually high market activity or other times, it may be difficult to reach Guggenheim Investments by telephone or access our internet site. Guggenheim Investments and its affiliates will not be liable for any losses resulting from a cause over which Guggenheim Investments or its affiliates do not have direct control, including but not limited to the failure of electronic or mechanical equipment or communication lines, telephone or other interconnect problems e.

If you are not able to reach Guggenheim Investments by telephone, fax, or internet, consider sending written instructions. You will receive statements and trade confirmations of your investment transactions. For more information on eDelivery, please visit the Guggenheim Investments web site at www. You may access information about the Fund and your Guggenheim Investments account anytime with the Guggenheim Investments Express Line.

This automated line gives you telephone access to Fund information including NAVs, daily factors, fund assets and distributions as well as balance and history information on your Guggenheim Investments account. Guggenheim Investments reserves the right to change any of these fees or add additional service fees at any time. You may pay the annual fee at any time during the calendar year by sending Guggenheim Investments a check.

If the annual maintenance fee is not paid separately prior to December, it will be deducted automatically from your account. This fee will be deducted from the proceeds of your redemption. Guggenheim Investments will waive the annual maintenance fee if a liquidation fee is being charged.

Guggenheim Investments also may waive the annual maintenance fee and any applicable account closing fee for certain b retirement plan accounts. For more information about the applicability of these fees, please contact Guggenheim Investments Client Services at For additional information on fees for employee accounts please refer to the SAI.

The Fund is not suitable for purchase by active investors. If you wish to engage in such practices, we request that you do not purchase shares of the Fund. The Fund does not accommodate frequent purchases and redemptions. Consequently, the Board of [Trustees] has adopted policies and procedures designed to prevent frequent purchases and redemptions of shares of the Fund.

In addition, the Fund reserves the right to reject any purchase request by any investor or group of investors for any reason without prior notice, including, in particular, if the Investment Manager reasonably believes that the trading activity would be harmful or disruptive to the Fund. This waiver may be extended in the future without notice to permit investments by additional funds of funds in the Fund. In its sole discretion, the Fund may revise its market timing procedures at any time without prior notice as it deems necessary or appropriate, including changing the criteria for monitoring market timing and other harmful trading including without limitation, imposing dollar or percentage limits on transfers.

Although these policies are designed to deter frequent trading, none of these measures alone nor all of them taken together eliminate the possibility that frequent trading in the Fund will occur, particularly with respect to trades placed by shareholders that invest in the Fund through omnibus accounts maintained by brokers, retirement plan accounts and other financial intermediaries.

The Fund reserves the right to close your account in cases of suspected fraudulent or illegal activity in accordance with applicable law. This action may be taken when, in the sole discretion of Fund management, it is deemed to be in the best interests of the Fund or in cases where the Fund is requested or compelled to do so by applicable law.

If your account is closed at the request of governmental or law enforcement authority or pursuant to applicable law, you may not receive proceeds of the redemption if the Fund is required to withhold such proceeds. This action may be taken when, in the sole discretion of Fund management, it is deemed to be in the best interest of the Fund or in cases where the Fund is requested or compelled to do so by applicable law.

Distribution and Shareholder Services. The Fund will pay distribution fees to the Distributor at an annual rate not to exceed 0. Because the Fund pays these fees out of assets on an ongoing basis, over time these fees may cost you more than other types of sales charges and will increase the cost of your investment.

The Fund has adopted a Distribution and Shareholder Services Plan pursuant to Rule 12b-1 under the Act, applicable to Class C Shares that allows the Fund to pay annual distribution and service fees of 1. The annual 0. The Investment Manager, at its expense, may provide compensation to financial intermediaries for the sale of Fund shares. These payments may be made, at the discretion of the Investment Manager, to certain dealers who have sold shares of the Fund.

The level of payments made to dealers will generally vary, but may be significant. The Investment Manager periodically determines the advisability of continuing these payments. The Investment Managers may also pay expenses associated with meetings that facilitate educating financial advisers and shareholders about the Fund that are conducted by dealers. Shareholders should inquire of an intermediary how the intermediary will be compensated for investments made in the Fund.

Shareholder Services. Shareholders who wish to receive regularly scheduled payments may establish a Systematic Withdrawal Plan. Please refer to the Systematic Withdrawal Plan Request form for additional payment options. The form can be found within the Customer Service section of the www. Shares are liquidated at NAV. The Program may be terminated upon notification, or it will terminate automatically if all shares are liquidated or redeemed from the account.

Shareholders of the Fund may exchange their shares for shares of other funds distributed by the Distributor. An exchange is two transactions: a sale of shares of one fund and the purchase of shares of another fund. Shares of a particular class of the Fund may be exchanged only for shares of the same class of another available Fund.

Shareholders should consult that prospectus prior to making such an exchange. Exchanges may be made only in those states where shares of the Fund into which an exchange is to be made are qualified for sale. No service fee or sales charge is presently imposed on such an exchange. Any applicable contingent deferred sales charge will be imposed upon redemption and calculated from the date of the initial purchase. For tax purposes, an exchange is a sale of shares which may result in a taxable gain or loss.

Special rules may apply to determine the amount of gain or loss on an exchange occurring within 90 days after purchase of the exchanged shares. Before exchanging your shares for shares of another mutual fund that is distributed by the Distributor and offered through another prospectus, you should request the prospectus of the mutual fund into which you are contemplating exchanging your shares and review it carefully, as the other mutual fund may be subject to fees, charges or expenses that are different from the shares that you are exchanging.

A current prospectus of the Fund into which an exchange is made will be given to each shareholder exercising this privilege. Contact your plan sponsor or administrator to determine if all of the exchange options discussed above are available under your plan. A shareholder may exchange shares by telephone by calling the Fund at Exchange requests received by telephone after the close of the NYSE normally p.

Eastern Time will be treated as if received on the next Business Day. The exchange privilege is not intended as a vehicle for short-term or excessive trading. The Fund also may reject future investments from a shareholder if the shareholder engages in, or is suspected of engaging in, short-term or excessive trading. Exchanges into the Rydex U. Government Money Market Fund, which is offered in a separate prospectus that you can obtain upon request and that you should consult prior to an exchange.

Government Money Market Fund have no distribution and shareholder service 12b-1 fees, initial up-front sales charges, initial investment minimum and minimum balance requirements. However, redemptions from the Rydex U. Government Money Market Fund may be subject to such deferred sales charge, as may redemptions from other Funds in which you could later invest, as discussed below. Government Money Market Fund and you redeem your shares, the deferred sales charge will be assessed at the time you redeem your Money Market Class Shares of the Rydex U.

Government Money Market Fund at the time of a subsequent exchange. Shareholders should note that, if your initial investment was subject to an initial sales charge, a further exchange of the Money Market Class Shares of the Rydex U. Government Money Market Fund will not be subject to a charge at the time of such exchange. For additional information, see the prospectus for the Rydex U. Dividends and Taxes. Your dividends and distributions will be reinvested in the Fund, unless you instruct the Investment Manager otherwise.

