ࡱ> |~{z_ b6bjbj *5\5\.90 0    8DtD 5"!"|5555555695 #@ # #55)()()( #85)( #5)()(R1!4.h#3q55053v:$v:<4v:4 # #)( # # # # #55]& # # #5 # # # #v: # # # # # # # # #0 > n: Valuation of Debt Contracts and Their Price Volatility Characteristics Part b Please review these notes for next week. I will answer questions and go over highlights of these notes briefly next week. This set of the chapter 18 notes has two purposes. Apply the concepts of chapter 18 to a note that is between coupon dates. Gain a functional knowledge of your calculators and Excel. The following 3 pages provide information about a Treasury note that was issued on December 31, 2006 and matured on December 31, 2010. The Wall Street Journal quotes are for March 11, 2007. Our goal is to provide a set of detailed calculations for this note using all the concepts in Chapter 18. The difference between this note and the material typically used in textbooks is that we are not evaluating bonds only on their last coupon date. Our evaluation period is in-between coupon dates. This will mean that each of our calculations will need some adjustment. Outline of the questions we will answer. Determine the accrued interest for this note. If you bought this note today, what would you pay for this note? Include the quoted price and the accrued interest. If you sold this note today, what would you pay for this note? Using your time value of money (TVM) keys can you show how this notes price was obtained? Using the note function keys on your financial calculator can you calculate this notes price, accrued interest, and yield to maturity (YTM)? Using Excel can you calculate this notes price, accrued interest, and yield to maturity (YTM)? What is this notes nominal rate and its effective annual rate. Calculate this notes modified duration using the approximation method. Calculate this notes Macaulay duration and modified duration using the precise method. Using the information just calculated in question 9, calculate the percentage change in price and the dollar change in price for this note. Assume interest rates increase by 30 basis points. Compare your calculations of price changes in question 10 with the price that you obtain from a financial calculator using a yield-to-maturity that is 30 basis points higher. Calculate the percentage change and the dollar value change using convexity. Assume a YTM that is 30 basis points higher. Rewritten from the Wall Street Journal (3/11/07) RateMo/YrBidAskedChgAsk YldBond 1 6 1/8Dec 31, 2010n101.6875%101.75%.093755.60Bond 2 9 1/4Aug 15, 2007n101.5625%101.625% 5.36 1. Determine the accrued interest for this note. The accrued interest is equal to:  EMBED Equation.2  PAR = Par value of bond CPN = Annual coupon payment A = Number of days from the beginning of the coupon period to the settlement date (today) E = Number of days in coupon period in which the settlement date falls Accrued interest in dollars as a percent of par: Bond 1Bond 2Accrued Interest (%) EMBED Equation.2  =1.18439% EMBED Equation.2  0.61326%A=70 days from 12/31/06 to 3/11/07 E=181 days from 12/31/06 to 6/30/07 A=24 days from 2/15/07 to 3/11/07 E= 181 days from 2/15/07 to 8/15/07Accrued interest in dollars: Accrued Interest ($) EMBED Equation.2  =$11.8439 EMBED