... konulu sunumlar: "Financial Applications of Linear Programming"— Sunum transkripti:
1Financial Applications of Linear Programming Prof.Dr.Aydın Ulucan
2Multiperiod Cash Balancing A company forecasts monthly cash inflow and outflows as shown below for 2013.MonthCash Flow(000 TL)Jan.-120Jul.-70Feb.-100Aug.-20Mar.-80Sep.150Apr.Oct.120May.-40Nov.Jun.50Dec.450
3Multiperiod Cash Balancing In order to proceed the payments company should get credit.There are two types of credit optins: Long and short term.Long term credit might be taken in the beginning of 2013 January. Every month 2.5% interest is paid and the credit is paid back in January.Short term credits might be taken every month. Monthly credit interest rate is 3.75%.Every month, excess cash earns 1% interest.
4Multiperiod Cash Balancing Company would like to maximize its cash balance in January using linear programming approach.They also would like to develop the model that minimize the total payment to credit interest.There is TL cash in hand at the beginning of 2013 an at the and of each month company would like to have at least TL cash in hand.
7Bond PortfolioYou are holding hold a bond portfolio of four bonds, 100 units of each of them. You are considering rebalancing it. The bid and ask prices of the bonds are given in the table below.
8The cash payments of the bonds in the next three years are as follows. Cash on hand earns 5% interest. You want to rebalance the portfolio in such a way that at any time in the future your cash position will be at least as good as the position that would result from your current portfolio. How much money you can take out today under this condition?
10Pension FundsThe pension fund manager of the Association of Business Professors identified three reliable mutual funds, which have a long time successful record of operation: the Growth Fund, the Global Fund and the Income Fund. All these funds invest in four asset categories: U.S. large capitalization stocks, U.S. small capitalization stocks, foreign stocks and U.S. bonds, in proportions given in the following table.
11The table also shows an average annual return of these funds observed over a long time period. The pension fund offers to its participants a Balanced Package. The minimum and maximum investments of the package in each asset category package is given in the table below.The pension fund has 5 million dollars. How much should the manager invest in the Growth Fund, Global Fund and Income Fund to construct the package and to maximize the annual return?
13Pension Fund-Matching Bir şirket emeklilik fonunu yönetiyorsunuz. Fon her yıl başında aşağıda görülen ödemeleri yapmak zorunda.Ödeme20101120151820202520111220162020213020121420172120223120131520182220232014162019242024
14Bu ödemeleri bono satın alarak finanse etmek istiyorsunuz Bu ödemeleri bono satın alarak finanse etmek istiyorsunuz. Üç bono arasından portföy oluşturacaksınız.Bono 1. Maliyet $980, kupon ödemesi $60, 2015 ödeme $1060Bono 2. Maliyet $970, kupon ödemesi $65, 2021 ödeme $1065Bono 3. Maliyet $1050, kupon ödemesi $75, 2024 ödeme $10751 Ocak 2010’da bonoları satın alacak ve dolarlık ödemeyi yapacaksınız. Her yıl elinizdeki nakit %4 faiz kazanıyor arası nakit gereksinimini karşılamak için 2010’da almanız gereken bonoları minimize eden modeli kurunuz