# Financial Applications of Linear Programming

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```					Financial Applications of Linear
Programming
Prof.Dr.Aydın Ulucan
Multiperiod Cash Balancing
 A company forecasts monthly cash inflow and outflows as
shown below for 2013.
Month     Cash Flow    Month      Cash Flow
(000 TL)                (000 TL)
Jan.      -120         Jul.       -70
Feb.      -100         Aug.       -20
Mar.      -80          Sep.       150
Apr.      -100         Oct.       120
May.      -40          Nov.       -70
Jun.      50           Dec.       450
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
2014 January.
 Short term credits might be taken every month. Monthly credit
interest rate is 3.75%.
 Every month, excess cash earns 1% interest.
Multiperiod Cash Balancing
 Company would like to maximize its cash balance in 2014
January using linear programming approach.
 They also would like to develop the model that minimize the
total payment to credit interest.
 There is 65000 TL cash in hand at the beginning of 2013 an
at the and of each month company would like to have at least
50000 TL cash in hand.
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)
Multiperiod Cash Balancing
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.
 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?
Excel Modeli
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.
 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?
Pension Fund-Matching

 Bir şirket emeklilik fonunu yönetiyorsunuz. Fon her yıl başında aşağıda
görülen ödemeleri yapmak zorunda.

Ödeme                   Ödeme                   Ödeme
2010        11       2015            18      2020           25
2011        12       2016            20      2021           30
2012        14       2017            21      2022           31
2013        15       2018            22      2023           31
2014        16       2019            24      2024           31
l Bu ödemeleri bono satın alarak finanse etmek istiyorsunuz. Üç bono arasından
portföy oluşturacaksınız.
l Bono 1. Maliyet \$980, 2011-2014 kupon ödemesi \$60, 2015 ödeme
\$1060
l Bono 2. Maliyet \$970, 2011-2020 kupon ödemesi \$65, 2021 ödeme
\$1065
l Bono 3. Maliyet \$1050, 2011-2023 kupon ödemesi \$75, 2024 ödeme
\$1075
l 1 Ocak 2010’da bonoları satın alacak ve 11000 dolarlık ödemeyi yapacaksınız.
Her yıl elinizdeki nakit %4 faiz kazanıyor. 2010-2024 arası nakit gereksinimini
karşılamak için 2010’da almanız gereken bonoları minimize eden modeli
kurunuz
Arbitraj Modeli

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