Equation.2  =$6.1326A=70 days from 12/31/06 to 3/11/07 E=181 days from 12/31/06 to 6/30/07 A=24 days from 2/15/07 to 3/11/07 E= 181 days from 2/15/07 to 8/15/07 2. If you bought this note today, what would you pay for this note? Include the quoted price and the accrued interest. Remember investors buy at the ask and sell at the bid price. Also when buying a bond you pay the quoted price plus accrued interest. Bond 1Bond 2Quoted Price (%)101.75%101.625%Accrued Interest (%) EMBED Equation.2  =1.18439% EMBED Equation.2  0.61326%A=70 days from 12/31/06 to 3/11/07 E=181 days from 12/31/06 to 6/30/07 A=24 days from 2/15/07 to 3/11/07 E= 181 days from 2/15/07 to 8/15/07Price Paid (% of par)102.9344%102.2383%Converting percents into price (par value is $1000)Price per note$1,029.34$1,022.38 3. If you sold this note today, what would you receive for this note? Remember investors buy at the ask and sell at the bid price. Also when selling a bond you receive the quoted price plus accrued interest. Bond 1 Bond 2Quoted Price (%)101.6875%101.5625%Accrued Interest (%) EMBED Equation.2  =1.18439% EMBED Equation.2  0.61326%A=70 days from 12/31/06 to 3/11/07 E=181 days from 12/31/06 to 6/30/07 A=24 days from 2/15/07 to 3/11/07 E= 181 days from 2/15/07 to 8/15/07Price Paid (% of par)102.8719%102.1758%Converting percents into price (par value is $1000)Price per note$1,028.72$1,021.76 The 0.0625% difference between the bid and the ask is the dealers revenue. This is separate from a brokerage commission that may be paid to a broker to contact the dealer. 4. Using your time value of money (TVM) keys can you show how this notes price was obtained? Finding the value of this bond, if the current interest rate for this risk class is known. Bond 1: 12/31/06 6/30/07 12/31/07 6/30/08 12/31/08 6/30/09 12/31/09 6/30/10 12/31/10 | | | | | | | | | 0 1 2 3 4 5 6 7 8 3.0625 3.0625 3.0625 3.0625 3.0625 3.0625 3.0625 3.0625 Coupon payments (%) 100 Maturity Value (%) Step 1: Find the value on the date of the last coupon payment (12/31/06) just after the coupon was paid. N 8 coupon semi-annual pmts till maturityI 5.60/2 = 2.80 semi-annual ratePV CptPMT 6.125/2 = 3.0625 semi-annual cpn pmt (as %)FV 100 the residual value (as %) -101.8583% (value on 12/31/2006) Step 2: Find the value today, 3/11/07. N 70/181= 0.38674 fraction of cpn period from last coupon (12/31/06)to today (3/11/07)I 5.60/2 = 2.80 semi-annual ratePV -101.8583PMT 0FV cpt (value 3/11/2007) 102.9529% Step 3: Find the quoted value by subtracting the accrued interest from the value in Step 2. 102.9529 1.18439 = 101.76851% = $1,017.69 Bond 2 This bond has no intermediate bond payments, so it can be valued as a lump sum, reducing one step. N (181-24) / 181= 0.8674 fraction period left till maturity (8/15/07) to today (3/11/07) I 5.36/2 = 2.68 semi-annual ratePV CptPMT 0FV 1000 + 1000*.0925/2 = 104.625 (% of par) 102.252 (ask + accrued interest) Step 2: Find the quoted value by subtracting the accrued interest from the value in the previous step. 102.252 0.61326 = 101.639% = $1,016.39 5. Using the bond function keys on your financial calculator can you calculate this notes price, accrued interest, and yield to maturity (YTM)? BAII PlusBAII PlusExcel2nd Bond2nd BondSTD 3-11-2007 Settlement