VALUE %. $100, (=MATURITY


 Angelina Baldwin
 2 years ago
 Views:
Transcription
1 NOTES H IX. How to Read Financial Bond Pages Understanding of the previously discussed interest rate measures will permit you to make sense out of the tables found in the financial sections of newspapers and magazines that report on U.S. Treasury debt instruments and corporate bonds traded on stock exchanges. He illustrates his discussion using the financial pages from the January 26, 2 issue of the Wall Street Journal. This section reviews the main points of textbook discussion, using the financial pages from the February 17, 1999 issue of the New York Times to illustrate and elaborate key points. As will be seen, the form in which financial information is reported in the New York Times is essentially the same as in the Wall Street Journal, with only minor notational differences. A. Treasury Bonds and Notes: Treasury bonds (Tbonds) are coupon bonds with a maturity greater than ten years, and Treasury notes (Tnotes) are coupon bonds with a maturity of between one and ten years. As in the Wall Street Journal, the New York Times provides a single table reporting on Tbonds and Tnotes because both have the same structure. Below is a sample listing from the Tbonds and Tnotes table appearing in the Wall Street Journal (September 16, 22, handout) which reports information for the previous trading day, September 15, 22: Rate Maturity Bid Ask Chg Ask. Yld Aug 3 18:15 18: Aug 3 n 11:25 11: Notational Note: For expositional simplicity, Tbonds and Tnotes will hereafter be lumped together and simply referred to as "bonds." The first column (Rate) identifies a bond's annual coupon rate, i.e., the annual coupon payment as a percentage of face value. Usually this annual coupon payment is paid in two equal semiannual installments. The second column (Month) of the sample listing identifies the month and year that a bond matures. A footnote may next be provided to indicate that a bond has some special feature. For example: the letter "n" denotes "Tnote". The third and fourth columns (Bid, Ask) provide information about a bond's bid and asked prices, which by convention are quoted as a percentage per $1 of face value (so that 1 = face value) with fractions in 32s. Unlike the Wall Street Journal, which uses a colon to indicate fractional values in 32s (e.g., 12:8 = 12 8/32), the New York Times uses a decimal point (e.g., 12.8 = 12 8/32). More precisely, the bid price quoted for a bond is the approximate market price offered by prospective buyers of the bond on the trading day in question, so it indicates approximately how much you would have received if you had sold the bond on that day. In contrast, the asked price quoted for a bond is the approximate market price demanded by prospective sellers of the bond on the trading day in question, so it indicates approximately how much you would have had to pay to purchase the bond on that day. The asked price minus the bid price  referred to as the bidask spread  reflects the profit margin of the bond dealers who handle trades in this bond. Hence, for obvious reasons, the asked price always exceeds the bid price. The fifth column (Chg) indicates the change in the BID price from the previous trading day's quotation. The sixth and final column (Yld) provides the yield to maturity on the bond using the currently quoted ASKED price as the purchase price. The asked price is used because the yield to maturity is most relevant for a person who intends to purchase and hold the bond and thus earn the yield. IMPORTANT: Both bid and ask prices are clean prices. That is, they do not include the accrued interest. See the following example based on quotes above. This ant the following example are only for illustration, this will not be required in tests! Assume that the Tbond has COUPON RATE equal to %. Its FACE VALUE of $1, will be paid on August 13 th, 23 (=MATURITY DATE). Note that Tbonds have semiannual coupons. 1/ What is accrued interest on September 15 th, 22 First notice that during the remaining 332 days this bond will pay total interest of %*$1,=$11,125 and the principal of $1,. There will be two payments. In 149 days (March 13 th, 23) owner of the bond will receive first of the two coupon payments of $5, days later (August 13 th, 23) she will receive $15,556.5 of second coupon and principal. On September 15 th, it was 33 days from the last payment of coupon on August 13 th. Thus, accrued interest is 33/(33+149) * $5,562.5=$1,8.6. 2/ How much would you pay on September 15 th, 22 to buy this bond You will have to pay both ask price and the accrued interest. Therefore you would pay $1, * (18+16/32) + $1,8.6 = $19, / What was this bond s ask yield to maturity on September 15 th, 22 Ask yield to maturity i, satisfies: Present Value of future payments = Purchasing price. That is, purchasing price of $19,58.6 equals to present value of 5, , i*(149/365) 1+i*(332/365) This is true only for i=.166=1.66%. Note: The treasury note with coupon rate has a maturity date August 29 th. It also pays interest twice a year (in 165 and 348 days). Thus, its price is $11,98.85 ($11,812.5 of clean price + $ of accrued interest), its ask yield to maturity is 1.7%. Note on Treasury Zero Coupon Issues: Coupon stripping is the act of removing the individual coupon payments from a coupon bond and treating each payment as a separate zero coupon bond. The remaining faceonly bond is then also in effect a 15
2 zero coupon bond. For example, a 2year bond with a face value of $1, and an annual coupon payment of $1, could be stripped into 21 separate zerocoupon instruments: namely, 2 "interest strips" consisting of the 2 annual coupon payments of $1,, each due on the specified annual coupon payment date; and one "principal strip" consisting of an instrument having a face value of $1, due in 2 years. Merrill Lynch began the market 1 1 for stripped securities in The U.S. Treasury introduced stripping of its coupon bond issues in February 1985, referring to the resulting zerocoupon securities as STRIPs (Separate Trading of Registered Interest and Principal of Securities). U.S. Treasury strips are mentioned in the explanatory notes for the Wall Street Journal bonds. B. Treasury bills: Treasury bills (Tbills) are discount bonds with a maturity of one year or less. Since a coupon rate is zero, they are identified solely by their maturity date. Below is a sample listing from the Tbills table appearing in the WSJ (September 16, 22) which reports information for the previous trading day, September 15, 22: Date Days to Mat. Bid Ask Chg Yield Jan Jan The first column (Date) gives the month, day, and year of the maturity date. The third column (Bid) gives the discount yield in percentage terms using as the purchase price Pd the BID price, i.e., the price offered by prospective buyers. The third column (Ask) gives the discount yield in percentage terms using as the purchase price Pd the ASKED price, i.e., the price demanded by prospective sellers. Recall that the discount yield varies inversely with the purchase price Pd. It follows that, for Tbill issues, the bid discount yield reported in the Bid column is always greater than the asked discount yield reported in the Ask column, indicating that the bid price is less than the asked price. The fourth column (Chg) reports the change in the asked discount yield from the previous trading day measured in terms of basis points, which are hundredths