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Text File | 1992-02-17 | 26.4 KB | 630 lines

GENERAL YieldBook (YB) is a shareware program that computes prices and yields for bonds to maturity and to the call according to the formulae and methods presented in "Standard Securities Calculation Methods", by Spence, Graudenz and Lynch, published by the Securities Industry Association in 1973 and according to Rule G-33 of the Municipal Securities Rulemaking Board. Calculations are made using either the municipal or corporate bond mode of 30/360 days or the government bond mode of actual days/actual days. The mode being used shows on the screen. YieldBook Version 1.2 properly computes prices and yields for bonds with maturities greater than 6 months including zero coupon bonds. OPERATION YB is simple to use. To begin YieldBook enter "YB" at the prompt. To print this file enter "copy YB.DOC prn" at the prompt. All entries are made from the data entry display in the upper right corner of the screen. After the entry is complete press the appropriate highlighted key to store the data. Use the backspace key to correct errors before pressing the applicable data storage key. YieldBook will validate all date entries and make sure other entries are reasonable. All data storage keys can be either upper or lower case. SETTLEMENT DATE: The Settlement Date is automatically computed to seven (7) calendar days after the current date in your computer. This is usually the regular settlement date. To change the settlement date simply enter the date you wish to use in the format "mm/dd/yy" or "mm-dd-yy" and press the "S" key. The same formats are used for entering all dates. CALC PRICE: Enter bond coupon as a percent (i.e., enter 4 1/2% as 4.50 - not .045) and press "C". Enter the maturity date and press "M". Enter the yield (as a percent) for the bond and press "Y". The bond price is calculated by pressing F1. CALC YIELD: Enter bond coupon as a percent and press "C". Enter the maturity date and press "M". Enter the price for the bond and press "P". Bond yield is calculated by pressing F2. -1- CALC PRICE-TO-CALL: Enter bond coupon as a percent and press "C". Enter the call date and press "D". Enter the call price (not the call premium; i.e 102 is the call price when 2% is the call premium) and press "r". Enter the yield for the bond and press "Y". Price-to-call is calculated by pressing F3. CALC YIELD-TO-CALL: Enter bond coupon as a percent and press "C". Enter the call date and press "D". Enter the call price and press "r". Enter the price for the bond and press "P". Yield-to-call is calculated by pressing F4. INTEREST ACCRUED DATE: The Interest Accrued Date is automatically calculated when a Maturity is entered. You need not change it unless you are working with a bond with an odd (long or short) first coupon period. The user can only access the Interest Accrued Date in the "Mun" calculation mode. When in the "Gov" calculation mode the Interest Accrued Date will be a date that is exactly 6 months before the next interest payment date. YB CALCULATIONS FOR "ODD" FIRST PERIODS DO NOT AGREE WITH RESULTS FROM OTHER CALCULATORS USED IN THE SECURITIES INDUSTRY. SEE "DISCUSSION OF ODD FIRST PERIODS". RESULTS: Results are computed by pressing the applicable function key. The answer is then shown in a blinking field. When new data is entered the field stops blinking. THE ANSWER SHOWN IS ONLY VALID FOR THE DATA SHOWN WHEN THE FIELD IS BLINKING! CURRENT YIELD: is the rate of actual cash flow as percent of the purchase price. ACCRUED INT/M: is the amount of accrued interest to be paid the seller of a bond on sales between interest payment dates. This result is per $1,000 par amount of bonds. DURATION: is a mathematical measure (Macaulay method) of how quickly an investor recovers his or her investment. Bonds of similar duration will have the similar price movements for a given move in interest rates. For a more complete discussion of Duration see "Duration Analysis, Managing Interest Rate Risk" by Gerald O. Bierwag, 1987, by Ballinger Publishing Company. CALCULATION PRIORITIES: YB will compute prices and yields to the call and to maturity if all information is available. If the call information is omitted, YB will only calculate the