date3.1107 ENTER (3.1107 ENTER (3/11/2007CPN Coupon6.125 ENTER (9.25 ENTER (.0925RDT Redemption date or maturity date12.3110 ENTER ( For date 12-31-20108.1507 ENTER ( For date 8-15-20078/15/07 RV Residual value I used as a percent.100 ENTER (100 ENTER (100360 Accounting year2nd SET ( will show ACT2nd SET ( will show ACT1= Actual/Actual2/Y payments per yr2nd SET ( Will show 2/Y2nd SET ( Will show 2/Y2= Semi-annualYLD Yield (calc)5.60 ENTER (5.36 ENTER (.0536 YIELDPRI Quote Price (calc)CPT =101.7676CPT =101.6348PRICE =101.6348AI Accrued interest (calc)CPT =1.1844CPT =0.6133ACCRINT =0.6133 Calculations using an HP12c HP12c Calculate PriceHP12c Calculate PriceHP12c Calculate Yieldf CLEAR FIN 5.60 i f CLEAR FIN 5.36 i f CLEAR FIN 101.75 PV6.125 PMT9.25 PMT6.125 PMTg M.DY 3.112007 ENTERg M.DY 3.112007 ENTERg M.DY 3.112007 ENTER12.3120108.15200712.152010f PRICE computes price of 101.7676f PRICE computes price of 101.6348f YTM computes price of 5.5906+ computes total price, including accrued interest 102.952+ computes total price, including accrued interest 102.2481Accrued interest 102.9520-101.7676 =1.1844Accrued interest 102.2481-101.6348 =0.6133 HP10Bs do not allow for bond calculations. Calculations using an HP17b HP17b Calculate PriceHP17b Calculate PriceHP17b Calculate YieldFIN Bond _ Clear Data FIN Bond _ Clear Data FIN Bond _ Clear Data Type ACTType ACTType ACTSemi ExitSemi ExitSemi Exit03.112007 Sett03.112007 Sett03.112007 Sett12.312010 Mat08.152007 Mat12.312010 Mat6.125 cpn%9.25 cpn%6.125 cpn% more more more5.6 yld%5.36 yld%101.75 pricePRICE computes price of 101.7676PRICE computes price of 101.6348YTM computes YTM of 5.5906+ computes total price, including accrued interest 102.952+ computes total price, including accrued interest 102.2481Accrued interest 102.9520-101.7676 =1.1844Accrued interest 102.2481-101.6348 =0.6133 6. Using Excel can you calculate this notes price, accrued interest, and yield to maturity (YTM)? Calculations using Excel (Excel insert: Please double click on this page to see the Excel sheet and use the function wizard to see the cell formulas.)  EMBED Excel.Sheet.5  7. What is this notes nominal rate and its effective annual rate. Bond 1 Nominal rate is 5.60 percent Effective annual rate is  EMBED Equation.3  Bond 2 Nominal rate is 5.36 percent Effective annual rate is  EMBED Equation.3  8. Calculate this notes modified duration using the approximation method. Using a Financial Calculator and our estimation formula: BAII PlusBAII PlusBAII PlusP0P+P-STD3-11-073-11-073-11-07CPN6.1256.1256.125RDT12-31-201012-31-201012-31-2010RV1001001003602nd set ACT2nd set ACT2nd set ACT2/Y2/Y2/Y2/YYLD5.605.705.50PRICPT=101.7676CPT=101.4259CPT=102.1107Macaulay Duration  EMBED Equation.2  Using Excel:  EMBED Excel.Sheet.5  Bond 2 Duration equals time to maturity. All cash flows occur at maturity. 157 days (0.4301 years) from 3/11/07 to 8/15/07. 9. Calculate this notes Macaulay duration and modified duration using the precise method. Double Checking our Duration Calculation: Method 1 for Calculating Exact Duration (recommended)  EMBED Excel.Sheet.5  Note: Since t is measured in 6-month periods, we use the semi-annual rate (equal to the YTM / 2). Method 2 for calculating exact Duration (alternative):  EMBED Excel.Sheet.5  Note: Since t is measured in 6-month periods, we use the semi-annual rate (equal to the YTM / 2). Method 3 for calculating exact Duration (alternative):  EMBED Excel.Sheet.5  Note: Since t is measured in years (instead of semi-annual periods), we must use the Effective Annual Rate in discounting. 