There are no fees or sales charges on reinvestments. Dividends and distributions will be paid in the form of additional Fund shares unless you have elected to receive payment in cash. If you did not elect to receive cash payments of dividends and distributions on your application, you must notify the Fund in writing to change your election prior to the date of the next distribution. Your election will become effective for dividends paid after the Fund receives your written notice. To cancel your election, simply send written notice to the Fund.

Fund dividends and distributions are taxable to shareholders, unless your investment is in an IRA or other tax-advantaged retirement account, whether you reinvest your dividends or distributions or take them in cash. In addition to federal tax, dividends and distributions may be subject to state and local taxes.

If the Fund declares a dividend or distribution in October, November or December but pays it in January, you may be taxed on that dividend or distribution as if you received it in the calendar year in which the dividend or distribution is declared. These rate reductions do not apply to corporate taxpayers or to foreign shareholders. A shareholder will also have to satisfy a more than day holding period with respect to any distributions of qualifying dividends in order to obtain the benefit of the lower tax rate.

Distributions of earnings from non-qualifying dividends, interest income, other types of ordinary income and short-term capital gains will be taxed at the ordinary income tax rate applicable to the taxpayer. Tax-deferred retirement accounts generally do not generate a tax liability unless you are taking a distribution or making a withdrawal.

Distributions designated by the Fund as long-term capital gain distributions will be taxable to you at your long-term capital gains rate no matter how long you have held your Fund shares. The Fund will mail you information concerning the tax status of the distributions for each calendar year early the following year.

You may be taxed on any sale, redemption or exchange of Fund shares. Generally, gain or loss realized upon the sale, redemption or exchange of Fund shares will be capital gain or loss if you hold the shares as capital assets and will be taxable as long-term capital gain or loss if you held the shares for more than one year, or as short-term capital gain or loss if you held the shares for one year or less, at the time of the sale, redemption or exchange.

If your tax basis in your shares exceeds the amount of proceeds you received from a sale, exchange or redemption of shares, you will recognize a taxable loss on the sale of shares of the Fund. Any loss recognized on shares held for six months or less will be treated as long-term capital loss to the extent of any long-term capital gain distributions that were received with respect to the shares. If disallowed, the loss will be reflected in an adjustment to the tax basis of the shares acquired.

Back-up withholding is not an additional tax; rather, it is a way in which the Internal Revenue Service ensures it will collect taxes otherwise due. Any amounts withheld may be credited against your U. Shareholders other than U. You should consult your tax professional about federal, state and local tax consequences to you of an investment in the Fund.

Please see the SAI for additional tax information. In the absence of an election, the Fund will use a default cost basis method which is the average cost method. The cost basis method elected by a Fund shareholder or the cost basis method applied by default for each sale of Fund shares may not be changed after the close of business on the trade date of each such sale of Fund shares. Fund shareholders should consult with their tax advisers prior to making redemptions to determine the best Internal Revenue Service accepted cost basis method for their tax situation and to obtain more information about the cost basis reporting rules.

Determination of Net Asset Value. The price at which you buy, sell and exchange shares is the net asset value per share plus any applicable front-end sales charge , which also is known as NAV. The Fund calculates its NAV by:. The Fund discloses its NAV on a daily basis. When calculating the NAV, the Fund will value the portfolio securities and assets of the Fund for which market quotations are readily available at the current market price of those securities and assets.

With respect to portfolio securities and assets of the Fund for which market quotations are not readily available, or which cannot be accurately valued with the established pricing procedures, the Fund will fair value those securities and assets. Securities traded on a domestic securities exchange including ETFs are usually valued at the last sale price on that exchange on the day the valuation is made, provided, however, that securities listed on NASDAQ will usually be valued at the NASDAQ Official Closing Price, which may not necessarily represent the last sale price.

If no sale is reported, the last current bid price is used. Debt securities with a remaining maturity greater than 60 days will usually be valued based on independent pricing services. Commercial paper and discount notes with a remaining maturity of 60 days or less may be valued at amortized cost.

For foreign securities and other assets that are priced in a currency other than U. Foreign securities may trade in their primary markets on weekends or other days when the Fund does not price its shares. If market prices are unavailable or the Investment Manager thinks that they are unreliable or a significant event has occurred, the Investment Manager prices those securities at fair value as determined in good faith using methods approved by the Board of [Trustees].

The Investment Manager may view market prices as unreliable when the value of a security has been materially affected by events occurring after the market closes, but prior to the time as of which the Fund calculates its NAV. The use of fair valuation in pricing a security involves the consideration of a number of subjective factors and therefore, is susceptible to the unavoidable risk that the valuation may be higher or lower than the price at which the security might actually trade if a reliable market price were readily available.

General Information. Shareholders who have questions concerning their account or wish to obtain additional information may call the Fund see back cover for address and telephone numbers or contact their securities dealer.

Client requests for historical account transcripts or the retrieval of a significant amount of documentation may be honored to the extent that those records are readily available. The Fund reserves the right, upon notice, to charge you a fee to cover the costs of special requests for information that require extensive research or employee resources.

Financial Highlights. Since the Fund does not have a full year of performance as of the date of this prospectus, financial highlights information has not been provided. For More Information. Information about the operation of the Public Reference Room may be obtained by calling the Commission at Copies may be obtained, upon payment of a duplicating fee, by electronic request at the following e-mail address: publicinfo sec.

This Statement of Additional Information is not an offer to sell these securities and is not soliciting an offer to buy these securities in any state where the offer or sale is not permitted. Statement of Additional Information. This Statement of Additional Information is not a prospectus. Santa Monica, California Guggenheim Distributors, LLC.

Rydex Distributors LLC. Rockville, Maryland Brooklyn, New York Investment Objectives and Policies of the Fund. Investment Methods and Risk Factors. Investment Restrictions. Fundamental Policies. Operating Policies. Disclosure of Portfolio Holdings. Management of the Fund. Board Responsibilities. Audit Committee. Contracts Review Committee. Nominating Committee. Remuneration of [Trustees] and Others. Principal Holders of Securities. How to Purchase Shares. Cancelled Purchase Order.

Alternative Purchase Options. Class C Shares. Institutional Class Shares. Minimum Account Balance. Distribution Plans. Rule 12b-1 Plan Expenses. Other Distribution or Service Arrangements. Purchases at Net Asset Value. Purchases for Retirement Plans.

Systematic Withdrawal Plan. Investment Management. Code of Ethics. Portfolio Managers. Other Accounts Managed by Portfolio Managers. Proxy Voting. Allocation of Portfolio Brokerage. How Net Asset Value is Determined. How to Redeem Shares. How to Exchange Shares. Independent Registered Public Accounting Firm. Financial Statements. Appendix A:. Description of Bond Ratings. The shell series of the Trust succeeded to the accounting and performance histories of the series of the Predecessor Corporation.