of a percentage point (e.g., .4 means the asked discount yield has fallen in percentage terms by 4 basis points). The fifth and final column (Yield) provides the yield to maturity using the current ASKED price as the current value. Can you verify that the presented yields to maturity is computed correctly Assume that F=$1. In case of the first Tbill, idb=1.64% and there are 114 days to maturity. Thus from equation (6) we can find price of the bill Pd: $1  Pd % = * > Pd = $99.48 $1 114 Yield to maturity equals to i, where $1 Pd= i*(114/365) thus, $1  Pd 365 i = * =.167 = 1.67%. Pd 114 C. Corporate Bonds Traded on Exchanges: A majority of bonds, and all municipal or taxexempt bonds, are not listed on exchanges; rather, they are traded overthecounter. However, the New York Stock Exchange (NYSE), and to a much less extent the American Stock Exchange (AMEX), do list various coupon bonds issued by corporations with strong credit ratings. Below is a sample listing from the NYSE corporate bond table appearing in the New York Times (February 17, 1999, page C17) which reports information for the previous trading day, February 16, 1999: Company Coupon Mat. Cur.Yld. Vol. Price Chg. Rate ATT 5 1/ /81/8 ARetire 5 3/4 2 cv / /2 The first column (Company) shows the issuing company, the second column gives the original coupon rate, and the third column gives the last two digits of the maturity year. The fourth column reports the annual current yield (Cur. Yld.). In some cases, a footnote may instead be inserted to call attention to a special feature of the bond; for example, the letters "cv" in the above table denote "convertible into stock under special conditions". The remaining three columns report the number of bonds traded for the day measured in $1 face value (Vol.), the bond's closing price for the day expressed as a percentage of face value with 1 equaling face value (Price), and the difference between the current trading day's closing price and the previous trading day's closing price (Chg). X. Interest Rates vs. Return Rates Given any asset A held over any given time period T, the return to A over the holding period T is, by definition: the sum of all payments (rents, coupon payments, dividends, etc.) generated by A during period T, assumed paid out at the end of the period, 16
3 NOTES I P (1) P (1) R ate of R etu rn PLUS the capital gain (+) or loss () in the market value of A over period T, measured as the market value of A at the end of period T minus the market value of A at the beginning of period T. C C C P (2) C + P (2) Y ield to M a tu rity P V = P (1) The return rate on asset A over the holding period T is then defined to be the return on A over period T divided by the market value of A at the beginning of period T. More precisely, suppose that an asset A is held over a time period that starts at some time t and ends at time t+1. Let the market value of A at time t be denoted by P(t) and the market value of A at time t+1 be denoted by P(t+1). Finally, let V(t,t+1) denote the sum of all payments accruing to the holder of asset A from t to t+1, assumed to be paid out at time t+1. Then, by definition, the return rate on asset A from t to t+1 is given by the following formula: (24) Return Rate on V(t,t+1) + P(t+1)  P(t) Asset A From = time t to t+1 P(t) C V(t,t+1) P(t+1)  P(t) = P(t) P(t) = payments + Capital Gain (if +) received as or Loss (if ) as percentage percentage of P(t) of P(t) Formula (24) holds for any asset A, whether physical or financial. In particular, it holds for bonds. The question then arises: For bonds, what is the connection between C C + F V C + F V the return rate defined by formula (24) and the interest rate on the bond defined by yield to maturity, current yield, or discount yield The return rate on a bond is not necessarily equal to the interest rate on that bond, whether defined by yield to maturity, the current yield, or the discount yield. The reason for this is that the return rate calculated for a particular holding period takes into account any capital gains or losses that occur during this holding period, in addition to payments received during the holding period. In contrast, the current yield ignores capital gains and losses altogether, and the yield to maturity and the discount yield only take into account the overall anticipated capital gain or loss that is incurred when the bond is held to maturity (as measured by the difference between the final face value payment and the initial purchase price). EXAMPLE A: COUPON BONDS Suppose you purchase a coupon bond at time t at a price P(t) with coupon payment C and face value F, you receive a coupon payment C at time t+1, and you also sell the coupon bond in a secondary market at a price P(t+1) at time t+1. By definition, the current yield that you receive on this coupon bond during the holding period from t to t+1 is given by (25) ic(t) = C/ P(t) Also, the percentage capital gain or loss you incur on the coupon bond during the holding period from t to t+1, denoted by g(t,t+1), is given by P(t+1)  P(t) (26) g(t,t+1) = P(t) It then follows from definition (9) that the return rate on the coupon bond from t to t+1 can be expressed as C + P(t+1)  P(t) (27) = ic(t) + g(t,t+1). P(t) Clearly the return rate (24) coincides with the current yield ic(t) if (28) P(t) = P(t+1). Condition (28) implies that there are no capital gains or losses on the coupon bond during the holding period from t to t+1, i.e., g(t,t+1) =. Conversely, if condition (28) fails to hold, then the return rate (27) does not coincide with the current yield ic(t). Thus, condition (28) is both necessary and sufficient for the return rate (27) from t to t+1 to equal the current yield ic(t). That is: if and only if Return Rate = ic(t) < > P(t) = P(t+1) From t To t+1 Now suppose, instead, that Time Period from t to t+1 = Bond Maturity Period: if and only if Return Rate = i(t) < > Period From t to t+1 From t To t+1 = Maturity Period 17
4 EXAMPLE B: DISCOUNT BOND For a discount bond with a purchase price Pd and a face value F, the return rate (9) over any holding period t to t+1 reduces to P(t+1)  Pd (29) Pd Recalling definition for the discount yield idb, it is seen that the return rate will generally differ from idb except in the degenerate case Pd = P(t+1) = F when both are zero. In summary, then, only under special conditions will the return rate for a bond over a given holding period coincide with the yield to maturity, the current yield, or the discount yield. XI. Real vs. Nominal Interest Rates The interest rate measures examined to date have all been "nominal" in the sense that they have not been adjusted for expected changes in prices. What actually concerns a "rational" saver considering the purchase of a debt instrument is not the nominal payment stream he or she expects to earn in future periods but rather the command over purchasing power that this nominal payment stream is expected to entail. This purchasing power depends on the behavior of prices. Let infe(t) denote the expected inflation rate at time t, and let i(t) denote the (nominal) interest rate for some debt instrument at time t. Then the real interest rate associated with i(t) is defined by the following "Fisher equation:" (3) ir(t) = i(t)  inf e (t). That is, the real interest rate is the nominal interest rate minus the expected inflation rate. Note: As explained by Mishkin, the real interest rate defined by (16) is more precisely called