...MEASURING YIELD CHAPTER SUMMARY In Chapter 2 we showed how to determine the price of a bond, and we described the relationship between price and yield. In this chapter we discuss various yield measures and their meaning for evaluating the relative attractiveness of a bond. We begin with an explanation of how to compute the yield on any investment. COMPUTING THE YIELD OR INTERNAL RATE OF RETURN ON ANY INVESTMENT The yield on any investment is the interest rate that will make the present value of the cash flows from the investment equal to the price (or cost) of the investment. Mathematically, the yield on any investment, y, is the interest rate that satisfies the equation. ------------------------------------------------- P = ------------------------------------------------- ------------------------------------------------- where CFt = cash flow in year t, P = price of the investment, N = number of years. The yield calculated from this relationship is also called the internal rate of return. ------------------------------------------------- ------------------------------------------------- Solving for the yield (y) requires a trial-and-error (iterative) procedure. The objective is to find the yield that will make the present value of the cash flows equal to the price. Keep in mind that the yield computed is the yield for the period. That is, if the cash flows are semiannual, the yield is a semiannual yield. If the cash flows are monthly, the yield is a...
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...Yield Curve and Bond Valuation Name: Lecturer: Course: Date: Yield Curve and Bond Valuation Question 1 and 2 Based on the information retrieved from the Board of Governors of the Federal Reserve System on a 1-month business day, the following information concerning historical dairy interest rates on the U.S treasury was obtained. The rates were picked from the current dates (1st January2012) back to five years a go (1st January 2007). Whereby, if that date was not a business date the preceding date was selected as shown in the table below. |Business Date chosen Five Years Ago |1st January 2007 | |1-month Nominal T-bill Rate on that date |5.02% | |3--month Nominal T-bill Rate on that date |4.79% | |6-month Nominal T-bill Rate on that date |5.11% | |1-year Nominal T-note Rate on that Date |5% | |5-year Nominal T-note Rate on that Date |4.68% | |10-year Nominal T-note Rate on that Date ...
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...MEASURES OF YIELD In order to be able to exhaust the measures of yield, the following terms will be of great essence in helping maximum elaboration of the measures. Coupon: The interest payment sent to the owner of an individual bond, usually twice a year. The coupon rate is the interest rate the issuer promises to pay to the investor. For fixed-income investments, this rate is fixed at the time a bond is issued and doesn't change. Market interest rates: The prevailing interest rates in the bond markets on any particular day. These rates change based on the economy, policies and other factors. There is no single market interest rate. The rates will vary based on the time to maturity for a particular bond, the credit quality of the issuer and other factors. Market price: The current value of an existing bond if you wanted to sell. This is the price you'd see on your quarterly statements. Market prices can be above (or at a premium to) the par value, or below (at a discount to) the par value, depending on current market interest rates, the promised coupon rate and other conditions. Maturity: The date that a bond's par (face) value is repaid and interest payments stop. The longer the time to maturity, generally, the higher the interest rate will be—but the higher the risk of a bond's price falling, as well, if market interest rates increase. As time passes and the maturity date approaches, the impact of interest rates declines. The price of a bond, if trading...
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...Why I like High Yields Bonds 1. Defaults LOW-now & and in the forseeable future are not a significant factor: * Fundamentals-reduced expenses, reducing debt(deleveraging), Diluting stock holders to raise capital-beautiful environment to service debt. “Companies are not expanding they are maintaining” “We have one the best credit quality periods in the HY space U.S. History” 2. Liquidity controlled-Keeping maturities shorter- Having the ability to move out of positions more easily is controlled by shorter maturities. This also helps reduce the effect of interest rate hikes. “We like modest inflation because of our shorter duration-as bonds roll off we can reinvest at better yields” 3. More predictable returns with reduced volatility: * Promise to pay * Increased claims right on company(better than stock, preferreds)-Have been increasing our senior secured positions.-now @35% * In Jan. 2004 the HY prices were a few percent higher on the index than they are now and the return on the index(Merrill Lynch HY Master) in 2004 was 10.76%. * In the last 25 years the index has had 20 positive years and only 5 negative. With a 25 year period return of over 9% * From 1992 thru Jan 1 2009 the standard deviation of HY bonds has been ½ of the SD of the S&P 500(source factset) 4. Non-coorelation to U.S. Treasury * As interest rate rise treasury prices increase and yield declines-our shorter term portfolio enjoy the strength of a growing...