10. Using the information just calculated in question 9, calculate the percentage change in price and the dollar change in price for this note. Assume interest rates increase by 30 basis points. Using the duration calculated in precise method:  EMBED Equation.2  (Price = -0.009980545 * 102.9520% = -1.0275% = -$10.28 Using the duration calculated in approximate method:  EMBED Equation.2  (Price = -0.01008 * 102.9520% = -1.0378% = -$10.38 11. Compare your calculations of price changes in question 10 with the price that you obtain from a financial calculator using a yield-to-maturity that is 30 basis points higher. BAII PlusBAII PlusSTD3-11-073-11-07CPN6.1256.125RDT12-31-201012-31-2010RV1001003602nd set ACT2nd set ACT2/Y2/Y2/YYLD5.605.90PRICPT=101.7676CPT=100.7467 101.7676% 100.7467% = 1.0209% = $10.21 reduction 12. Calculate the percentage change and the dollar value change using convexity. Duration:  EMBED Equation.2  Total Convexity:  EMBED Equation.2  Expected Price Change assuming +30 basis points :  EMBED Equation.2  (Price = -0.01 * 102.9520% = -1.02952% = -$10.30 reduction in price The convexity measurement is slightly better than the approximate of $10.38 found in part 10.     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Actual/365   $2 SMacaulay Duration =      2 S3.418729  !2 SMac Dur / (1+r/2)    $2 nModified Duration =      2 n3.325612  2 nr= 2 n3.325612  "System# n\ww 0w f -'- - -Q- @ !7Q-R- @ !6R-QQ- @ !Q-- @ !--'- -'#A ( F&Microsoft Office Excel 2003 WorksheetBiff8Excel.Sheet.89qOh+'08@Ph kencAdministratorMicrosoft Excel@8՜.+,0 PWorkbook;5SummaryInformation(HJ+DocumentSummaryInformation8/ _1440615235U'O F j*h0*h \p Administrator Ba==P(f!P <X@"1Arial1Arial1Arial1Arial1Arial1hArial1h>BCambria1,>BCalibri1>BCalibri1>BCalibri1BCalibri1BCalibri1BCalibri1>BCalibri1?BCalibri1 BCalibri1 BCalibri1 BCalibri1 BCalibri1BArial1BCalibri1BCalibri1 BCalibri1BCalibri"$"#,##0_);\("$"#,##0\)!"$"#,##0_);[Red]\("$"#,##0\)""$"#,##0.00_);\("$"#,##0.00\)'""$"#,##0.00_);[Red]\("$"#,##0.00\)7*2_("$"* #,##0_);_("$"* \(#,##0\);_("$"* "-"_);_(@_).))_(* #,##0_);_(* \(#,##0\);_(* "-"_);_(@_)?,:_("$"* #,##0.00_);_("$"* \(#,##0.00\);_("$"* "-"??_);_(@_)6+1_(* #,##0.00_);_(* \(#,##0.00\);_(* "-"??_);_(@_)                                                                      ff + ) , *     P  P       `            a8    " "    (@@  ( @  (@  ( ||F ㋎}-}; 00\);_(*}A}1 00\);_(*;_(@_) }A}2 00\);_(*?;_(@_) }A}3 00\);_(*23;_(@_) }-}4 00\);_(*}A}0 a00\);_(*;_(@_) }A}( 00\);_(*;_(@_) }A}7 e00\);_(*;_(@_) }}5 ??v00\);_(*̙;_(@_)    }}9 ???00\);_(*;_(@_) ??? ??? ??? ???}}) }00\);_(*;_(@_)    }A}6 }00\);_(*;_(@_) }}* 00\);_(*;_(@_) ??? ??? ??? ???}-}= 00\);_(*}x}800\);_(*;_(??? ??? ???}-}/ 00\);_(*}U}< 00\);_(*;_( }A}" 00\);_(*;_(}A} 00\);_(*ef;_(}A} 00\);_(*L;_(}A} 00\);_(*23;_(}A}# 00\);_(*;_(}A} 00\);_(*ef;_(}A} 00\);_(*L;_(}A} 00\);_(*23;_(}A}$ 00\);_(*;_(}A} 00\);_(*ef;_(}A} 00\);_(*L;_(}A} 00\);_(*23;_(}A}% 00\);_(*;_(}A} 00\);_(*ef;_(}A} 00\);_(*L;_(}A} 00\);_(*23;_(}A}& 00\);_(*;_(}A} 00\);_(*ef;_(}A} 00\);_(*L;_(}A}  00\);_(*23;_(}A}' 00\);_(* ;_(}A} 00\);_(*ef ;_(}A} 00\);_(*L ;_(}A}! 