the ex ante real interest rate because it adjusts for expected changes in the price level. If the expected inflation rate in (16) is replaced by the actual inflation rate, one obtains the ex post real interest rate. Real interest rates provide a more accurate measure of the true costs of borrowing and the true gains from lending than nominal interest rates, and hence provide a better indicator of the incentives to borrow and lend. In particular, for any given nominal interest rate i on a debt instrument D, the incentive to borrow (issue D) will be higher if the real interest rate associated with i is lower (i.e., the expected inflation rate is higher). This is so since a higher expected inflation rate means the borrower (issuer of D) can expect to pay off his future nominal debt obligations using cheaper dollars than he borrowed. For this same reason, the incentive to lend (purchase D) will be lower if the real interest rate associated with i is lower. A similar distinction is made between the (nominal) return rate defined by (9), which has not been adjusted for expected changes in prices, and the "real return rate" which is subject to such adjustment. More precisely, the real return rate on any asset A over any holding period from t to t+1 is defined to be the (nominal) return rate (9) minus the expected inflation rate inf e (t). TABLE OneYear Returns on Bonds When Interest Rates Rise from 1% to (1) (2) (3) (4) (5) (6) Years to Initial Initial Price Rate of Rate of maturity current price next capital Return when bond yield year gain (2+5) is purchased (%) ($) ($) (%) (%) XII. Interest Rate Risk As previously seen, at any time t, the yield to maturity i(t) for a bond with a maturity date greater than t moves inversely with its current acquisition price P(t)  that is, if $ 1, $ 1, infinite % $ 1 + $1, 1% P(2) $ 1 + P(2) $1 one goes up, the other goes down. $ 1 + $ 1, $ 1, $ P(1) 1, $ 1 + P(2) A fall in the price of an already held bond signals a capital loss to the holder. Consequently, the net effect of an increase in the yield to maturity for an already held bond can be a decrease in the return rate to its holder. P(2) 1% 1% $ 1 + P(2) P(2) $ 1 + $ 1, $1 $1 $ 1 + $ 1 18
5 NOTES J The uncertainty regarding return rate that bond holders face due to possible changes in yield to maturity is called interest rate risk. Table illustrates interest rate risk for bonds of different maturities, each with a coupon payment of $1 and a face value of $1. This illustration is worth reviewing with some care. First note that, for each bond in the Table, the initial yield to maturity i(1) for year 1 ("this year") is equal to the initial current yield ic(1) = 1 percent for year 1 because the initial price of the bond is set at its face value of $1. However, by assumption, the yield to maturity i(2) for year 2 ("next year") increases to 2 percent. The coupon bond listed in the Table with a 1year maturity has a price P(2) in year 2 that is fixed (by contract) at the bond's face value, $1. For all other listed coupon bonds, however, their maturities exceed one year. Consequently, when i(2) increases, their price P(2) in year 2 decreases to some value smaller than their original price P(1) = $1 in year 1 and hence smaller than the bond's face value of $1. For example, for the coupon bond with a 3year maturity, P(2) = $53. The return rate from year 1 to year 2 for each of the coupon bonds in Table 2 is given by the sum of the current yield ic(1) = C/P(1) for year 1 and the capital loss g(1,2) = [P(2)P(1)]/P(1) from year 1 to year 2. Consequently, except for the bond with a oneyear maturity, these return rates are smaller than they would have been without the increase in the yield to maturity in year 2. Indeed, for the coupon bond with a 3year maturity, the capital loss g(1,2) is so large (49.7 percent) that it overwhelms the 1 percent initial current yield ic(1) = 1 percent, resulting in a negative return rate of percent from year t=1 to t=2. More precisely, examining the return rates in column (6) of the Table as the maturity is decreased from 3 years to 1 year, it is seen that the coupon bonds with longer maturities experience a greater decline in their return rates when the yield to maturity i(2) increases. This is due to the fact that this increase in i(2) results in a smaller decline in the price P(2) for coupon bonds with smaller maturities and hence a smaller capital loss. [To see why, consider the formula Pb = PV(i) from which the yield to maturity i is determined.] Indeed, for coupon bonds with a oneyear maturity, P(2) remains fixed at the face value $1. Increase in yield to maturity from year 1 to year 2 / \ i(1)=ic(1) i(2) (3) /\/\/\ Year 1 2 N P(1) P(2) Maturity Date (N > 2) \ / Capital loss from t=1 to t=2 An important implication of this illustration is that the return rates of bonds with longerterm maturities respond more dramatically to changes in the yield to maturity than bonds with shorterterm maturities. That is, longerterm bonds are more subject to interest rate risk. This is one reason why investment in longerterm bonds is considered more risky than investment in shorterterm bonds. XIII. More Basic Concepts and Key Issues Current yield Discount yield (Nominal) return rate Real interest rate Real return rate Consol bond (perpentuity) Capital gain or loss Interest rate risk Expected inflation rate Calculating the current yield for a consol bond For a coupon bond, how does its maturity affect the relationship between its current yield and its yield to maturity What is the relationship between its current yield, its coupon rate, its purchase price, and its face value What is the relationship between its current yield, its yield to maturity, its purchase price, and its face value What is the relationship between its current yield and its purchase price, given any fixed level for its coupon payment For a discount bond, all else remaining the same, why do its discount yield and its yield to maturity always move together How to read financial bond pages for information on Treasury bonds and notes, Treasury bills, and corporate bonds traded on stock exchanges. Why is the return rate on a bond not necessarily equal to its interest rate How does the maturity of a bond affect its interest rate risk Why do bonds with long maturities expose bond holders to greater interest rate risk than bonds with shorter maturities What is the relationship between real and nominal interest rates Why do real interest rates provide a more accurate measure of the true costs of borrowing and the true gains from lending than nominal interest rates Why do real return rates provide a more accurate measure of the true gains or losses from holding an asset than nominal return rates 19