The Fund, a series of the Trust, has its own investment objective and policies. While there is no present intention to do so, the investment objective and policies of the Fund, unless otherwise noted, may be changed by the Board of Trustees without the approval of shareholders. The Fund is also required to operate within limitations imposed by its fundamental investment policies, which may not be changed without shareholder approval.

There are risks inherent in the ownership of any security, and there can be no assurance that the investment objectives will be achieved. The Fund seeks to provide total return, comprised of capital appreciation and current income. The following is a description of certain additional risk factors related to various securities, instruments and techniques. Also included is a general description of some of the investment instruments, techniques and methods which may be used by the Fund.

Although the Fund may employ the techniques, instruments and methods described below, consistent with its investment objective and policies and any applicable law, the Fund will not be required to do so. The value of fixed-income securities held by the Fund generally fluctuates inversely with interest rate movements. In other words, bond prices generally fall as interest rates rise and generally rise as interest rates fall. Longer term bonds held by the Fund are subject to greater interest rate risk.

There is no assurance that the Fund will achieve its investment objective. Debt securities with longer maturities tend to produce higher yields and are generally subject to potentially greater capital appreciation and depreciation than obligations with shorter maturities and lower yields. The market prices of debt securities usually vary, depending upon available yields. An increase in interest rates will generally reduce the value of portfolio investments, and a decline in interest rates will generally increase the value of portfolio investments.

The ability of the Fund to achieve its investment objectives is also dependent on the continuing ability of the issuers of the debt securities in which the Fund invest to meet their obligations for the payment of interest and principal when due. Although high levels of debt do not necessarily indicate or cause economic problems, high levels of debt may create certain systemic risks if sound debt management practices are not implemented.

A high national debt level may increase market pressures to meet government funding needs, which may increase borrowing costs and cause a government to issue additional debt, thereby increasing the risk of refinancing. A high national debt also raises concerns that a government may be unable or unwilling to repay the principal or interest on its debt. Unsustainable debt levels can decline the valuation of currencies, and can prevent a government from implementing effective counter-cyclical fiscal policy during economic downturns.

It also could generate an economic downturn. Treasury notes and bonds. The Fund also may invest in zero coupon and other deep discount securities issued by foreign governments and domestic and foreign corporations, including certain Brady Bonds and other foreign debt and payment-in-kind securities. Zero coupon securities pay no interest to holders prior to maturity, and payment-in-kind securities pay interest in the form of additional securities. Accordingly, for the Fund to qualify for tax treatment as a regulated investment company and to avoid certain taxes, the Fund may be required to distribute an amount that is greater than the total amount of cash it actually receives.

The Fund will not be able to purchase additional income-producing securities with cash used to make such distributions, and its current income ultimately may be reduced as a result. Zero coupon and payment-in-kind securities usually trade at a deep discount from their face or par value and will be subject to greater fluctuations of market value in response to changing interest rates than debt obligations of comparable maturities that make current distributions of interest in cash.

PIPE transactions may be entered into with smaller capitalization public companies, which will entail business and financial risks comparable to those of investments in the publicly-issued securities of smaller capitalization companies, which may be less likely to be able to weather business or cyclical downturns than larger companies and are more likely to be substantially hurt by the loss of a few key personnel. In addition, PIPE transactions will generally result in the Fund acquiring either restricted stock or an instrument convertible into restricted stock.

As with investments in other types of restricted securities, such an investment may be illiquid. Any number of factors may prevent or delay a proposed registration. Alternatively, it may be possible for securities acquired in a PIPE transaction to be resold in transactions exempt from registration in accordance with Rule under the Act, as amended, or otherwise under the federal securities laws.

There can be no guarantee that there will be an active or liquid market for the stock of any small capitalization company due to the possible small number of stockholders. As a result, even if the Fund is able to have securities acquired in a PIPE transaction registered or sell such securities through an exempt transaction, the Fund may not be able to sell all the securities on short notice, and the sale of the securities could lower the market price of the securities.

Included among direct obligations of the U. Bills, Treasury Notes and Treasury Bonds, which differ in terms of their interest rates, maturities, and dates of issuance. Treasury Bills have maturities of less than one year, Treasury Notes have maturities of one to 10 years and Treasury Bonds generally have maturities of greater than 10 years from the date of issuance.

Included among the obligations issued by agencies and instrumentalities of the U. In September , the U. Treasury announced a federal takeover of Fannie Mae and Freddie Mac, placing the two federal instrumentalities in conservatorship. Under the takeover, the U. In May , the U. In December , the U.

Treasury further amended the SPAs to allow the cap on the U. At the start of , the unlimited support the U. Instead, they will transfer to the U. It is anticipated that the new amendment would put Fannie Mae and Freddie Mac in a better position to service their debt. Also in December , the U. Treasury amended the SPAs to provide Fannie Mae and Freddie Mac with some additional flexibility to meet the requirement to reduce their mortgage portfolios.

The actions of the U. Treasury are intended to ensure that Fannie Mae and Freddie Mac maintain a positive net worth and meet their financial obligations, preventing mandatory triggering of receivership. No assurance can be given that the U. Treasury initiatives will be successful. Other U. Because the U.

The Fund may also invest in separately traded principal and interest components of securities guaranteed or issued by the U. The Fund may invest in fixed rate or variable rate commercial paper, issued by U. Commercial paper consists of short-term, usually from 1 to days unsecured promissory notes issued by U. Any commercial paper issued by a foreign entity corporation and purchased by the Fund must be U. Investing in foreign commercial paper generally involves risks relating to obligations of foreign banks or foreign branches and subsidiaries of U.

The Fund may invest in commercial paper collateralized by other financial assets, such as asset-backed commercial paper. These securities are exposed not only to the risks relating to commercial paper, but also the risks relating to the collateral. The Fund may also invest in variable rate master demand notes. A variable rate master demand note a type of commercial paper represents a direct borrowing arrangement involving periodically fluctuating rates of interest under a. Investors in CLOs bear the credit risk of the underlying collateral.

The bank loans are used as collateral supporting the various debt tranches issued by the SPV. Multiple tranches of securities are issued by the CLO, offering investors various maturity and credit risk characteristics. The key feature of the CLO structure is the prioritization of the cash flows from a pool of debt securities among the several classes of the CLO.

The Fund may invest in the equity or residual portion of the capital structure of CLOs. The SPV is a company founded solely for the purpose of securitizing payment claims. On this basis, marketable securities are issued which, due to the diversification of the underlying risk, generally represent a lower level of risk than the original assets. The redemption of the securities issued by the SPV takes place at maturity out of the cash flow generated by the collected claims.