price or yield to maturity. Similarly, if the maturity is omitted, YB will only calculate the price or yield to the call. -2- If all information is entered calculations are made both to maturity and the call date. The following priorities apply: 1. F1: Calc Px - YB Calculates both the price-to-maturity and the price-to-call using the yield in "Y"; 2. F3: Calc Px-Call - YB first calculates the price-to-call using the yield in "e" and then computes yield-to-maturity using the price in "i"; 3. F2: Calc Yld - YB calculates both yield-to-maturity and yield-to-call using the price in "P"; 4. F4: Calc Yld-Call - YB calculates both yield-to-maturity and yield-to-call using the price in "i"; Examples of Calculation Priorities: 1. Calc Px (F1) - A 7% bond matures 9-1-14 and is callable 9-1-94 at 104. The Broker wants to sell at a 7.50% yield. Under industry rules bonds are sold at lower of (i) price to maturity or (ii) price to the call. Assume Settlement Date of 11-1-91. To find the selling price enter 7 in "C", 9-1- 14 in "M", 9-1-94 in "D", 104 in "r" and 7.5 in "Y". Press F1 and The Price field will show 94.560 and blink. Yield-to-Call will show 7.50% and show a dollar price of 101.977. The broker should sell the bonds at 94.560 plus accrued interest. If the broker wants to know the Yield-to-Call, if the bonds are called, he or she should press F2 and using calculation priority 4 above, a Yield-to-Call of 10.509% is calculated using the selling price of 94.560. 2. Calc Px-Call (F3) - A 0% bond matures 2-15-07 and is callable 2-15-02 at 61.391. The broker is bidding the bond to yield a 6.90% to the call. Assuming a Settlement Date of 11-1-91, what is the Price-to-Call and what is the Yield-to-Maturity if the bond is not called. Enter 0 in "C", 2-15- 07 in "M", 2-15-02 in "D", 61.391 in "r", and 6.9 in "e". Press F3 and YieldBook and the Price-to-Call field will show 30.548 and a Yield to Maturity of 7.908%. MISCELLANEOUS Version 2 of YB will include: 1. A calculator for regular arithmetic, 2. Commonly used note computations, 3. Step coupon bonds computations, and 4. An option to use YB as a TSR program (One that sits in memory until needed). -3- DISCLAIMER - AGREEMENT Users of YieldBook must accept this disclaimer of warranty: "YIELDBOOK IS SUPPLIED AS IS. THE AUTHOR DISCLAIMS ALL WARRANTIES, EXPRESSED OR IMPLIED, INCLUDING, WITHOUT LIMITATION, THE WARRANTIES OF MERCHANTABILITY AND OF FITNESS FOR ANY PURPOSE. THE AUTHOR ASSUMES NO LIABILITY FOR DAMAGES, DIRECT OR CONSEQUENTIAL, WHICH MAY RESULT FROM THE USE OF YIELDBOOK." YieldBook is a "shareware program" and is provided at no charge to the user for evaluation. Feel free to share it with your friends, but please do not give it away altered or as part of another system. The essence of "user-supported" software is to provide personal computer users with quality software without high prices, and yet to provide incentive for programmers to continue to develop new products. If you find this program useful and find that you are using YieldBook and continue to use YieldBook after a reasonable trial period, you must make a registration payment of $25.00 to Compound Solutions. The $25.00 registration fee will license one copy for use on any one computer at any one time. You must treat this software just like a book. An example is that this software may be used by any number of people and may be freely moved from one computer location to another, so long as there is no possibility of it being used at one location while it's being used at another. Just as a book cannot be read by two different persons at the same time. Commercial users of YieldBook must register and pay for their copies of YieldBook within 30 days of first use or their license is withdrawn. Site-License arrangements may be made by contacting Compound Solutions. Anyone distributing YieldBook for any kind of remuneration must first contact Compound Solutions at the address below for authorization. This authorization will be automatically granted to distributors recognized by the (ASP) as adhering to its guidelines for shareware distributors, and such distributors may begin offering YieldBook immediately (However Compound Solutions must still be advised so that the distributor can be kept up-to-date with the