6 XIV. Practice Questions Answers for questions below: 1D 2A 3B 4 22% 5 6D 7B 8C 9C 1 C 11D 12D Q1. Which of the following statements is/are true in general for FIXED PAYMENT loans A. At maturity the borrower makes one fixed payment, equal to face value. B. The borrower makes only one fixed payment, at maturity, and this payment combines interest and principal repayment. C. The borrower makes the same fixed payment in every payment period until maturity, where the payments consist entirely of principal repayments. D. The borrower makes the same fixed payment in every payment period until maturity, where the payments consist of both interest and principal. Q2. Which of the following statements is/are true in general for COUPON BONDS A. The issuer makes a fixed coupon payment in every payment period during the life of the bond, plus a face value payment at maturity. B. The issuer makes a fixed coupon payment in every payment period during the life of the bond, where the present value of these cumulated payments equals the face value of the bond. C. Treasury bills are examples of coupon bonds. D. Only A and C of the above E. Only B and C of the above Q3. The COUPON RATE on a coupon bond with a purchase price of $25, a $3 face value, annual coupon payments of $125, and a 4year maturity is A. the coupon payment $125 divided by the purchase price $25. B. the coupon payment $125 divided by the face value $3. C. the average coupon payment per year, which here is $125. D. total coupon payments ($5) divided by the purchase price $25. Q4. Assume the following simple loan contract: Principal=5, Interest payment = 22, Maturity is 2 years (maturity date is 2 years from today). What is the SIMPLE (annual) INTEREST RATE Q5. In the example from question Q4, what is the yield to maturity i A. 1% B. 11% C. D.22% Q6. Letting "*" denote multiplication, if the annual interest rate is 5 percent, then the PRESENT VALUE of a payment stream ($5,$,$,$7) with $5 to be received at the end of the FIRST year, $ to be received at the end of the SECOND and THIRD years, and $7 to be received at the end of the FOURTH year is given by A. $5/(1.5) + $7/(1.2) B. $5*(1.5) + $7*(1.5) 4 C. [$5 + $7]/(1.2) D. $5/(1.5) + $7/(1.5) 4 Q7. The (ANNUAL) YIELD TO MATURITY i on a coupon bond with a purchase price $65, a face value $75, a 2year coupon payment stream ($5,$5), and a 2year maturity is calculated as follows: i equals the annual interest rate that, when used to calculate the present value of the income stream, results in a present value equal to. A. ($5,$5), $65. B. ($5,$8), $65. C. ($5,$5), $75. D. ($5,$8), $75. Q8. Which of the following $6 facevalue securities has the HIGHEST yield to maturity A coupon bond with a coupon rate of percent that sells for. A. 5 ; $6, B. 1 ; $6, C. 15 ; $6, D. 15 ; $6,2 Q9. The current yield on a coupon bond with a $7 face value, a 5 percent coupon rate, an 8 year maturity, and a current purchase price of $35 is A. 5 % B. 8 % C. 1 % D. 16 % E. 2 % Q1. Which of the following statements is/are FALSE for the current yield ic of a coupon bond with coupon payment C, face value F, and maturity N. A. For a consol bond, the ic equals the yield to maturity. B. For fixed C and F, the ic is a better approximation for the yield to maturity the greater is the bond's time to maturity N. C. For fixed C, F, and N, the ic is a better approximation for the yield to maturity the more the bond's purchase price exceeds the face value F. D. all of the above are false statements E. only A and B are false statements Q11. Consider a coupon bond that has an annual coupon payment C=$1, a face value F=$3,, and a maturity date January 1, 28. Suppose you BUY this bond on January 1, 23 for Pb=$25 and you SELL it on January 1, 24 for $2. Which of the following statements is/are TRUE for this bond: A. Your (annual) current yield on this bond from 1/1/23 to 1/1/24 is equal to C=$1 divided by the purchase price Pb=$25. B. Your return rate on this bond from 1/1/23 to 1/1/24 can be expressed as the sum of the current yield and the rate of your capital gain or loss. C. Your return rate on this bond from 1/1/23 to 1/1/24 is LESS than the current yield on the bond. D. All of the above are true. E. Only A and B are true. Q12 Suppose a consol bond pays $1 at 11:59 P.M. on December 31 of each year. Suppose you purchased the consol bond for $1 at midnight on December 31, 2, and you sold it for $19 at midnight on December 31, 21. Suppose the inflation rate during 21 was 3 percent. Then your NOMINAL return rate on the consol bond for 21 was and your REAL return rate on the consol bond for 21 was. A. 1 %; 2 % B. 1 %; 4 % C. 9 %; 6 % D. 1 %; 7 %t E. 1 %; 13 % 2
7 NOTES K Summary of major interest rates on the market Government securities Municipal Issues (notice that some are tax free and so their yield is adjusted by 31% tax bracket) Private Bonds 9
NOTES E. Borrower Receives: Loan Value LV MATURITY START DATE. Lender Fixed Fixed Fixed Receives: Payment FP Payment FP Payment FP
NOTES E DEBT INSTRUMENTS Debt instrument is defined as a particular type of security that requires the borrower to pay the lender certain fixed dollar amounts at regular intervals until a specified time
More informationChapter 8 Interest Rates and Bond Valuation
University of Science and Technology Beijing Dongling School of Economics and management Chapter 8 Interest Rates and Bond Valuation Oct. 2012 Dr. Xiao Ming USTB 1 Key Concepts and Skills Know the important
More informationCoupon Bonds and Zeroes
Coupon Bonds and Zeroes Concepts and Buzzwords Coupon bonds Zerocoupon bonds Bond replication Noarbitrage price relationships Zero rates Zeroes STRIPS Dedication Implied zeroes Semiannual compounding
More informationFNCE 301, Financial Management H Guy Williams, 2006
REVIEW We ve used the DCF method to find present value. We also know shortcut methods to solve these problems such as perpetuity present value = C/r. These tools allow us to value any cash flow including
More informationChapter Review Problems
Chapter Review Problems State all stock and bond prices in dollars and cents. Unit 14.1 Stocks 1. When a corporation earns a profit, the board of directors is obligated by law to immediately distribute
More informationOverview of Lecture 5 (part of Lecture 4 in Reader book)
Overview of Lecture 5 (part of Lecture 4 in Reader book) Bond price listings and Yield to Maturity Treasury Bills Treasury Notes and Bonds Inflation, Real and Nominal Interest Rates M. Spiegel and R. Stanton,
More informationPricing of Financial Instruments
CHAPTER 2 Pricing of Financial Instruments 1. Introduction In this chapter, we will introduce and explain the use of financial instruments involved in investing, lending, and borrowing money. In particular,
More informationIntroduction to Bond Valuation. Types of Bonds
Introduction to Bond Valuation (Text reference: Chapter 5 (Sections 5.15.3, Appendix)) Topics types of bonds valuation of bonds yield to maturity term structure of interest rates more about forward rates
More informationInvestments 320 Dr. Ahmed Y. Dashti Chapter 3 Interactive Qustions
Investments 320 Dr. Ahmed Y. Dashti Chapter 3 Interactive Qustions 31. A primary asset is an initial offering sold by a business, or government, to raise funds. A) True B) False 32. Money market instruments
More informationMoney Market and Debt Instruments
Prof. Alex Shapiro Lecture Notes 3 Money Market and Debt Instruments I. Readings and Suggested Practice Problems II. Bid and Ask III. Money Market IV. Long Term Credit Markets V. Additional Readings Buzz
More informationReview for Exam 1. Instructions: Please read carefully
Review for Exam 1 Instructions: Please read carefully The exam will have 20 multiple choice questions and 5 work problems. Questions in the multiple choice section will be either concept or calculation
More informationIn this chapter we will learn about. Treasury Notes and Bonds, Treasury Inflation Protected Securities,
2 Treasury Securities In this chapter we will learn about Treasury Bills, Treasury Notes and Bonds, Strips, Treasury Inflation Protected Securities, and a few other products including Eurodollar deposits.