00\);_(*23 ;_( 20% - Accent1M 20% - Accent1 ef % 20% - Accent2M" 20% - Accent2 ef % 20% - Accent3M& 20% - Accent3 ef % 20% - Accent4M* 20% - Accent4 ef % 20% - Accent5M. 20% - Accent5 ef % 20% - Accent6M2 20% - Accent6  ef % 40% - Accent1M 40% - Accent1 L % 40% - Accent2M# 40% - Accent2 L湸 % 40% - Accent3M' 40% - Accent3 L % 40% - Accent4M+ 40% - Accent4 L % 40% - Accent5M/ 40% - Accent5 L % 40% - Accent6M3 40% - Accent6  Lմ % 60% - Accent1M 60% - Accent1 23 % 60% - Accent2M$ 60% - Accent2 23ٗ % 60% - Accent3M( 60% - Accent3 23֚ % 60% - Accent4M, 60% - Accent4 23 % 60% - Accent5M0 60% - Accent5 23 %! 60% - Accent6M4 60% - Accent6  23 % "Accent1AAccent1 O % #Accent2A!Accent2 PM % $Accent3A%Accent3 Y % %Accent4A)Accent4 d % &Accent5A-Accent5 K % 'Accent6A1Accent6  F %(Bad9Bad  %) Calculation Calculation  }% * Check Cell Check Cell  %????????? ???+ Comma,( Comma [0]-&Currency.. 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Warning Text %XTableStyleMedium9PivotStyleLight168 ``i̜̙3f3333f3ffff333ff333f33f33BBB\`,Sheet1:# MDURATION#DURATIONg SettlementMaturityCouponYieldFreq.BasisSemi- Actual/365Macaulay Duration =Modified Duration ==Mac Dur / (1+r/2)+ ),Zcc   dMbP?_*+%&A Page &P&?'?(?)?MHP LaserJet 5<C odhXLetterDINU"<" SMTJHP LaserJet 5InputBinOption1RESDLLUniresDLLOrientationPORTRAITResolutionOption1PaperSizeLETTEREconomodeOption1RETOption1HalftoneHT_PATSIZE_AUTODuplexNONEGraphicsModeHPGL2MODE"dhX??&U} >} >} >}  >} m>} $>} $ >@ > > > > > >?@?@@@@y&1?@@@?>>>> > > >>?>X㵎Y @)9$$$$$$B> B C > >?>#ښ @)9$$$$$$B A 5D#ښ @Dy&1??ESPTD.}>@ښښ7ggD X|  Indiana University _IUPUI Sheet1  Worksheets*F! _1009689684LFFO',  FMicrosoft Excel 2003 WorksheetOle 4:PIC LN5LMETA *PRINTMQ       !"#$%&'PQ+,-./0123456789:;<=>?@ABCDEFGHIJKLMNORxyTUVWXYZ[\]^_`abcdefghjklmnopqrstuvw|}~FFO \    ,V,,,V,,,,V,VVVVVV,V,V,V,,,V,,,,,,,,,V,,,,,,,,V,,V,VV,V,V,V,,,,V,,,,,,,V,,,,,,,V,,,,V,VVVVVV,V,,VV,V,V,V,VVV,VVVVVVVVVVVV,VVVVVVV,VVVVVVV,VVVVVV,V,,,V,,,,V,VVVVVV,V,V,V,V,,,V,,,,V,VVVVVV,V,V,V,V,,,V,,,,V,VVVVVV,V,V,V%%%,,,444<<<DDDMMMVVV___iiirrr}}}45'  ' -  -- !-- !-'-  -- !-88- !8-TT- !T-pp- !p-- !-- !-- !-- !-- !-- !-11- !1-LL- !L-gg- !g-- !-- !-- !-- !-- !-  - ! -%%- !%-@@- !@-[[- ![-vv- !v-- !-- !-- !-- !-- !-``- !`-- !-  - ! -- !-&&- !&-tt- !t-- !-  ! !s !9 !89% !sq !t !t7 !S! !o- '- !  !$-'- ! !-'- Arial 2b~wk~wWw 2 --"System  -'-- Arial +b~wk~wWw + - Arial Sb~wk~wWw S - -    !_ !a ! ! ! !! ! ! !% !' a2 <Wall Street Journal Quote 3/11/98: (Understanding Duration)                2 6.125%  2 dDec 01n  2 101:22  2 $101:24  2  +3 2 45.60%  2 ;Maurity  2 ;i12/15/01   2 ;fEFF0 2 ;5.68%  2 WToday 2 Wu3/11/981     !q_ !qa $2 sCalculate Duration:        2 t 2 CF  Arial 2b~wk~wWw 2 -- --'- -  -- --  2 3PV(CF)  - 2 x#- 2 PV*t --'- -   2 6/15/98   2 96 2 30.625  2 E$30.18  2 2,897.60   2  02  2 12/15/98   2 2791 2 30.625  2 E$29.36  2 8,191.16   2  62  2 6/15/996   2 4615 2 30.625  2 E$28.56  2  13,166.86   2  62  32 12/15/99   2 6441 2 30.625  2 E$27.78  2  17,891.27   2  12  2 6/15/00   2 8275 2 30.625  ,2 E$27.02  ,2  22,347.80   ,2  72  F2 4 12/15/00   2 41010 2 430.625  G2 4E$26.28  G2 4 26,547.56   G2 4 72 4 2 O6/15/01   2 O1192 2 O30.625  b2 OE$25.57  b2 O 30,480.30   b2 O 02 O 62 j 12/15/01   2 j1375 2 j1030.63  }2 j9$837.03  }2 j 1,150,917.75    2 j 2 ' $1,031.79.   