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Portfolio Management - Risk and Return

# Portfolio Management - Risk and Return - Portfolio...

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Copyright © 1996-2006 Investment Analytics Portfolio Management – Risk & Return Slide: 2 Time Value of Money Simple vs compound interest Daycount methods Discounting principles
Copyright © 1996-2006 Investment Analytics Portfolio Management – Risk & Return Slide: 3 Time Value of Money Basic principle Money received today is different from money received in the future This difference in value is called the time value of money When we borrow or lend, this difference is reflected by the interest rate

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Copyright © 1996-2006 Investment Analytics Portfolio Management – Risk & Return Slide: 4 Time Value of Money Example: I lend you 100 today but you have to pay me back 110 in one year interest rate is 10% Meaning: 110 in one year has the same value as 100 today or: the 1-year interest rate is 10%
Copyright © 1996-2006 Investment Analytics Portfolio Management – Risk & Return Slide: 5 Present and Futures Value 110 is the future value of 100 today 100 is the present value of 110 in 1 year’s time Meaning: 110 in one year has the same value as 100 today or: the 1-year interest rate is 10%

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Copyright © 1996-2006 Investment Analytics Portfolio Management – Risk & Return Slide: 6 Compound Interest Example Suppose interest rate = 10% and I have \$100 to invest What will I get in 1 year time? Simple answer: \$110 \$100 x (1 + 0.1) = \$110 Complex answer: depends on how compute interest By computing interest more frequently I can earn more than \$110
Copyright © 1996-2006 Investment Analytics Portfolio Management – Risk & Return Slide: 7 Compounding Suppose interest is calculated every 6 months After 6 months, I get interest how much: (1/2)(\$100 x 0.1) = \$5 this is (1/2) a year’s interest now, my account balance is \$105. At the end of the year, I earn interest for the second half of the year on \$105 how much: (1/2)(\$105 x 0.1) = \$5.25 Now I have \$110.25 I made \$0.25 extra!

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Copyright © 1996-2006 Investment Analytics Portfolio Management – Risk & Return Slide: 8 Compound Interest The extra bit is the “interest on the interest” 10% applied for six months on \$5 (1/2)(\$5*0.1) = \$0.25 This is called compounding If you are a lender, compounding more frequently is better If you are a borrower, you don’t like compounding
Copyright © 1996-2006 Investment Analytics Portfolio Management – Risk & Return Slide: 9 Compounding Frequency So you have to be careful to take account of how frequently interest is compounded annually: r applied once semi-annually: r/2 applied every 6 months quarterly: r/4 applied every 3 months daily: r/365 applied every day “continuously”: applied at every instant of time! how does this work?

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Copyright © 1996-2006 Investment Analytics Portfolio Management – Risk & Return Slide: 10 Compounding over Multiple Periods Initially invest P 0 , at interest rate r, for n periods Compound by (1+r/n) each period: P 0 P 0 (1+r/n) P 0 (1+r/n)(1+r/n) = P 0 (1+r/n) 2 0 1 2
Copyright © 1996-2006 Investment Analytics Portfolio Management – Risk & Return Slide: 11 Compounding over Multiple Periods Year Investment Compound Future Factor Value 1 P 0 (1+r/n) P 0 (1+r/n) 2 P 0

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Portfolio Management - Risk and Return - Portfolio...

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