More informationof Investments Fundamentals Security Types C h a p t e r Valuation & Management second edition Charles J.Corrado Bradford D.
3 C h a p t e r Security Types 31 Fundamentals of Investments Valuation & Management second edition Charles J.Corrado Bradford D.Jordan Slides by YeeTien (Ted) Fu 32 Security Types Goal Our goal in
More informationMishkin ch.4: Interest Rates. Present Value Yield to Maturity Total Return. Task in Exams: Problem solving
Mishkin ch.4: Interest Rates Summary 1. Three key concepts: Present Value Yield to Maturity Total Return 2. Know how to work with the key concepts: Task in Exams: Problem solving 3. Applications: Real
More informationCHAPTER 23: FUTURES, SWAPS, AND RISK MANAGEMENT
CHAPTER 23: FUTURES, SWAPS, AND RISK MANAGEMENT PROBLEM SETS 1. In formulating a hedge position, a stock s beta and a bond s duration are used similarly to determine the expected percentage gain or loss
More informationChapter. Bond Prices and Yields. McGrawHill/Irwin. Copyright 2008 by The McGrawHill Companies, Inc. All rights reserved.
Chapter Bond Prices and Yields McGrawHill/Irwin Copyright 2008 by The McGrawHill Companies, Inc. All rights reserved. Bond Prices and Yields Our goal in this chapter is to understand the relationship
More informationInterest Rates and Bond Valuation
Interest Rates and Bond Valuation Chapter 6 Key Concepts and Skills Know the important bond features and bond types Understand bond values and why they fluctuate Understand bond ratings and what they mean
More informationANALYSIS OF FIXED INCOME SECURITIES
ANALYSIS OF FIXED INCOME SECURITIES Valuation of Fixed Income Securities Page 1 VALUATION Valuation is the process of determining the fair value of a financial asset. The fair value of an asset is its
More informationU.S. Treasury Securities
U.S. Treasury Securities U.S. Treasury Securities 4.6 Nonmarketable To help finance its operations, the U.S. government from time to time borrows money by selling investors a variety of debt securities
More informationChapter 4 Valuing Bonds
Chapter 4 Valuing Bonds MULTIPLE CHOICE 1. A 15 year, 8%, $1000 face value bond is currently trading at $958. The yield to maturity of this bond must be a. less than 8%. b. equal to 8%. c. greater than
More informationChapter. Overview of Security Types. McGrawHill/Irwin. Copyright 2008 by The McGrawHill Companies, Inc. All rights reserved.
Chapter Overview of Security Types McGrawHill/Irwin Copyright 2008 by The McGrawHill Companies, Inc. All rights reserved. Security Types Our goal in this chapter is to introduce the different types of
More informationAn Investor s Guide to the US Treasury Market
an INVESTOR S GUIDE TO THE US TreASURY MARKET february 2014 An Investor s Guide to the US Treasury Market summary in brief Many investors concerned with principal preservation turn to US Treasury securities
More information1 Pricing of Financial Instruments
ESTM 60202: Financial Mathematics ESTEEM Fall 2009 Alex Himonas 01 Lecture Notes 1 September 30, 2009 1 Pricing of Financial Instruments These lecture notes will introduce and explain the use of financial
More informationAnalysis of Deterministic Cash Flows and the Term Structure of Interest Rates
Analysis of Deterministic Cash Flows and the Term Structure of Interest Rates Cash Flow Financial transactions and investment opportunities are described by cash flows they generate. Cash flow: payment
More informationInternational Money and Banking: 12. The Term Structure of Interest Rates
International Money and Banking: 12. The Term Structure of Interest Rates Karl Whelan School of Economics, UCD Spring 2015 Karl Whelan (UCD) Term Structure of Interest Rates Spring 2015 1 / 35 Beyond Interbank
More informationReview for Exam 1. Instructions: Please read carefully
Review for Exam 1 Instructions: Please read carefully The exam will have 21 multiple choice questions and 5 work problems. Questions in the multiple choice section will be either concept or calculation
More informationMEDICAID ELIGIBILITY MANUAL, VOLUME III REVISED 110196 PAGE 6280
REVISED 110196 PAGE 6280 G. INVESTMENTS Other common investment vehicles include stocks and CONTRACTS bonds and contracts refer to promissory notes, loans and property agreements. 1. Stocks Shares of
More informationPRACTICE EXAMINATION NO. 5 May 2005 Course FM Examination. 1. Which of the following expressions does NOT represent a definition for a n
PRACTICE EXAMINATION NO. 5 May 2005 Course FM Examination 1. Which of the following expressions does NOT represent a definition for a n? A. v n ( 1 + i)n 1 i B. 1 vn i C. v + v 2 + + v n 1 vn D. v 1 v
More informationCHAPTER 8 INTEREST RATES AND BOND VALUATION
CHAPTER 8 INTEREST RATES AND BOND VALUATION Solutions to Questions and Problems 1. The price of a pure discount (zero coupon) bond is the present value of the par value. Remember, even though there are
More informationCHAPTER 7: FIXEDINCOME SECURITIES: PRICING AND TRADING
CHAPTER 7: FIXEDINCOME SECURITIES: PRICING AND TRADING Topic One: Bond Pricing Principles 1. Present Value. A. The presentvalue calculation is used to estimate how much an investor should pay for a bond;
More informationFixed Income: Practice Problems with Solutions
Fixed Income: Practice Problems with Solutions Directions: Unless otherwise stated, assume semiannual payment on bonds.. A 6.0 percent bond matures in exactly 8 years and has a par value of 000 dollars.