2  1,272,440.30    2    !_ !a ! ! ! !! 92 !t is based on a 365 day year         !_ !a ! ! ! !! ! ! O2 0# Used the effective rate to be most precise              --'- -    2  Duration =    --'- -   2 31,233.23   1 2 + 32 1  2 Days  2 ]3.38  [2 + 2 [ F2 Years   2 Excel   2 ]3.38  [2 + 2 [ 2 Years     !&_ !&a 2 (Accrued Interest       !A !A 2 CdLast Coupon Date    2 C:12/15/97     !\ !\ !\ !\! -2 ^dPrice from Duration Table       q2 ^1,031.79   q2 ^$ 2 ^ 6  !w !w !w !w! -2 yd Less Accrued Interest      2 y14.43e  2 y 2 y   ! ! 2 d Quoted Price   2 1,017.36   2 $ 2   2 G101:  2 24 2    ! ! ! !! 32 dPrice Calculated using Excel         2 1,017.49   2 $ 2  F  ! ! !% !'--'- -  t!  92 $!which matches the WSJ quote price          --'- -  -  -4 'XR _d  *')  '' ' 8')' (')' (')' (') Arial- d2 5>Wall Street Journal Quote 3/11/2007: (Understanding Duration);;JJYJJY;JJJJJJJJYYJ;JYJ;Y2 h}6.125%J2 h^Dec 10nJZ2 hU 101.6875JZF 2 h  JJ 2 hF  JZ 2 h101.7500JZs2 h JJJJJJ 2 hs J2 hF0.09375J2 h$$5.60%J2 5MaurityY;J2 / 12/31/2010JJ2 5Today2  3/11/2007JJ2 R5Last Coupon DateJJJJ2 R/ 12/31/2006JJ Arial-2 ! Col. for JJJYhJ--2 5Calculate Exact Duration:;;JJJJYJ;J-2 ' convexity onlyJYJJ- 2 q tJ 2 q CFN Arial--"Systemt (/ttB 4/-'-  ): ---- 2 h PV(CF)YY- 2 6 t#c-- 2 q PV*thJ2 q o! PV*t*(t+1)hJhYJY-'- (') 2 d 6/30/2007JJ 2 k 12 30.625J 2 $29.79J 2 29.79J 2  JJJJJJJJJJ 2  J &2 $$59.58J #2 JJJJJJJJJJJ 2 # J2   12/31/2007JJ 2  k 22  30.625J 2  $28.98J 2  57.96J 2   JJJJJJJJJJ 2   J &2  #173.88J U#2  JJJJJJJJJ 2  U# J2 O d 6/30/2008JJ 2 O k 32 O 30.625JA 2 O $28.19JA2 O 84.57JA2 O  JJJJJJJJJJ 2 O  JA&2 O #338.28JAU#2 O JJJJJJJJJ 2 O U# J2  12/31/2008JJ 2 k 42 30.625J 2 $27.42J2 109.69Jf2  JJJJJJJJ 2 f J&2 #548.45JU#2  JJJJJJJJJ 2 U# J2 d 6/30/2009JJ 2 k 52 30.625J 2 $26.68J2 133.38Jf2  JJJJJJJJ 2 f J&2 #800.26JU#2  JJJJJJJJJ 2 U# J2 - 12/31/2009JJ 2 -k 62 -30.625J 2 -$25.95J2 -155.69Jf2 - JJJJJJJJ 2 -f J&2 -"1,089.85JJw"2 -  JJJJJJ 2 -w" J2 wd 6/30/2010JJ 2 wk 72 w30.625Ji 2 w$25.24Ji2 w176.69Jif2 w JJJJJJJJ 2 wf Ji&2 w"1,413.55JJiw"2 w  JJJJJJ 2 ww" J2  12/31/2010JJ 2 k 82  1030.625J 2 H$826.33J2 6,610.67JJ2  JJJJJ 2  J&2 " 59,496.07JJ! 2   JJJJ 2 ! J 2 j $1,018.58JJ2 7,358.45JJ2  JJJJJ 2  J&2 " 63,919.92JJ! 2   JJJJ 2 ! J32 U5t is semi-annual periodsJJJJJJJ;J;Y;JY;<2 5## Used the 6 month rate (YTM/2)JJJJJJJJJJJYJJYJYo  2 }7.22Jo2 } JJJJJJJJJJJJJJ 2 } J$2 }Semi-annual periods;Y;JY;---'- )-- 2 5Duration as ofYJ;JJJ-!2  last coupon dateJJYJJY- 2 @ isJ;--  2 3.61J2  JJJJJJJJJJJJJJ 2  J2 YearsY-'- (')- 32 5Adjusting Duration for today.JYJJhYJJYhJYJ-62 Subtract last coupon from todayJYJJ;JJJJYJJM  2 [0.19JM 2 [ JJJJJJJJJJJJJJ 2 [ J72 [ =70/365=(3/11/98 - 12/31/97)/365JYJJJYJJJYJ-'- !)  <2 5#Exact Duration (as of Trading Date)JJYJ;JYJJJY;JJY 2 is;---!  2 3.42J!2  JJJJJJJJJJJJJJ 2  J-2 Years (Macaulay Duration)hJYJJhYJY-'- (')- !2 "B Excel calculation;J;;J;"  2 "3.42J"2 " JJJJJJJJJJJJJJ 2 " J-2 "Years (Macaulay Duration)YJY;JYJ;Y-02 Q#5Total Convexity CalculationYJJJYJJJYJ-% 2 $ 59.38J% 2 $ JJJJ 2 $ J$2 $Y semi-annual periods;Y;JY;-%2 $14.85J%2 $ JJJJJJJJJJ 2 $ J-2 $b yearly convexityY;J;J-'- )')-  @ ! 