Portfolio Management - Risk and Return

Portfolio Management - Risk and Return - Portfolio...

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1 Portfolio Management – Risk and Return Copyright Copyright © © 1996 1996 - - 2006 2006 Investment Analytics Investment Analytics
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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
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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%
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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
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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
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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 12
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Copyright © 1996-2006 Investment Analytics
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This document was uploaded on 11/04/2011 for the course ECON 421 at CUNY York.

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Portfolio Management - Risk and Return - Portfolio...

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