The vast majority of CLOs are actively managed by an independent investment manager. The underlying assets e. If the credit support or enhancement is exhausted, losses or delays in payment may result if the required payments of principal and interest are not made. The transaction documents relating to the issuance of CLOs may impose eligibility criteria on the assets of the issuing SPV, restrict the ability of the investment manager to trade investments and impose certain portfolio-wide asset quality requirements.

In addition, other parties involved in structured products, such as third party credit enhancers and investors in the rated tranches, may impose requirements that have an adverse effect on the returns of the various tranches of CLOs.

Furthermore, CLO transaction documents generally contain provisions that, in the event that certain tests are not met generally interest coverage and over-collateralization tests at varying levels in the capital structure , proceeds that would otherwise be distributed to holders of a junior tranche must be diverted to pay down the senior tranches until such tests are satisfied.

Failure or increased likelihood of failure of a CLO to make timely payments on a particular tranche will have an adverse effect on the liquidity and market value of such tranche. Payments to holders of CLOs may be subject to deferral. If cash flows generated by the underlying assets are insufficient to make all current and, if applicable, deferred payments on the CLOs, no other assets will be available for payment of the deficiency and, following realization of the underlying assets, the obligations of the issuer to pay such deficiency will be extinguished.

Furthermore, the leveraged nature of each subordinated class may magnify the adverse impact on such class of changes in the value of the assets, changes in the distributions on the assets, defaults and recoveries on the assets, capital gains and losses on the assets, prepayment on the assets and availability, price and interest rates of the assets.

CLOs are typically privately offered and sold, and thus are not registered under the securities laws. As a result, investments in CLOs may be illiquid; however, an active dealer market may exist which would allow such securities to be considered liquid in some circumstances. General Risks.

The Fund may invest in municipal securities issued by or on behalf of states, territories and possessions of the United States and the District of Columbia and their political subdivisions, agencies and. Non-Municipal Tax-Exempt Securities could include trust certificates or other instruments evidencing interest in one or more long term municipal securities.

Non-Municipal Tax- Exempt Securities also may include securities issued by other investment companies that invest in Municipal Bonds, to the extent such investments are permitted by applicable law. Municipalities and municipal projects that rely directly or indirectly on federal funding mechanisms may be negatively affected by current budgetary constraints of the federal government.

The value of Municipal Bonds may also be affected by uncertainties in the municipal market related to legislation or litigation involving the taxation of Municipal Bonds or the rights of Municipal Bond holders in the event of a bankruptcy. From time to time, Congress has introduced proposals to restrict or eliminate the federal income tax exemption for interest on Municipal Bonds.

Municipal bankruptcies have in the past been relatively rare, and certain provisions of the U. Bankruptcy Code governing such bankruptcies are unclear and remain untested. Further, the application of state law to municipal issuers could produce varying results among the states or among Municipal Bond issuers within a state. These legal uncertainties could affect the Municipal Bond market generally, certain specific segments of the market, or the relative credit quality of particular securities.

Any of these effects could have a significant impact on the prices of some or all of the Municipal Bonds held by the Fund. Similar Projects Risk. Below are some of the risks of such investments. Higher Education. Bonds issued to supply educational institutions with funds are subject to the risk of unanticipated revenue decline resulting primarily from a decrease in student enrollment or reductions in state and federal funding.

Student loan revenue bonds are generally offered by state authorities or commissions and are backed by pools of student loans. Underlying student loans may be guaranteed by state guarantee agencies and may be subject to reimbursement by the United States Department of Education through its guaranteed student loan program.

Others student loans may be private, uninsured loans made to parents or students that are supported by reserves or other forms of credit enhancement. Independent Analysis For Energy Leaders. Related Articles. Iran backs Biden into a corner. Rejoining the nuclear deal might be easier said than done. Hormuz threats lose their sting. Flare capture offers easy wins. Reducing gas flaring can both accelerate progress to net-zero and offer a swift boost to industry credibility.

Lebanon targets gas and aid. The crisis-hit nation dreams of better diplomatic relations to help boost its crippled economy and unlock a gas bonanza. But dreams they may remain. Local firms take Iranian field reins. Iran has succeeded in expanding its oil and gas production capacity without the help of foreign partners. But at what future cost? Iran finds more export custom. As Iran ramps up output, it is beginning to turn the tide on exports too.

Kadhimi woos Washington. Iraq and Iran move further apart. Baghdad targets greater gas security. As US-Iranian tensions threaten energy imports, Iraq is ramping-up domestic gas development. Report Iran. Robin M Mills. Forward article link. Share PDF with colleagues. Also in this section. Letter from Norway: Tax stimulus medicine gets to work. New legislation aids the country in reaching peak hydrocarbon production. But increased interest in renewables still poses stranded resources risk.

PE Live: Safeguarding Mexican investment. The suspension of licensing rounds may have disappointed the private sector.

Весьма types of foreign investment in china МРАК!!!

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Edmund Learned, C. Roland Christensen, Kenneth Andrews, and others develop the SWOT strengths, weaknesses, opportunities, threats model of analysis, useful for making decisions when time is short and circumstances complex. John D. Little develops the underlying theory and advances the capability of decision-support systems. Fischer Black and Myron Scholes in one paper and Robert Merton in another show how to accurately value stock options, beginning a revolution in risk management. Henry Mintzberg describes several kinds of decision makers and positions decision making within the context of managerial work.

Victor Vroom and Philip Yetton develop the Vroom-Yetton model, which explains how different leadership styles can be harnessed to solve different types of problems. Amos Tversky and Daniel Kahneman publish their Prospect Theory, which demonstrates that the rational model of economics fails to describe how people arrive at decisions when facing the uncertainties of real life. John Rockart explores the specific data needs of chief executives, leading to the development of executive information systems.

Daniel Isenberg explains that executives often combine rigorous planning with intuition when faced with a high degree of uncertainty. Max Bazerman and Margaret Neale connect behavioral decision research to negotiations in Negotiating Rationally. Anthony Greenwald develops the Implicit Association Test, meant to reveal unconscious attitudes or beliefs that can influence judgment. In Blink, Malcolm Gladwell explores the notion that our instantaneous decisions are sometimes better than those based on lengthy, rational analysis.

The Hindu-Arabic numeral system which, radically, included zero simplified calculations and enticed philosophers to investigate the nature of numbers. The tale of our progression from those early fumblings with base 10 is masterfully told by Peter Bernstein in Against the Gods: The Remarkable Story of Risk. It progresses quickly to a new interest in mathematics and measurement, spurred, in part, by the growth of trade.

During the Renaissance, scientists and mathematicians such as Girolamo Cardano mused about probability and concocted puzzles around games of chance. Some years later, French mathematicians Blaise Pascal and Pierre de Fermat developed a way to determine the likelihood of each possible result of a simple game balla, which had fascinated Pacioli. Bernoulli who also introduced the far-reaching concept of human capital focused not on events themselves but on the human beings who desire or fear certain outcomes to a greater or lesser degree.