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Warning Text %XTableStyleMedium9PivotStyleLight168 ``i̜̙3f3333f3ffff333ff333f33f33BBB\`~3Sheet1:#DURATION 8{MaurityTodaytCFPV(CF)#PV*tYearsLast Coupon DateSemi-annual periodst is semi-annual periods## Used the 6 month rate (YTM/2)Adjusting Duration for today.Subtract last coupon from todayExcel calculationYears (Macaulay Duration) =70/365=(3/11/98 - 12/31/97)/365 PV*t*(t+1)semi-annual periodsyearly convexityTotal Convexity Calculationconvexity only Col. for Dec 10n>Wall Street Journal Quote 3/11/2007: (Understanding Duration)Calculate Exact Duration:"Duration as of last coupon date is%Exact Duration (as of Trading Date)is#"0 1Y1J2cc g2  dMbP?_*+%&A Page &P&?'?(?)?MAdobe PDF (redirected 1)C odhXLetterPRIV ''''0\KhCFFSMTJAdobe PDF ConverterResolution1200dpiPageSizeLetterPageRegionLeadingEdgeInputSlotOnlyOne0EBDAStandard"dhX??&U} @}  @} @} I@} I@} m@} @} @}  @  HHH H       @@@@@@@~ A@ B!blY@ e !bpY@ e ~ P?Cy&1?@ [ \\~ ]@ RHH F HH~ S@ HHH D EE~ T@@ HHHFHOHH aH FHHHH aHF G G G G GHI+@H?$H>@D1Juuu=@DDDB8"Kuuu=@ DD-NuuuM@DDDH IB@H@$ H>@D1 J) <@DD D B8" K) L@ D D - N7 e@D D D  H IY@H@$ H>@D1 J0<@DD D B8" KГh;$U@ D D - NГh;$u@D D D  H Ip@H@$ H>@D1 JX(l;@DD D B8" KX(l[@ D D - N79ʐ#@D D D  H I@@H@$ H>@D1 JJâV:@DD D B8" K%V`@ D D - N8@D D D  H I@@H@$ H>@D1 JMi9@DD D B8" K'+vc@ D D - N-Sf@D D D  HI@H@$H>@D1Jb=9@DDDB8"KFt7f@ DD-NFt7@DDDHI@H @(H@D1L'҉@DDDB8"M'ҹ@ DD-Z @DDDH FHH#JvIԏ@ %#KLvxr@ %#KS5@ %H F HHJKHH F HHJKHHFHHJKHH@HHJKHH FHQ"Np2^@ DD H HH F HH Np2^ @ D H HH V HHN H HH FHH'NĈ#F?DDm W HH F HH"Xs\ @ DD Y UH HH Q ;NX㵎Y @%9$$$$B H HH ^@@@@@@@6_|eaa߰M@ DDD @@ `|eaa߰-@ D @@>0$:::,8Z$$R\:W^w$>@߰ڰ 7ggD DocumentSummaryInformation8> _1440615166Y F0*h0*hOle C:PIC VXDLIndiana University _IUPUI Sheet1  Worksheets*F! _1174726309LFFO',  FMicrosoft Excel 2003 WorksheetBiff8Excel.Sheet.89qMETA S*PRINTW[iCompObjFkObjInfoZ]HFFO \    ,V,,,V,,,,V,VVVVVV,V,V,V,,,V,,,,,,,,,V,,,,,,,,V,,V,VV,V,V,V,,,,V,,,,,,,V,,,,,,,V,,,,V,VVVVVV,V,,VV,V,V,V,VVV,VVVVVVVVVVVV,VVVVVVV,VVVVVVV,VVVVVV,V,,,V,,,,V,VVVVVV,V,V,V,V,,,V,,,,V,VVVVVV,V,V,V,V,,,V,,,,V,VVVVVV,V,V,V%%%,,,444<<<DDDMMMVVV___iiirrr}}}45'  ' -  -- !-- !-'-  -- !-88- !8-TT- !T-pp- !p-- !-- !-- !-- !-- !-- !-11- !1-LL- !L-gg- !g-- !-- !-- !-- !-- !-  - ! -%%- !%-@@- !@-[[- ![-vv- !v-- !-- !-- !-- !-- !-``- !`-- !-  - ! -- !-&&- !&-tt- !t-- !-  ! !s !9 !89% !sq !t !t7 !S! !o- '- !  !$-'- ! !-'- Arial 2b~wk~wWw 2 --"System  -'-- Arial +b~wk~wWw + - Arial Sb~wk~wWw S - -    !_ !a ! ! ! !! ! ! !% !' a2 <Wall Street Journal Quote 3/11/98: (Understanding Duration)                2 6.125%  2 dDec 01n  2 101:22  2 $101:24  2  +3 2 45.60%  2 ;Maurity  2 ;i12/15/01   2 ;fEFF0 2 ;5.68%  2 WToday 2 Wu3/11/981     !q_ !qa $2 sCalculate Duration:        2 t 2 CF  Arial 2b~wk~wWw 2 -- --'- -  -- --  2 3PV(CF)  - 2 x#- 2 PV*t --'- -   2 6/15/98   2 96 2 30.625  2 E$30.18  2 2,897.60   2  02  2 12/15/98   2 2791 2 30.625  2 E$29.36  2 8,191.16   2  62  2 6/15/996   2 4615 2 30.625  2 E$28.56  2  13,166.86   2  62  32 12/15/99   2 6441 2 30.625  2 E$27.78  2  17,891.27   2  12  2 6/15/00   2 8275 2 30.625  ,2 E$27.02  ,2  22,347.80   ,2  72  F2 4 12/15/00   2 41010 2 430.625  G2 4E$26.28  G2 4 26,547.56   G2 4 72 4 2 O6/15/01   2 O1192 2 O30.625  b2 OE$25.57  b2 O 30,480.30   b2 O 02 O 62 j 12/15/01   2 j1375 2 j1030.63  }2 j9$837.03  }2 j 1,150,917.75    2 j 2 ' $1,031.79.   