latest version of YieldBook.). You are encouraged to pass a copy of YieldBook along to your friends for evaluation. Please encourage them to register their copy if they find that they can use it. All registered users will receive a copy of the latest version of the YieldBook program. Please register by sending your name and address, the version of YieldBook you are using, the disk format you require and your check for $25.00 to: Compound Solutions Suite 614 1170 Bower Hill Road Pittsburgh, PA 15243 -4- Registered users will receive support and assistance for 3 months after registration by mail at the above address. All registration fees received will be acknowledged. All support will be by mail at the above address. Any major bugs or deficiencies will be corrected. All registered users will receive a copy of the most recent version of YieldBook and Version 2, when released. We expect Version to be ready in the 2nd quarter of 1992. Also registered users will receive BONDS.XLM, a user-defined function macro sheet that contains the bond pricing and yield calculation functions for inclusion in Excel 3.0 spreadsheets. We would appreciate having your comments and recommendations for enhancements to YieldBook. YieldBook UPDATE HISTORY Version 1.0 - 11/16/91: Initial release Version 1.1 - 11/24/91: Correct bug in ODD First Period calculations - See "DISCUSSION OF ODD FIRST PERIODS" - changes to YB.DOC to reflect correction of bug and alterations to shareware and registration requirements. Version 1.2 - 2/17/92: Correct calculations to conform with MSRB Rule G-33 as to price and yield computations when bonds are sold at "par" or when the coupon equals the yield on the bond. A bond sold at the same yield as the coupon will have price other than "par" unless the settlement date is an interest payment date. (MSRB Interpretation dated May 31, 1984) - Recognizes Association of Shareware Professionals membership. ASSOCATION OF SHAREWARE PROFESSIONALS Compound Solutions is a member of the Association of Shareware Professionals (ASP). ASP wants to make sure that the shareware principle works for you. If you are unable to resolve a shareware-related problem with an ASP member by contacting the member directly, ASP may be able to help. The ASP Ombudsman can help you resolve a dispute or problem with an ASP member, but does not provide technical support for members' products. Please write to the ASP Ombudsman at 545 Grover Road, Muskegon, MI 49442 or send a CompuServe message via CompuServe Mail to ASP Ombudsman 70007,3536. DEFINITION OF SHAREWARE Shareware distribution gives users a chance to try software before buying it. If you try a Shareware program and continue using it, you are expected to register. Individual programs differ on details -- some request registration while others require it, some specify a maximum trial period. With registration, you get anything from the simple right to continue using the software to an updated program with printed manual. -5- Copyright laws apply to both Shareware and commercial software, and the copyright holder retains all rights, with a few specific exceptions as stated below. Shareware authors are accomplished programmers, just like commercial authors, and the programs are of comparable quality. (In both cases, there are good programs and bad ones!) The main difference is in the method of distribution. The author specifically grants the right to copy and distribute the software, either to all and sundry or to a specific group. For example, some authors require written permission before a commercial disk vendor may copy their Shareware. Shareware is a distribution method, not a type of software. You should find software that suits your needs and pocketbook, whether it's commercial or Shareware. The Shareware system makes fitting your needs easier, because you can try before you buy. Because the overhead is low, prices are low also. Shareware has the ultimate money-back guarantee -- if you don't use the product, you don't pay for it. -6- DISCUSSION OF ODD FIRST PERIODS Because of a user comment I became aware of a discrepancy between the results presented by YieldBook and several different machines commonly used in the securities industry on calculations involving long or short first