In the nineteenth century, other scientific disciplines became fodder for the risk thinkers. Carl Friedrich Gauss brought his geodesic and astronomical research to bear on the bell curve of normal distribution. The insatiably curious Francis Galton came up with the concept of regression to the mean while studying generations of sweet peas.

He later applied the principle to people, observing that few of the sons—and fewer of the grandsons—of eminent men were themselves eminent. Today, of course, corporations try to know as much as is humanly and technologically possible, deploying such modern techniques as derivatives, scenario planning, business forecasting, and real options. In the fifth century BC, Athens became the first albeit limited democracy.

In the seventeenth century, the Quakers developed a decision-making process that remains a paragon of efficiency, openness, and respect. Starting in , the United Nations sought enduring peace through the actions of free peoples working together. There is nobility in the notion of people pooling their wisdom and muzzling their egos to make decisions that are acceptable—and fair—to all. During the last century, psychologists, sociologists, anthropologists, and even biologists studying everything from mandrills to honeybees eagerly unlocked the secrets of effective cooperation within groups.

The scientific study of groups began, roughly, in , as part of the burgeoning field of social psychology. A breakthrough in understanding group dynamics occurred just after World War II, sparked—oddly enough—by the U. Enlisted to help, psychologist Kurt Lewin discovered that people were more likely to change their eating habits if they thrashed the subject out with others than if they simply listened to lectures about diet.

Over the next decades, knowledge about group dynamics and the care and feeding of teams evolved rapidly. Victor Vroom and Philip Yetton established the circumstances under which group decision making is appropriate. Meredith Belbin defined the components required for successful teams. And Peter Drucker suggested that the most important decision may not be made by the team itself but rather by management about what kind of team to use.

Poor group decisions—of the sort made by boards, product development groups, management teams—are often attributed to the failure to mix things up and question assumptions. Consensus is good, unless it is achieved too easily, in which case it becomes suspect. It seems that decisions reached through group dynamics require, above all, a dynamic group.

But comparable vitality and progress were evident two decades earlier at the Carnegie Institute of Technology in Pittsburgh. There, a group of distinguished researchers laid the conceptual—and in some cases the programming—foundation for computer-supported decision making. Cyert, and James March were among the CIT scholars who shared a fascination with organizational behavior and the workings of the human brain.

By the mids, transistors had been around less than a decade, and IBM would not launch its groundbreaking mainframe until But already scientists were envisioning how the new tools might improve human decision making. The collaborations of these and other Carnegie scientists, together with research by Marvin Minsky at the Massachusetts Institute of Technology and John McCarthy of Stanford, produced early computer models of human cognition—the embryo of artificial intelligence.

AI was intended both to help researchers understand how the brain makes decisions and to augment the decision-making process for real people in real organizations. Decision support systems, which began appearing in large companies toward the end of the s, served the latter goal, specifically targeting the practical needs of managers. In a very early experiment with the technology, managers used computers to coordinate production planning for laundry equipment, Daniel Power, editor of the Web site DSSResources.

Over the next decades, managers in many industries applied the technology to decisions about investments, pricing, advertising, and logistics, among other functions. But while technology was improving operational decisions, it was still largely a cart horse for hauling rather than a stallion for riding into battle. At the same time, a growing concern with risk led more companies to adopt complex simulation tools to assess vulnerabilities and opportunities. In the s, technology-aided decision making found a new customer: customers themselves.

The Internet, which companies hoped would give them more power to sell, instead gave consumers more power to choose from whom to buy. From our admiration for entrepreneurs and firefighters, to the popularity of books by Malcolm Gladwell and Gary Klein, to the outcomes of the last two U. Pragmatists act on evidence. Heroes act on guts. Gut decisions testify to the confidence of the decision maker, an invaluable trait in a leader. Gut decisions are made in moments of crisis when there is no time to weigh arguments and calculate the probability of every outcome.

They are made in situations where there is no precedent and consequently little evidence. Financier George Soros claims that back pains have alerted him to discontinuities in the stock market that have made him fortunes. Such decisions are the stuff of business legend. Decision makers have good reasons to prefer instinct. Henry Mintzberg explains that strategic thinking cries out for creativity and synthesis and thus is better suited to intuition than to analysis.

And a gut is a personal, nontransferable attribute, which increases the value of a good one. Readers can parse every word that Welch and Lutz and Rudolph Giuliani write. For example, in an investment decision-making situation, one is faced with the following question: What will the state of the economy be next year? Then, a typical representation of our uncertainty could be depicted as follows: Further Readings: Howson C.

Gheorghe A. Kouvelis P. Provides a comprehensive discussion of motivation for sources of uncertainty in decision process, and a good discussion on minmax regret and its advantages over other criteria. In such cases, the decision making depends merely on the decision-maker's personality type. Worse case scenario. Bad things always happen to me.

B 3 a Write min in each action row, S -2 b Choose max and do that action. Good things always happen to me. My decision should be made so that it is worth repeating. I should only do those things that I feel I could happily repeat. This reduces the chance that the outcome will make me feel regretful, or disappointed, or that it will be an unpleasant surprise. Regret is the payoff on what would have been the best decision in the circumstances minus the payoff for the actual decision in the circumstances.

Therefore, the first step is to setup the regret table: a Take the largest number in each states of nature column say, L. L - Xi,j. Limitations of Decision Making under Pure Uncertainty Decision analysis in general assumes that the decision-maker faces a decision problem where he or she must choose at least and at most one option from a set of options.

In some cases this limitation can be overcome by formulating the decision making under uncertainty as a zero-sum two-person game. In decision making under pure uncertainty, the decision-maker has no knowledge regarding which state of nature is "most likely" to happen. He or she is probabilistically ignorant concerning the state of nature therefore he or she cannot be optimistic or pessimistic.

In such a case, the decision-maker invokes consideration of security. Notice that any technique used in decision making under pure uncertainties, is appropriate only for the private life decisions. Moreover, the public person i. Otherwise, the decision-maker is not capable of making a reasonable and defensible decision.

You might try to use Decision Making Under Uncertainty JavaScript E-lab for checking your computation, performing numerical experimentation for a deeper understanding, and stability analysis of your decision by altering the problem's parameters. Further Readings: Biswas T. Martin's Press, Driver M. Brousseau, and Ph. Eiser J. Flin R. Ghemawat P.

Decision Making Under Risk Risk implies a degree of uncertainty and an inability to fully control the outcomes or consequences of such an action. Risk or the elimination of risk is an effort that managers employ. However, in some instances the elimination of one risk may increase some other risks. Effective handling of a risk requires its assessment and its subsequent impact on the decision process.