More informationFinancial Markets And Financial Instruments  Part I
Financial Markets And Financial Instruments  Part I Financial Assets Real assets are things such as land, buildings, machinery, and knowledge that are used to produce goods and services. Financial assets
More informationBonds and Yield to Maturity
Bonds and Yield to Maturity Bonds A bond is a debt instrument requiring the issuer to repay to the lender/investor the amount borrowed (par or face value) plus interest over a specified period of time.
More informationMULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.
ECON 4110: Sample Exam Name MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. 1) Economists define risk as A) the difference between the return on common
More informationExam 1 Sample Questions
Exam 1 Sample Questions 1. Asset allocation refers to. A. the allocation of the investment portfolio across broad asset classes B. the analysis of the value of securities C. the choice of specific assets
More informationChapter 3 Fixed Income Securities
Chapter 3 Fixed Income Securities Road Map Part A Introduction to finance. Part B Valuation of assets, given discount rates. Fixedincome securities. Stocks. Real assets (capital budgeting). Part C Determination
More informationBond Valuation. Capital Budgeting and Corporate Objectives
Bond Valuation Capital Budgeting and Corporate Objectives Professor Ron Kaniel Simon School of Business University of Rochester 1 Bond Valuation An Overview Introduction to bonds and bond markets» What
More informationSpot rates, forward rates and plot of the term structure of interest rate.
A N A L Y T I C A L F I N A N C E I I BILLS, NOTES AND BONDS MARKETS: Spot rates, forward rates and plot of the term structure of interest rate FOTSING ARMAND HAMADOU H TAKOETA FRED 1 INTRODUCTION: 3 11
More informationCHAPTER 14: BOND PRICES AND YIELDS
CHAPTER 14: BOND PRICES AND YIELDS PROBLEM SETS 1. The bond callable at 105 should sell at a lower price because the call provision is more valuable to the firm. Therefore, its yield to maturity should
More informationFinance for Cultural Organisations Lecture 5. Interest Rates and Bond Valuation
Finance for Cultural Organisations Lecture 5. Interest Rates and Bond Valuation Lecture 5: Interest Rates and Bond Valuation Know the important bond features and bond types Understand bond values and why
More informationCHAPTER 11 CURRENCY AND INTEREST RATE FUTURES
Answers to endofchapter exercises ARBITRAGE IN THE CURRENCY FUTURES MARKET 1. Consider the following: Spot Rate: $ 0.65/DM German 1yr interest rate: 9% US 1yr interest rate: 5% CHAPTER 11 CURRENCY
More informationCHAPTER 4. Definition 4.1 Bond A bond is an interestbearing certificate of public (government) or private (corporate) indebtedness.
CHAPTER 4 BOND VALUATION Gentlemen prefer bonds. Andrew Mellon, 18551937 It is often necessary for corporations and governments to raise funds to cover planned expenditures. Corporations have two main
More informationAnswers to EndofChapter Questions
Answers to EndofChapter Questions 1. The bond with a C rating should have a higher risk premium because it has a higher default risk, which reduces its demand and raises its interest rate relative to
More information2. What is your best estimate of what the price would be if the riskless interest rate was 9% (compounded semiannually)? (1.04)
Lecture 4 1 Bond valuation Exercise 1. A Treasury bond has a coupon rate of 9%, a face value of $1000 and matures 10 years from today. For a treasury bond the interest on the bond is paid in semiannual
More informationBond Market Overview and Bond Pricing
Bond Market Overview and Bond Pricing. Overview of Bond Market 2. Basics of Bond Pricing 3. Complications 4. Pricing Floater and Inverse Floater 5. Pricing Quotes and Accrued Interest What is A Bond? Bond:
More informationNotes for Lecture 3 (February 14)
INTEREST RATES: The analysis of interest rates over time is complicated because rates are different for different maturities. Interest rate for borrowing money for the next 5 years is ambiguous, because
More informationIntroduction to Money & Banking Lecture notes 2010 Matti Estola
Introduction to Money & Banking Lecture notes 2010 Matti Estola Literature Henderson & Poole: Principles of Economics, Mishkin: The Economics of Money, Banking, and Financial Markets, Extra material given
More informationReview for Exam 2. Instructions: Please read carefully
Review for Exam 2 Instructions: Please read carefully The exam will have 20 multiple choice questions and 4 work problems. Questions in the multiple choice section will be either concept or calculation
More informationChoice of Discount Rate
Choice of Discount Rate Discussion Plan Basic Theory and Practice A common practical approach: WACC = Weighted Average Cost of Capital Look ahead: CAPM = Capital Asset Pricing Model Massachusetts Institute
More informationFUNDING INVESTMENTS FINANCE 238/738, Spring 2008, Prof. Musto Class 2 Treasury Market
FUNDING INVESTMENTS FINANCE 238/738, Spring 2008, Prof. Musto Class 2 Treasury Market Today: I. Treasury Auction Schedule II. YieldtoMaturity and Discount Rate III. Bonds vs. STRIPs IV. Spread between
More informationBonds and the Term Structure of Interest Rates: Pricing, Yields, and (No) Arbitrage
Prof. Alex Shapiro Lecture Notes 12 Bonds and the Term Structure of Interest Rates: Pricing, Yields, and (No) Arbitrage I. Readings and Suggested Practice Problems II. Bonds Prices and Yields (Revisited)
More informationMidterm Exam 1. 1. (20 points) Determine whether each of the statements below is True or False:
Econ 353 Money, Banking, and Financial Institutions Spring 2006 Midterm Exam 1 Name The duration of the exam is 1 hour 20 minutes. The exam consists of 11 problems and it is worth 100 points. Please write
More informationChapter 3. Fixed Income Securities
IE 5441 1 Chapter 3. Fixed Income Securities IE 5441 2 Financial instruments: bills, notes, bonds, annuities, futures contracts, mortgages, options,...; assortments that are not real goods but they carry
More informationDescription. Investment Project. Common Stock. Some Portfolio Assets for Investment Project. Econ 422 Summer 2007 Eric Zivot July 25, 2007