2  1,272,440.30    2    !_ !a ! ! ! !! 92 !t is based on a 365 day year         !_ !a ! ! ! !! ! ! O2 0# Used the effective rate to be most precise              --'- -    2  Duration =    --'- -   2 31,233.23   1 2 + 32 1  2 Days  2 ]3.38  [2 + 2 [ F2 Years   2 Excel   2 ]3.38  [2 + 2 [ 2 Years     !&_ !&a 2 (Accrued Interest       !A !A 2 CdLast Coupon Date    2 C:12/15/97     !\ !\ !\ !\! -2 ^dPrice from Duration Table       q2 ^1,031.79   q2 ^$ 2 ^ 6  !w !w !w !w! -2 yd Less Accrued Interest      2 y14.43e  2 y 2 y   ! ! 2 d Quoted Price   2 1,017.36   2 $ 2   2 G101:  2 24 2    ! ! ! !! 32 dPrice Calculated using Excel         2 1,017.49   2 $ 2  F  ! ! !% !'--'- -  t!  92 $!which matches the WSJ quote price          --'- -  -  -4 'XR Qd  ')  '' '  ')' ')' ')' ') Arial- d2 5>Wall Street Journal Quote 3/11/2007: (Understanding Duration);;JJYJJY;JJJJJJJJYYJ;JYJ;Y2 h}6.125%J2 h^Dec 10nJZ2 hU 101.6875JZF 2 h  JJ 2 hF  JZ 2 h101.7500JZs2 h JJJJJJ 2 hs J2 hF0.09375J2 h$$5.60%J2 5MaurityY;J2 / 12/31/2010JJ2 5Today2  3/11/2007JJ2 R5Last Coupon DateJJJJ2 R/ 12/31/2006JJ Arial-2 !Col. forJJJYh-+2 5Calculate Exact Duration;;JJJJYJ;-2 ' convexity onlyJYJJ- 2 q tJ 2 q CFN Arial--"Systemtx (/ttB 4/-'-  ): ---- 2 h PV(CF)YY- 2 6 t#c-- 2 q PV*thJ2 q o! PV*t*(t+1)hJhYJY-'- ') 2 d 6/30/2007JJ2 0.608219J2 30.625J 2 $30.11J 2 18.32J 2  JJJJJJJJJJ 2  J &2 $$29.46J #2 JJJJJJJJJJJ 2 # J2   12/31/2007JJ2  1.616438J2  30.625J 2  $29.29J 2  47.34J 2   JJJJJJJJJJ 2   J &2  #123.87J U#2  JJJJJJJJJ 2  U# J2 O d 6/30/2008JJ2 O 2.613699J2 O 30.625JA 2 O $28.49JA2 O 74.47JA2 O  JJJJJJJJJJ 2 O  JA&2 O #269.11JAU#2 O JJJJJJJJJ 2 O U# J2  12/31/2008JJ2 3.621918J2 30.625J 2 $27.71J2 100.36Jf2  JJJJJJJJ 2 f J&2 #463.87JU#2  JJJJJJJJJ 2 U# J2 d 6/30/2009JJ2 4.613699J2 30.625J 2 $26.96J2 124.39Jf2  JJJJJJJJ 2 f J&2 #698.30JU#2  JJJJJJJJJ 2 U# J2 - 12/31/2009JJ2 -5.621918J2 -30.625J 2 -$26.22J2 -147.41Jf2 - JJJJJJJJ 2 -f J&2 -#976.16JU#2 - JJJJJJJJJ 2 -U# J2 wd 6/30/2010JJ2 w6.613699J2 w30.625Ji 2 w$25.51Ji2 w168.73Jif2 w JJJJJJJJ 2 wf Ji&2 w"1,284.69JJiw"2 w  JJJJJJ 2 ww" J2  12/31/2010JJ2 7.621918J2  1030.625J 2 H$835.01J2 6,364.36JJ2  JJJJJ 2  J&2 " 54,872.95JJ! 2   JJJJ 2 ! J 2 j $1,029.31JJ2 7,045.39JJ2  JJJJJ 2  J&2 " 58,718.40JJ! 2   JJJJ 2 ! J32 U5t is semi-annual periodsJJJJJJJ;J;Y;JY;<2 5## Used the 6 month rate (YTM/2)JJJJJJJJJJJYJJYJY12 35Caculation of Exact Duration;J;JJJJJYJ;$2 }pMacaulay Duration =;JYJ;Jo  2 }6.84Jo2 } JJJJJJJJJJJJJJ 2 } J$2 }Semi-annual periods;Y;JY;  2 3.42J2  JJJJJJJJJJJJJJ 2  J2 YearsY!2 B Excel calculation;J;;J;  2 3.42J2  JJJJJJJJJJJJJJ 2  J-2 Years (Macaulay Duration)YJY;JYJ;Y-02 [5Total Convexity CalculationYJJJYJJJYJ-! 2 53.98J! 2  JJJJ 2  J$2 Y semi-annual periods;Y;JY;-!2 13.50J!2  JJJJJJJJJJ 2  J-2 b yearly convexityY;J;J-'- ')-  @ ! N @ !V n4' @ !  @ ! <'N @ ! <' @ ! -1E'- @ !1--'- ')-'- '),') ---'Oh+'08@Pl kencCarow, Kenneth A.Microsoft Excel@՜.+,0 PX|  Indiana University _IUPUI Workbook{HSummaryInformation(\^IDocumentSummaryInformation8M _1440615510c F0*h@*h.$% g2\pCarow, Kenneth A. 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