The decision process allows the decision-maker to evaluate alternative strategies prior to making any decision. The process is as follows: The problem is defined and all feasible alternatives are considered. The possible outcomes for each alternative are evaluated. Outcomes are discussed based on their monetary payoffs or net gain in reference to assets or time. Various uncertainties are quantified in terms of probabilities. The quality of the optimal strategy depends upon the quality of the judgments.

The decision-maker should identify and examine the sensitivity of the optimal strategy with respect to the crucial factors. In such cases, the problem is classified as decision making under risk. The decision-maker is able to assign probabilities based on the occurrence of the states of nature. Expected Payoff: The actual outcome will not equal the expected value.

What you get is not what you expect, i. Value B 0. Expected Opportunity Loss EOL : a Setup a loss payoff matrix by taking largest number in each state of nature column say L , and subtract all numbers in that column from it, L - Xij, b For each action, multiply the probability and loss then add up for each action, c Choose the action with smallest EOL.

Loss Payoff Matrix G 0. Since I don't know anything about the nature, every state of nature is equally likely to occur: a For each state of nature, use an equal probability i. Payoff Bonds 0. One important factor is the emotion of regret. This occurs when a decision outcome is compared to the outcome that would have taken place had a different decision been made. This is in contrast to disappointment, which results from comparing one outcome to another as a result of the same decision.

Accordingly, large contrasts with counterfactual results have a disproportionate influence on decision making. Regret results compare a decision outcome with what might have been. Therefore, it depends upon the feedback available to decision makers as to which outcome the alternative option would have yielded.

Altering the potential for regret by manipulating uncertainty resolution reveals that the decision-making behavior that appears to be risk averse can actually be attributed to regret aversion. There is some indication that regret may be related to the distinction between acts and omissions. Some studies have found that regret is more intense following an action, than an omission. For example, in one study, participants concluded that a decision maker who switched stock funds from one company to another and lost money, would feel more regret than another decision maker who decided against switching the stock funds but also lost money.

People usually assigned a higher value to an inferior outcome when it resulted from an act rather than from an omission. Presumably, this is as a way of counteracting the regret that could have resulted from the act. You might like to use Making Risky Decisions JavaScript E-lab for checking your computation, performing numerical experimentation for a deeper understanding, and stability analysis of your decision by altering the problem's parameters.

Further Readings: Beroggi G. George Ch. Rowe W. Krieger Pub. Suijs J. For example, consider the following decision problem a company is facing concerning the development of a new product: States of Nature High Sales Med. Sales Low Sales A 0. We will refer to these subjective probability assessments as 'prior' probabilities. However, the manager is hesitant about this decision. Based on "nothing ventured, nothing gained" the company is thinking about seeking help from a marketing research firm.

The marketing research firm will assess the size of the product's market by means of a survey. The manager has to make a decision as to how 'reliable' the consulting firm is. By sampling and then reviewing the past performance of the consultant, we can develop the following reliability matrix : 1.

What the Ap 0. These records are available to their clients free of charge. To construct a reliability matrix, you must consider the marketing research firm's performance records for similar products with high sales. Then, find the percentage of which products the marketing research firm correctly predicted would have high sales A , medium sales B , and little C or almost no sales.

Similar analysis should be conducted to construct the remaining columns of the reliability matrix. Note that for consistency, the entries in each column of the above reliability matrix should add up to one. In this example, what is the numerical value of P A A p? That is, what is the chance that the marketing firm predicts A is going to happen, and A actually will happen?

This important information can be obtained by applying the Bayes Law from your probability and statistics course as follows: a Take probabilities and multiply them "down" in the above matrix, b Add the rows across to get the sum, c Normalize the values i. Many managerial problems, such as this example, involve a sequence of decisions. When a decision situation requires a series of decisions, the payoff table cannot accommodate the multiple layers of decision-making.

Thus, a decision tree is needed. Do not gather useless information that cannot change a decision: A question for you: In a game a player is presented two envelopes containing money. He is told that one envelope contains twice as much money as the other envelope, but he does not know which one contains the larger amount. The player then may pick one envelope at will, and after he has made a decision, he is offered to exchange his envelope with the other envelope.

If the player is allowed to see what's inside the envelope he has selected at first, should the player swap, that is, exchange the envelopes? The outcome of a good decision may not be good, therefor one must not confuse the quality of the outcome with the quality of the decision. As Seneca put it "When the words are clear, then the thought will be also".

It utilizes a network of two types of nodes: decision choice nodes represented by square shapes , and states of nature chance nodes represented by circles. Construct a decision tree utilizing the logic of the problem. For the chance nodes, ensure that the probabilities along any outgoing branch sum to one. Calculate the expected payoffs by rolling the tree backward i. You may imagine driving your car; starting at the foot of the decision tree and moving to the right along the branches.

At each square you have control, to make a decision and then turn the wheel of your car. At each circle , Lady Fortuna takes over the wheel and you are powerless. Here is a step-by-step description of how to build a decision tree: Draw the decision tree using squares to represent decisions and circles to represent uncertainty, Evaluate the decision tree to make sure all possible outcomes are included, Calculate the tree values working from the right side back to the left, Calculate the values of uncertain outcome nodes by multiplying the value of the outcomes by their probability i.

On the tree, the value of a node can be calculated when we have the values for all the nodes following it. The value for a choice node is the largest value of all nodes immediately following it. The value of a chance node is the expected value of the nodes following that node, using the probability of the arcs. By rolling the tree backward, from its branches toward its root, you can compute the value of all nodes including the root of the tree.

Putting these numerical results on the decision tree results in the following graph: A Typical Decision Tree Click on the image to enlarge it Determine the best decision for the tree by starting at its root and going forward. Based on proceeding decision tree, our decision is as follows: Hire the consultant, and then wait for the consultant's report. If the report predicts either high or medium sales, then go ahead and manufacture the product.

Otherwise, do not manufacture the product. Clearly the manufacturer is concerned with measuring the risk of the above decision, based on decision tree. Coefficient of Variation as Risk Measuring Tool and Decision Procedure: Based on the above decision, and its decision-tree, one might develop a coefficient of variation C. V risk-tree, as depicted below: Coefficient of Variation as a Risk Measuring Tool and Decision Procedure Click on the image to enlarge it Notice that the above risk-tree is extracted from the decision tree, with C.

For example the consultant fee is already subtracted from the payoffs. From the above risk-tree, we notice that this consulting firm is likely with probability 0. Clearly one must not consider only one consulting firm, rather one must consider several potential consulting during decision-making planning stage. The risk decision tree then is a necessary tool to construct for each consulting firm in order to measure and compare to arrive at the final decision for implementation.

You may start with the following extreme and interesting cases by using this JavaScript for the needed computation: Consider a flat prior, without changing the reliability matrix. Consider a perfect reliability matrix i. Consider a perfect prior, without changing the reliability matrix. Consider a flat reliability matrix i. Consider the consultant prediction probabilities as your own prior, without changing the reliability matrix.