Investment Project Econ 422 Summer 2007 Eric Zivot July 25, 2007 Description Objectives: learn financial institutions and conventions Essential features:» Create a $100,000 portfolio, describe it in Report
More informationC(t) (1 + y) 4. t=1. For the 4 year bond considered above, assume that the price today is 900$. The yield to maturity will then be the y that solves
Economics 7344, Spring 2013 Bent E. Sørensen INTEREST RATE THEORY We will cover fixed income securities. The major categories of longterm fixed income securities are federal government bonds, corporate
More informationCHAPTER 7 INTEREST RATES AND BOND VALUATION
CHAPTER 7 INTEREST RATES AND BOND VALUATION Answers to Concepts Review and Critical Thinking Questions 1. No. As interest rates fluctuate, the value of a Treasury security will fluctuate. Longterm Treasury
More informationBond Price Arithmetic
1 Bond Price Arithmetic The purpose of this chapter is: To review the basics of the time value of money. This involves reviewing discounting guaranteed future cash flows at annual, semiannual and continuously
More informationOPTIONS ON SHORTTERM INTEREST RATE FUTURES*
OPTIONS ON SHORTTERM INTEREST RATE FUTURES* Anatoli Kuprianov Options are contracts that give their owners the right, but not the obligation, to buy or sell a specified item at a set price on or before
More informationCHAPTER 8 INTEREST RATES AND BOND VALUATION
CHAPTER 8 INTEREST RATES AND BOND VALUATION Answers to Concept Questions 1. No. As interest rates fluctuate, the value of a Treasury security will fluctuate. Longterm Treasury securities have substantial
More informationCHAPTER 5. Interest Rates. Chapter Synopsis
CHAPTER 5 Interest Rates Chapter Synopsis 5.1 Interest Rate Quotes and Adjustments Interest rates can compound more than once per year, such as monthly or semiannually. An annual percentage rate (APR)
More information2. Determine the appropriate discount rate based on the risk of the security
Fixed Income Instruments III Intro to the Valuation of Debt Securities LOS 64.a Explain the steps in the bond valuation process 1. Estimate the cash flows coupons and return of principal 2. Determine the
More information2. Exercising the option  buying or selling asset by using option. 3. Strike (or exercise) price  price at which asset may be bought or sold
Chapter 21 : Options1 CHAPTER 21. OPTIONS Contents I. INTRODUCTION BASIC TERMS II. VALUATION OF OPTIONS A. Minimum Values of Options B. Maximum Values of Options C. Determinants of Call Value D. BlackScholes
More informationThis lesson plan is from the Council for Economic Education's publication: To purchase Learning, Earning and Investing: Middle School, visit:
This lesson plan is from the Council for Economic Education's publication: Learning, Earning and Investing: Middle School To purchase Learning, Earning and Investing: Middle School, visit: http://store.councilforeconed.org/leimiddle.html
More informationUnderstanding Fixed Income
Understanding Fixed Income 2014 AMP Capital Investors Limited ABN 59 001 777 591 AFSL 232497 Understanding Fixed Income About fixed income at AMP Capital Our global presence helps us deliver outstanding
More informationThe Time Value of Money
The Time Value of Money This handout is an overview of the basic tools and concepts needed for this corporate nance course. Proofs and explanations are given in order to facilitate your understanding and
More informationProblems and Solutions
Problems and Solutions CHAPTER Problems. Problems on onds Exercise. On /04/0, consider a fixedcoupon bond whose features are the following: face value: $,000 coupon rate: 8% coupon frequency: semiannual
More informationChapter 07 Interest Rates and Present Value
Chapter 07 Interest Rates and Present Value Multiple Choice Questions 1. The percentage of a balance that a borrower must pay a lender is called the a. Inflation rate b. Usury rate C. Interest rate d.
More informationFIN 472 FixedIncome Securities Debt Instruments
FIN 472 FixedIncome Securities Debt Instruments Professor Robert B.H. Hauswald Kogod School of Business, AU The Most Famous Bond? Bond finance raises the most money fixed income instruments types of bonds
More informationBond valuation. Present value of a bond = present value of interest payments + present value of maturity value
Bond valuation A reading prepared by Pamela Peterson Drake O U T L I N E 1. Valuation of longterm debt securities 2. Issues 3. Summary 1. Valuation of longterm debt securities Debt securities are obligations
More informationPRESENT VALUE AND INTEREST RATES
PRESENT VALUE AND INTEREST RATES Many economic decisions involve time in an important way. Students forego current consumption in favor of an education that presumably raises their incomes later on. Firms
More informationChapter 8. Step 2: Find prices of the bonds today: n i PV FV PMT Result Coupon = 4% 29.5 5? 100 4 84.74 Zero coupon 29.5 5? 100 0 23.
Chapter 8 Bond Valuation with a Flat Term Structure 1. Suppose you want to know the price of a 10year 7% coupon Treasury bond that pays interest annually. a. You have been told that the yield to maturity
More informationCHAPTER 14: BOND PRICES AND YIELDS
CHAPTER 14: BOND PRICES AND YIELDS 1. a. Effective annual rate on 3month Tbill: ( 100,000 97,645 )4 1 = 1.02412 4 1 =.10 or 10% b. Effective annual interest rate on coupon bond paying 5% semiannually:
More informationInterest Rate Futures. Chapter 6
Interest Rate Futures Chapter 6 1 Day Count Convention The day count convention defines: The period of time to which the interest rate applies. The period of time used to calculate accrued interest (relevant
More informationInvestment Appraisal INTRODUCTION
8 Investment Appraisal INTRODUCTION After reading the chapter, you should: understand what is meant by the time value of money; be able to carry out a discounted cash flow analysis to assess the viability
More informationThe Language of the Stock Market
The Language of the Stock Market Family Economics & Financial Education Family Economics & Financial Education Revised November 2004 Investing Unit Language of the Stock Market Slide 1 Why Learn About
More informationUS TREASURY SECURITIES  Issued by the U.S. Treasury Department and guaranteed by the full faith and credit of the United States Government.