periods. A hypothetical issue's ("Subject Bonds") particulars are Dated Date: 1/15/90 Coupon: 5.750% First Coupon: 7/1/90 Maturity: 7/1/10 Yield: 7.875% Sett Date: 2/4/90 YieldBook calculated a price of 78.573 while the other machines calculated a price of 78.586 (the price calculated by YieldBook and the other machines ("OMs") when the Dated Date is 1/1/90 - NOT AN ODD FIRST PERIOD). Since the author is not privy to the algorithms and methods used by OMs, I attempted to reproduce the OMs results and could do so by changing the Interest Accrued Date (Dated Date) to a date exactly 6 months before the Next Interest Payment Date - not exactly the best mathematical method. Back to the theory books. Theory of Bond Pricing: Essentially the price of a bond represents the discounted present value of all the future income streams that includes (i) all interest payments to be paid in the future and (ii) the repayment of principal, less accrued interest paid. This theory is explained more fully in "Inside the Yield Book" by Sidney Homer and Martin L. Leibowtiz, 1972, Prentice-Hall and in Chapter 2 of Bierwag's "Duration Analysis" as well as many other sources. The methods for implementing this theory are presented in "Standard Securities Calculation Methods", by Spence, Graudenz and Lynch, published by the Securities Industry Association in 1973 and in Rule G-33 of the Municipal Securities Rulemaking Board. These formulae are as follows: PV(Principal) = P/(1+Y/2)^(N-1+(E-A)/E) PV(Int Pmts) = SUMMATION of for X = 1 to N (C/2)/(1+Y/2)^(N-1+(E-A)/E) Accrued = C/2 * A/E where N = Number of interest payments to be made E = Number of days in the coupon period in which settlement occurs (30/360 day basis) A = Number of days from the Dated Date or Last Interest Payment date to the Settlement Date (30/360 day basis) Y = Yield on the bond as a decimal (6.6% = .066) P = Payment of principal due on the maturity date C = Coupon on the bond as a decimal -7- Schedule A below demonstrates this for the Subject Bonds assuming a Dated Date of 1/1/90 and provides a bond price of 78.586. YieldBook and the OMs agree on this calculation and all calculations except those that involve ODD First Periods. ODD First Periods: The author believes that OMs implement the above formulae and ignore the fact that for ODD First Periods, in the first period and the first period only, the interest paid to a bondholder is NOT Principal * Coupon / 2 but is Principal * Coupon * E / 360. Therefore, for the bonds used in this example the interest payment due 7/1/90 will be $26.51 (166 days @ 5.75%) per $1,000 and not the $28.75 per $1,000 that will be paid on all subsequent interest payment dates. It is this difference that affects the bond price and is, in the author's opinion, the source of the difference in price between YieldBook and OMs on ODD First Period calculations. Schedule B below demonstrates this for the subject bonds assuming a Dated Date of 1/15/90. Schedule B produces a Bond Price of 78.383 not the 78.586 calculated by OMs. 78.383 is the price YieldBook (Versions 1.1 or later) calculates given the same data. This represents an actual Yield to Maturity of 7.851% given a price of 78.586 (the OMs price) or a 2.4 basis point yield reduction for the investor from the 7.875% yield the investor bargained for. Conclusion: YieldBook (Versions 1.1 or later) calculates ODD First Period prices and yields using the methods in Schedule B. While they do not match the results from OMs, the author believes that YieldBook is mathematically correct and OMs are not. (It appears that the SIA and MSRB formulae do not take Odd First Periods into consideration.) Since, as stated earlier, the author does not have access to the algorithms used by the OMs, and has not been able to match their results without altering the critical data, YieldBook will continue to generate what the author believes is an accurate result instead of the result in common use in the securities industry. If any user can provide information that will prove that YieldBook is incorrect, it will be changed immediately and all registered users will receive updated versions. Bonds with ODD First Periods are a very small part of the bond industry and the results of incorrect methods only affect