Influence diagrams: As can be seen in the decision tree examples, the branch and node description of sequential decision problems often become very complicated. At times it is downright difficult to draw the tree in such a manner that preserves the relationships that actually drive the decision. The need to maintain validation, and the rapid increase in complexity that often arises from the liberal use of recursive structures, have rendered the decision process difficult to describe to others.

The reason for this complexity is that the actual computational mechanism used to analyze the tree, is embodied directly within the trees and branches. The probabilities and values required to calculate the expected value of the following branch are explicitly defined at each node. Influence diagrams are also used for the development of decision models and as an alternate graphical representations of decision trees. The following figure depicts an influence diagram for our numerical example.

In the influence diagram above, the decision nodes and chance nodes are similarly illustrated with squares and circles. Arcs arrows imply relationships, including probabilistic ones. Finally, decision tree and influence diagram provide effective methods of decision-making because they: Clearly lay out the problem so that all options can be challenged Allow us to analyze fully the possible consequences of a decision Provide a framework to quantify the values of outcomes and the probabilities of achieving them Help us to make the best decisions on the basis of existing information and best guesses Visit also: Decision Theory and Decision Trees Further Readings Bazerman M.

Connolly T. Arkes, and K. Cooke R. Describes much of the history of the expert judgment problem. It also includes many of the methods that have been suggested to do numerical combination of expert uncertainties. Furthermore, it promotes a method that has been used extensively by us and many others, in which experts are given a weighting that judge their performance on calibration questions.

This is a good way of getting around the problem of assessing the "quality" of an expert, and lends a degree of objectivity to the results that is not obtained by other methods. Bouyssou D. Daellenbach H. Klein D. Thierauf R. Work they do not want to do themselves. Work they do not have time to do themselves.

All such work falls under the broad umbrella of consulting service. Regardless of why managers pay others to advise them, they typically have high expectations concerning the quality of the recommendations, measured in terms of reliability and cost. The following figure depicts the process of the optimal information determination.

The Determination of the Optimal Information Deciding about the Consulting Firm: Each time you are thinking of hiring a consultant you may face the danger of looking foolish, not to mention losing thousands or even millions of dollars. To make matters worse, most of the consulting industry's tried-and-true firms have recently merged, split, disappeared, reappeared, or reconfigured at least once. How can you be sure to choose the right consultants? Test the consultant's knowledge of your product.

It is imperative to find out the depth of a prospective consultant's knowledge about your particular product and its potential market. Ask the consultant to provide a generic project plan, task list, or other documentation about your product. Is there an approved budget and duration?

What potential customers' involvement is expected? Who is expected to provide the final advice and provide sign-off? Even the best consultants are likely to have some less-than-successful moments in their work history. Conducting the reliability analysis process is essential. Ask specific questions about the consultants' past projects, proud moments, and failed efforts.

Of course it's important to check a potential consultant's references. Ask for specific referrals from as many previous clients or firms with similar businesses to yours. Get a clearly written contract, accurate cost estimates, the survey statistical sample size, and the commitment on the completion and written advice on time. Further Reading Holtz H. Weinberg G. Revising Your Expectation and its Risk In our example, we saw how to make decision based on objective payoff matrix by computing the expected value and the risk expressed as coefficient of variation as our decision criteria.

You may like using Revising the Mean and Variance JavaScript to performing some numerical experimentation. You may apply it for validating the above example and for a deeper understanding of the concept where more than 2-sources of information are to be combined. Determination of the Decision-Maker's Utility Function We have worked with payoff tables expressed in terms of expected monetary value. Expected monetary value, however, is not always the best criterion to use in decision making.

The value of money varies from situation to situation and from one decision maker to another. Generally, too, the value of money is not a linear function of the amount of money. In such situations, the analyst should determine the decision-maker's utility for money and select the alternative course of action that yields the highest expected utility, rather than the highest expected monetary value.

Individuals pay insurance premiums to avoid the possibility of financial loss associated with an undesirable event occurring. However, utilities of different outcomes are not directly proportional to their monetary consequences. If the loss is considered to be relatively large, an individual is more likely to opt to pay an associated premium. If an individual considers the loss inconsequential, it is less likely the individual will choose to pay the associated premium.

Individuals differ in their attitudes towards risk and these differences will influence their choices. Therefore, individuals should make the same decision each time relative to the perceived risk in similar situations. This does not mean that all individuals would assess the same amount of risk to similar situations.

Further, due to the financial stability of an individual, two individuals facing the same situation may react differently but still behave rationally. An individual's differences of opinion and interpretation of policies can also produce differences. The expected monetary reward associated with various decisions may be unreasonable for the following two important reasons: 1. Dollar value may not truly express the personal value of the outcome. Expected monetary values may not accurately reflect risk aversion.

The gamble's outcome depends on the toss of a fair coin. Clearly, the second choice is preferred to the first if expected monetary reward were a reasonable criterion. Why do some people buy insurance and others do not? The decision-making process involves psychological and economical factors, among others. The utility concept is an attempt to measure the usefulness of money for the individual decision maker.

It is measured in 'Utile'. The utility concept enables us to explain why, for example, some people buy one dollar lotto tickets to win a million dollars. Therefore, in order to make a sound decision considering the decision-maker's attitude towards risk, one must translate the monetary payoff matrix into the utility matrix. The main question is: how do we measure the utility function for a specific decision maker? Consider our Investment Decision Problem.

By changing the value of p and repeating a similar question, there exists a value for p at which the decision maker is indifferent between the two scenarios. Suppose we find the following utility matrix: Monetary Payoff Matrix Utility Payoff Matrix A B C D A B C D 12 8 7 3 58 28 20 13 15 9 5 -2 30 18 0 7 7 7 7 20 20 20 20 At this point, you may apply any of the previously discussed techniques to this utility matrix instead of monetary in order to make a satisfactory decision.

Clearly, the decision could be different. Notice that any technique used in decision making with utility matrix is indeed very subjective ; therefore it is more appropriate only for the private life decisions. You may like to check your computations using Determination of Utility Function JavaScript, and then perform some numerical experimentation for a deeper understanding of the concepts. Utility Function Representations with Applications Introduction: A utility function transforms the usefulness of an outcome into a numerical value that measures the personal worth of the outcome.

The utility of an outcome may be scaled between 0, and , as we did in our numerical example, converting the monetary matrix into the utility matrix. This utility function may be a simple table, a smooth continuously increasing graph, or a mathematical expression of the graph. The aim is to represent the functional relationship between the entries of monetary matrix and the utility matrix outcome obtained earlier.

You may ask what is a function? What is a function? A function is a thing that does something. For example, a coffee grinding machine is a function that transforms the coffee beans into powder. A utility function translates converts the input domain monetary values into output range, with the two end-values of 0 and utiles. In other words, a utility function determines the degrees of the decision-maker sensible preferences.