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...What fundamentals affect the yield of bonds (Singapore market) By: G8 Lee Kang Wee Olivia Tan Daryle-‐alexis Tan Ho Guoming FIIM FNCE 102 Professor Huang Sheng Introduction As an international financial centre with about 11% of GDP from financial services, we felt it would be interesting to find out more about the Singapore money market. Since the start of the new millennium, Singapore’s bond market has taken off and has now one of the most developed bond markets in Asia with about SGD357 billion in 2011 and this number is expected to grow further with more and more money flying into Asia from the West due to various economic situations. One area of high growth is in the Islamic debt area. For the purpose of ...
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...The percentage yield acts as a guideline to tell the successfulness of the synthesis experiment. A low percentage yield enable d means that the conditions were not most favorable and could be better. The percentage yield of the synthesized aspirin obtained in this experiment is 13.8%, which is considered as relatively low. Some errors like random human errors and mechanism errors may have occurred. One of the sources of error might occur during the addition of ice water to the mixture for complete recrystallisation. There is a possibility that the ice water is not at its optimal temperature. The temperature of the ice water will increase because it is placed under room temperature for a period of time when waiting for the Erlenmeyer flask...
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...What’s That Smell? Due Date/Submission Date: 02/17/2014 I. Purpose To synthesize a fragrance used commercially in two steps by using a chemoselective reduction reaction, and a polymer-supported reaction. II. Reaction Equations and Mechanisms III. Calculations Part 1 Theoretical Yield 1) (1.62 g ethyl vanillin x 154.16 g ethyl vanillyl alcohol) / (166.18 g ethyl vanillin) = 1.503 g ethyl vanillyl alcohol 2) (0.3 g NaBH4 x 154.16 g ethyl vanillyl alcohol) / (37.83 g NaBH4) = 1.223 g ethyl vanillyl alcohol Percent Yield = (1.03 g / 1.223 g) x 100 = 84.2% Melting Point Range ( ̊C): 83.9, 84.4, 85.0 Melting Point Average ( ̊C): 84.43 Rf Values Starting material = 4.0/5.5 = 0.73 Final product = 1.7/5.5 = 0.31 Part 2 Theoretical Yield 3) (1.00 g ethyl vanillyl alcohol x 182.2 g methyl diantilis) / (154.16 g ethyl vanillyl alcohol) = 1.182 g methyl diantilis 4) (0.5 g NaHCO3 x 182.2 g methyl diantilis) / (84.007 g NaHCO3) = 1.084 g methyl diantilis Percent Yield = (0.812 g / 1.084 g) x 100 = 74.9% Rf Values Starting material = 1.9/5.4 = 0.35 Final product = 3.6/5.4 = 0.67 Starting material = 1.9/4.9 = 0.38 Methyl Diantilis = 2.9/4.9 = 0.59 IV. Results Part 1 Initial Mass Ethyl Vanillin = 1.621 g Initial Mass NaBH4 = 0.308 g Final Mass Ethyl Vanillyl Alcohol = 1.03 g When NaOH was added to ethyl vanillin, solution turned yellow in color and after refluxing, it remained yellow. While adding 6 mL of HCl...
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...Lab: STOIOCHIOMETRY OF A PRECIPITATION OF REACTION By: Ruth Pierre 6/1/15 PURPOSE Stoichiometry is a section of chemistry that involves using relationships between reactants and products in a chemical reaction to determine desired quantitative data. Stoichiometry means the measure of elements. In order to use stoichiometry it is important to understand the relationships that exist between products and reactants and why they exist, which require understanding how to balanced reactions. The purpose of this experiment is to predict the amount of product produced in a precipitation reaction using stoichiometry. This experiment will also to determine the actual yield versus the theoretical yield in order to calculate the percent yield. MATERIALS * Distilled water * Paper towels * Small paper cup * Coffee cup or mug * Beaker 100 ml glass * Funnel * Cylinder 25 ml * Goggles for safety * Scale Digital-500g * Weighing boat plastic * CaCl2·2 H2O-Calcium Chloride, Dihydrate - 2.5 g * Filter Paper 12.5-cm, Na2CO3 -Sodium Carbonate - 2 g PROCUDURE 1. Put on your goggles. 2. Weigh out 1.0 g of CaCl2·2H2O and put it into the 100-mL beaker. Add 25 mL of distilled water and stir to form the calcium chloride solution. Use only distilled water since tap water may have impurities that interfere with the experiment. 3. Use stoichiometry to determine how much Na2CO3 you will need for a full reaction. 4. Weigh the calculated...