transactions made during the ODD First Period. Nevertheless, issuers, sellers, and purchasers of bonds are receiving a value other than that for which they bargained during ODD First Periods. A letter covering these issues is being sent to the SIA and the MSRB for comment. -8- SCHEDULE A IAD: 1/1/90 Days in Period 180 Cpn: 5.750% Accrued Days 33 Yld: 7.875% No of Int Pmts 41 NID: 7/1/90 Frac = 0.816666667 SD: 2/4/90 Mat: 7/1/10 Price: 78.586 Accrued: 0.527 Date Cash Flow PV Factor PV 1 7/1/90 0.028750 0.96895286 0.027857 2 1/1/91 0.028750 0.93224569 0.026802 3 7/1/91 0.028750 0.89692910 0.025787 4 1/1/92 0.028750 0.86295043 0.024810 5 7/1/92 0.028750 0.83025898 0.023870 6 1/1/93 0.028750 0.79880600 0.022966 7 7/1/93 0.028750 0.76854455 0.022096 8 1/1/94 0.028750 0.73942952 0.021259 9 7/1/94 0.028750 0.71141745 0.020453 10 1/1/95 0.028750 0.68446658 0.019678 11 7/1/95 0.028750 0.65853670 0.018933 12 1/1/96 0.028750 0.63358913 0.018216 13 7/1/96 0.028750 0.60958665 0.017526 14 1/1/97 0.028750 0.58649347 0.016862 15 7/1/97 0.028750 0.56427514 0.016223 16 1/1/98 0.028750 0.54289851 0.015608 17 7/1/98 0.028750 0.52233170 0.015017 18 1/1/99 0.028750 0.50254403 0.014448 19 7/1/99 0.028750 0.48350598 0.013901 20 1/1/00 0.028750 0.46518916 0.013374 21 7/1/00 0.028750 0.44756624 0.012868 22 1/1/01 0.028750 0.43061093 0.012380 23 7/1/01 0.028750 0.41429795 0.011911 24 1/1/02 0.028750 0.39860296 0.011460 25 7/1/02 0.028750 0.38350255 0.011026 26 1/1/03 0.028750 0.36897419 0.010608 27 7/1/03 0.028750 0.35499621 0.010206 28 1/1/04 0.028750 0.34154777 0.009819 29 7/1/04 0.028750 0.32860880 0.009448 30 1/1/05 0.028750 0.31616000 0.009090 31 7/1/05 0.028750 0.30418280 0.008745 32 1/1/06 0.028750 0.29265934 0.008414 33 7/1/06 0.028750 0.28157242 0.008095 34 1/1/07 0.028750 0.27090552 0.007789 35 7/1/07 0.028750 0.26064271 0.007493 36 1/1/08 0.028750 0.25076869 0.007210 37 7/1/08 0.028750 0.24126874 0.006936 38 1/1/09 0.028750 0.23212867 0.006674 39 7/1/09 0.028750 0.22333486 0.006421 40 1/1/10 0.028750 0.21487419 0.006178 41 7/1/10 1.028750 0.20673404 0.212678 -------- PV = 0.791132 Accrued = 0.005270 -------- Price = 0.785861 SCHEDULE B IAD: 1/15/90 Days in Period 166 Cpn: 5.750% Accrued Days 19 Yld: 7.875% No of Int Pmts 41 NID: 7/1/90 Frac = 0.885542169 SD: 2/4/90 Mat: 7/1/10 Price: 78.383 Accrued: 0.303 Date Cash Flow PV Factor PV 1 7/1/90 0.026514 0.96637893 0.025622 2 1/1/91 0.028750 0.92976926 0.026731 3 7/1/91 0.028750 0.89454649 0.025718 4 1/1/92 0.028750 0.86065808 0.024744 5 7/1/92 0.028750 0.82805348 0.023807 6 1/1/93 0.028750 0.79668404 0.022905 7 7/1/93 0.028750 0.76650299 0.022037 8 1/1/94 0.028750 0.73746529 0.021202 9 7/1/94 0.028750 0.70952764 0.020399 10 1/1/95 0.028750 0.68264836 0.019626 11 7/1/95 0.028750 0.65678736 0.018883 12 1/1/96 0.028750 0.63190606 0.018167 13 7/1/96 0.028750 0.60796734 0.017479 14 1/1/97 0.028750 0.58493551 0.016817 15 7/1/97 0.028750 0.56277619 0.016180 16 1/1/98 0.028750 0.54145635 0.015567 17 7/1/98 0.028750 0.52094417 0.014977 18 1/1/99 0.028750 0.50120907 0.014410 19 7/1/99 0.028750 0.48222159 0.013864 20 1/1/00 0.028750 0.46395343 0.013339 21 7/1/00 0.028750 0.44637732 0.012833 22 1/1/01 0.028750 0.42946705 0.012347 23 7/1/01 0.028750 0.41319741 0.011879 24 1/1/02 0.028750 0.39754411 0.011429 25 7/1/02 0.028750 0.38248381 0.010996 26 1/1/03 0.028750 0.36799404 0.010580 27 7/1/03 0.028750 0.35405320 0.010179 28 1/1/04 0.028750 0.34064048 0.009793 29 7/1/04 0.028750 0.32773588 0.009422 30 1/1/05 0.028750 0.31532015 0.009065 31 7/1/05 0.028750 0.30337477 0.008722 32 1/1/06 0.028750 0.29188192 0.008392 33 7/1/06 0.028750 0.28082445 0.008074 34 1/1/07 0.028750 0.27018588 0.007768 35 7/1/07 0.028750 0.25995034 0.007474 36 1/1/08 0.028750 0.25010255 0.007190 37 7/1/08 0.028750 0.24062783 0.006918 38 1/1/09 0.028750 0.23151204 0.006656 39 7/1/09 0.028750 0.22274159 0.006404 40 1/1/10 0.028750 0.21430340 0.006161 41 7/1/10 1.028750 0.20618487 0.212113 -------- PV = 0.786869 Accrued = 0.003034 -------- Price = 0.783834 YieldBook (Version 1.2 - 2/17/92) by Compound Solutions Suite 614 1170 Bower Hill Road Pittsburgh, PA 15243 _______ ____|__ | (R) --| | |------------------- | ____|__ | Association of | | |_| Shareware |__| o | Professionals -----| | |--------------------- |___|___| MEMBER