Financial Applications of Linear Programming

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1 Financial Applications of Linear Programming
Prof.Dr.Aydın Ulucan

2 Multiperiod Cash Balancing
A company forecasts monthly cash inflow and outflows as shown below for 2013. Month Cash Flow (000 TL) Jan. -120 Jul. -70 Feb. -100 Aug. -20 Mar. -80 Sep. 150 Apr. Oct. 120 May. -40 Nov. Jun. 50 Dec. 450

3 Multiperiod 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.

4 Multiperiod 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.

5 Multiperiod Cash Balancing
ND(t)= ND(t-1)+ FaizGeliri(t-1) +AlınanBorç(t) + NakitGirişi(t) – UDönemBorçFaiziÖdeme(t) - KDönemBorçFaiziÖdeme(t-1) – UDönemKrediGeriÖdemesi (Ocak2011) – KDönemKrediGeriÖdemesi(t-1)

6 Multiperiod Cash Balancing

7 Bond Portfolio You 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.

8 The 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?

9 Excel Modeli

10 Pension Funds The 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.

11 The 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?

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13 Pension Fund-Matching
Bir şirket emeklilik fonunu yönetiyorsunuz. Fon her yıl başında aşağıda görülen ödemeleri yapmak zorunda. Ödeme 2010 11 2015 18 2020 25 2011 12 2016 20 2021 30 2012 14 2017 21 2022 31 2013 15 2018 22 2023 2014 16 2019 24 2024

14 Bu 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 $1060 Bono 2. Maliyet $970, kupon ödemesi $65, 2021 ödeme $1065 Bono 3. Maliyet $1050, kupon ödemesi $75, 2024 ödeme $1075 1 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

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16 Arbitraj Modeli