This chapter presents a general process for determining utility function. The presentation is in the context of the previous chapter's numerical results, although there are repeated data therein. Utility Function Representations with Applications: There are three different methods of representing a function: The Tabular, Graphical, and Mathematical representation.

The selection of one method over another depends on the mathematical skill of the decision-maker to understand and use it easily. The three methods are evolutionary in their construction process, respectively; therefore, one may proceed to the next method if needed. The utility function is often used to predict the utility of the decision-maker for a given monetary value. The prediction scope and precision increases form the tabular method to the mathematical method.

Tabular Representation of the Utility Function: We can tabulate the pair of data D, U using the entries of the matrix representing the monetary values D and their corresponding utiles U from the utility matrix obtained already. The Tabular Form of the utility function for our numerical example is given by the following paired D, U table: Utility Function U of the Monetary Variable D in Tabular Form D 12 8 7 3 15 9 5 -2 7 7 7 7 U 58 28 20 13 30 18 0 20 20 20 20 Tabular Representation of the Utility Function for the Numerical Example As you see, the tabular representation is limited to the numerical values within the table.

One may apply an interpolation method: however since the utility function is almost always non-linear; the interpolated result does not represent the utility of the decision maker accurately. To overcome this difficulty, one may use the graphical method.

Graphical Representation of the Utility Function: We can draw a curve using a scatter diagram obtained by plotting the Tabular Form on a graph paper. Having the scatter diagram, first we need to decide on the shape of the utility function. The utility graph is characterized by its properties of being smooth, continuous, and an increasing curve. Often a parabola shape function fits well for relatively narrow domain values of D variable.

For wider domains, one may fit few piece-wise parabola functions, one for each appropriate sub-domain. For our numerical example, the following is a graph of the function over the interval used in modeling the utility function, plotted with its associated utility U-axis and the associated Dollar values D-axis.

Note that in the scatter diagram the multiple points are depicted by small circles. Reading a value from a graph is not convenient; therefore, for prediction proposes, a mathematical model serves best. Mathematical Representation of the Utility Function: We can construct a mathematical model for the utility function using the shape of utility function obtained by its representation by Graphical Method.

For wider domains, one may fit a few piece-wise parabola functions, one for each appropriate sub-domain. We know that we want a quadratic function that best fits the scatter diagram that has already been constructed. Therefore, we use a regression analysis to estimate the coefficients in the function that is the best fit to the pairs of data D, U.

The above mathematical representation provides more useful information than the other two methods. For example, by taking the derivative of the function provides the marginal value of the utility; i. Notice that for this numerical example, the marginal utility is an increasing function, because variable D has a positive coefficient; therefore, one is able to classify this decision- maker as a mild risk-taker. You might like to use Quadratic Regression JavaScript to check your hand computation.

For higher degrees than quadratic, you may like to use the Polynomial Regressions JavaScript. It allows the decision maker to examine the risk within its expected return, and identify the critical issues in assessing, limiting, and mitigating risk. This process involves both the qualitative and quantitative aspects of assessing the impact of risk. Decision theory does not describe what people actually do since there are difficulties with both computations of probability and the utility of an outcome.

Decisions can also be affected by people's subjective rationality and by the way in which a decision problem is perceived. Traditionally, the expected value of random variables has been used as a major aid to quantify the amount of risk. However, the expected value is not necessarily a good measure alone by which to make decisions since it blurs the distinction between probability and severity.

Of course, this is a subjective assessment. The following charts depict the complexity of probability of an event and the impact of the occurrence of the event, and its related risk indicator, respectively: From the previous section, you may recall that the certainty equivalent is the risk free payoff. Moreover, the difference between a decision maker's certainty equivalent and the expected monetary value EMV is called the risk premium.

We may use the sign and the magnitude of the risk premium in classification of a decision maker's relative attitude toward risk as follows: If the risk premium is positive, then the decision maker is willing to take the risk and the decision maker is said to be a risk seeker.

Clearly, some people are more risk-accepting than others: the larger is the risk premium, the more risk-accepting the decision-maker. If the risk premium is negative, then the decision-maker would avoid taking the risk and the decision maker is said to be risk averse. If the risk premium is zero, then the decision maker is said to be risk neutral.

Buying Insurance: As we have noticed, often it is not probability, but expectation that acts a measuring tool and decision-guide. Many decision cases are similar to the following: The probability of a fire in your neighborhood may be very small. But, if it occurred, the cost to you could be very great. Not only property but also your "dear ones", so the negative expectation of not ensuring against fire is so much greater than the cost of premium than ensuring is the best.

Further Readings Christensen C. Hammond J. Keeney, and H. Richter M. Wong, Computable preference and utility, Journal of Mathematical Economics , 32 3 , , Tummala V. The Discovery and Management of Losses In discovery and management of losses expressed in the monetary terms perception and measuring the chance of events is crucial. Losses might have various sources. These sources include Employees, Procedures, and External factors. Employees: Some employees may have concentration problem, insufficient knowledge, and engage in fraud.

Procedures: Some procedures are wrongly designed, or they are wrongly implemented. External factors: These include dependency on external unreliable services and suppliers, lack of security form external criminal activities, and finally disasters, such as strong earthquakes.

A rare or unexpected event with potentially significant consequences for decision-making could be conceived as a risk or an opportunity. The main concerns are: How to predict, identify or explain chance events and their consequences? How to assess, prepare for or manage them? A decision-maker who is engaged in planning, needs to adopt a view for the future, in order to decide goals, and to decide the best sequence of actions to achieve these goals by forecasting their consequences.

Unfortunately, the unlikeness of such events makes them difficult to predict or explain by methods that use historical data. However, focusing on the decision-maker's psychological-attitude factors and its environment is mostly relevant. The following figure provides a classification of the loss frequency function together with the ranges for the Expected, Unexpected, and the Stress, which must be determined by the decision-makers ability and resources.

The manager's ability to discover both unexpected and stress loss events and forecast their consequences is the major task. This is because, these event are very unlikely, therefore making them difficult to predict or explain. However, once a rare event has been identified, the main concern is its consequences for the organization. A good manager cannot ignore these events, as their consequences are significant.

For example, although strong earthquakes occur in major urban centers only rarely such earthquakes tend to have human and economic consequences well beyond that of the typical tremor. A rational public safety body for a city in an earthquake-prone area would plan for such contingencies even though the chance of a strong quake is still very small.

Further Readings Belluck D. Koller G. Hoffman D. Risk is the downside of a gamble, which is described in terms of probability. Risk assessment is a procedure of quantifying the loss or gain values and supplying them with proper values of probabilities. In other words, risk assessment means constructing the random variable that describes the risk. Risk indicator is a quantity describing the quality of the decision.

The expected value i. The expected value alone is not a good indication of a quality decision. The variance must be known so that an educated decision may be made. Have you ever heard the dilemma of the six-foot tall statistician who drowned in a stream that had an average depth of three feet?

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