Member NASD/SIPC Bond Basics TYPES OF ISSUERS There are essentially five entities that issue bonds: US TREASURY SECURITIES  Issued by the U.S. Treasury Department and guaranteed by the full faith and
More informationChapter 11. Stocks and Bonds. How does this distribution work? An example. What form do the distributions to common shareholders take?
Chapter 11. Stocks and Bonds Chapter Objectives To identify basic shareholder rights and the means by which corporations make distributions to shareholders To recognize the investment opportunities in
More informationBehavior of Interest Rates
Behavior of Interest Rates Notes on Mishkin Chapter 5 (pages 91108) Prof. Leigh Tesfatsion (Iowa State U) Last Revised: 21 February 2011 Mishkin Chapter 5: Selected Key InClass Discussion Questions and
More informationWaiting to Extend: A ForwardLooking Approach to Fixed Income Investing
Waiting to Extend: A ForwardLooking Approach to Fixed Income Investing Market Commentary May 2016 Investors sometimes want to invest with a money manager who will shorten portfolio duration in advance
More informationAmerican Options and Callable Bonds
American Options and Callable Bonds American Options Valuing an American Call on a Coupon Bond Valuing a Callable Bond Concepts and Buzzwords Interest Rate Sensitivity of a Callable Bond exercise policy
More informationBond Valuation. FINANCE 350 Global Financial Management. Professor Alon Brav Fuqua School of Business Duke University. Bond Valuation: An Overview
Bond Valuation FINANCE 350 Global Financial Management Professor Alon Brav Fuqua School of Business Duke University 1 Bond Valuation: An Overview Bond Markets What are they? How big? How important? Valuation
More informationTimeVarying Rates of Return, Bonds, Yield Curves
1/1 TimeVarying Rates of Return, Bonds, Yield Curves (Welch, Chapter 05) Ivo Welch UCLA Anderson School, Corporate Finance, Winter 2014 January 13, 2015 Did you bring your calculator? Did you read these
More informationIntroduction to Investments FINAN 3050
Introduction to Investments FINAN 3050 : Introduction (Syllabus) Investments Background and Issues (Chapter 1) Financial Securities (Chapter 2) Syllabus General Information The course is going to be organized
More informationBond Pricing Fundamentals
Bond Pricing Fundamentals Valuation What determines the price of a bond? Contract features: coupon, face value (FV), maturity Riskfree interest rates in the economy (US treasury yield curve) Credit risk
More informationAdditional Practice Questions for Midterm I
1 Finance 333 Investments Additional Practice Questions for Midterm I Winter 2004 Professor Yan 1. Financial assets. A) directly contribute to the country's productive capacity *B) indirectly contribute
More informationBond Pricing Problems with YTM YTM is the stated internal rate of return It is not guaranteed to be the realized return due to interest rate risk It may not be a correct description of expected
More informationEcon 330 Exam 1 Name ID Section Number
Econ 330 Exam 1 Name ID Section Number MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. 1) If during the past decade the average rate of monetary growth
More informationYou just paid $350,000 for a policy that will pay you and your heirs $12,000 a year forever. What rate of return are you earning on this policy?
1 You estimate that you will have $24,500 in student loans by the time you graduate. The interest rate is 6.5%. If you want to have this debt paid in full within five years, how much must you pay each
More informationMoney, Banking, and the Financial Sector
Introduction Money, Banking, and the Financial Sector Chapter 13 Real goods and services are exchanged in the real sector of the economy. For every real transaction, there is a financial transaction that
More informationPDEx GUIDELINES ON THE TRADING AND SETTLEMENT ENVIRONMENT FOR LONGTERM BANKISSUED NOTES
PDEx GUIDELINES ON THE TRADING AND SETTLEMENT ENVIRONMENT FOR LONGTERM BANKISSUED NOTES A. BACKGROUND These Guidelines on the Trading and Settlement Environment of BankIssued Notes (the Guidelines )
More informationEconomics Chapter 16 Class Notes
Section 1: Stocks Stocks and Bonds Economics Chapter 16 Class Notes Financial Markets o and are bought and sold in a financial market. o Financial markets money from some people to other people. They bring
More informationChapter 4 Discounted Cash Flow Valuation
University of Science and Technology Beijing Dongling School of Economics and management Chapter 4 Discounted Cash Flow Valuation Sep. 2012 Dr. Xiao Ming USTB 1 Key Concepts and Skills Be able to compute
More informationChapter 12 Practice Problems
Chapter 12 Practice Problems 1. Bankers hold more liquid assets than most business firms. Why? The liabilities of business firms (money owed to others) is very rarely callable (meaning that it is required
More informationChoice of Discount Rate: Basic Theory
Choice of Discount Rate Discussion in 2 Parts 1. Basic Theory 2. A Common Practical Approach: Weighted Average Cost of Capital Massachusetts Institute of Technology Choice of Discount Rate Slide 1 of 24
More informationINTERACTIVE BROKERS DISCLOSURE STATEMENT FOR BOND TRADING
INTERACTIVE BROKERS DISCLOSURE STATEMENT FOR BOND TRADING THIS DISCLOSURE STATEMENT DISCUSSES THE CHARACTERISTICS AND RISKS OF TRADING BONDS THROUGH INTERACTIVE BROKERS (IB). BEFORE TRADING BONDS YOU SHOULD
More informationSection 5.2 Compound Interest
Section 5.2 Compound Interest With annual simple interest, you earn interest each year on your original investment. With annual compound interest, however, you earn interest both on your original investment
More informationUntangling F9 terminology
Untangling F9 terminology Welcome! This is not a textbook and we are certainly not trying to replace yours! However, we do know that some students find some of the terminology used in F9 difficult to understand.
More informationExercise 6 Find the annual interest rate if the amount after 6 years is 3 times bigger than the initial investment (3 cases).
Exercise 1 At what rate of simple interest will $500 accumulate to $615 in 2.5 years? In how many years will $500 accumulate to $630 at 7.8% simple interest? (9,2%,3 1 3 years) Exercise 2 It is known that
More informationEstimating Risk free Rates. Aswath Damodaran. Stern School of Business. 44 West Fourth Street. New York, NY 10012. Adamodar@stern.nyu.
Estimating Risk free Rates Aswath Damodaran Stern School of Business 44 West Fourth Street New York, NY 10012 Adamodar@stern.nyu.edu Estimating Risk free Rates Models of risk and return in finance start
More information