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...9/23/2015 (Laura Williams) (Jasmine Threadcraft) Alice Chon Friedel-Crafts Alkylation Friedel-Crafts Alkylation Reaction: Abstract This experiment demonstrates a synthesis of a 1,4-di-t-buytl-2,5-dimethoxybenzene by reacting 1,4-dimethoxybenzene with a tertiary-butyl alcohol with the presence of a Lewis acid, sulfuric acid (H2SO4), called a Friedel-Crafts mechanism. This reaction yield a product of 67.96% yield and a melting point starting at 103˚C and a complete melting point around 106˚C. Am HNMR spectrum revealed that the end product of 1,4-di-t-buytl-2,5-dimethoxybenzene was synthesized successfully. The small range of the melting point indicated the good purity which also indicated the formation of a Friedel-Crafts reaction. Introduction Charles Friedel and James Crafts were the first to develop a method that alkylates and acylates aromatic rings in an easy synthesis. This is one of the oldest methods of forming C-C bonds by functioning unbiased arenas with unactivated C-H bonds. In their research, they isolated a pentylbenzene after a reaction of 1-chloropentane and benzene using a stoichiometric amount of a Lewis Acid promoter, AlCl3. With this success, many Lewis acids have been tested throughout the years in the Friedel-Crafts alkylation to develop more synthetic use. Research is still ongoing and being done today of finding more efficient and easily executed Lewis acids to produce non-toxic, metal free by-products...
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...Bond Valuation -Par Value$1000 / 4% coupon Paid Annually -5 years to maturity / Market yield 0 | 1 | 2 | 3 | 4 | 5 | | 40 | 40 | 40 | 40 | 40 | | | | | | 1000 | Calculator Solution N=5 Bond Terminology Face Value or Par Value- Amount to be repaid at end of loan Coupon- Stated interest payment made on bond Coupon Rate- The annual coupon/ Face Value of Bond Maturity- Specific Date the bond principle must be repaid Time to Maturity- the number of years until maturity Yield to Maturity- Return to bond holder if they hold the bond to maturity, Market driven rate, I/Y on your calculator Current Yield= (Annual coupon$/Current bond price) *100 Bond Par Value | 1,000.00 | FV | 1,000 | Years to Maturity | 5.00 | N | 5 | Coupon Rate | 6.0% Paid Annually | PMT | 60.00 | Yield to Maturity | 6.8% | I/Y | 6.80 | Current Price | ???? | CPT PV | | Par Value | 1,000.00 | FV | 1,000 | Years to Maturity | 5.00 | N | 10 | Coupon Rate | 6.0% Paid Semiannually | PMT | 30.00 | Yield to Maturity | 6.8% | I/Y | 3.40 | Current Price | ???? | CPT PV | 966.57 | Bond Information $1,000 Face or Par Values 10 Years to Maturity 6.6% coupon rate/ Paid SEMIANNUALLY Market Yield to Maturity 6.2% N | 20 | I/Y | 3.1 | PMT | 33 | FV | 1000 | CPT PV | $1029.48 | Bond Price | 980.00 | N | 16 | Par Value | 1000.00 | PV | (980.00) | Coupon Rate | 6% PAID SEMIANNUALLY | PMT | 30.00 | Years to Maturity | 8 | FV | 1,000 | Yield to Maturity...
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...that dividends would be steady or will increase at a perpetual rate for years. But we know that due to the ups and downs of the economy it can be pretty tricky to forecast exactly what the dividends would be year from now. #3 Yes I was noticing in order to calculate the DDM there are three main inputs to have and I was missing at least one or tow to be able to calculate it. DPS(1) = Dividends expected to be received in one year Ks= requires rate of return for a specific investment G=growth rate in dividends in years from now at some point I found it tricky to come up with these components to calculate for DDM. As I searched on line there are more than one way to calculate DDM so it was a bit challenging. !!! #4 In bond investing, yield is the tool to measure the return of...
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...Bond Practice Problems II 1. Seven years ago your firm issued $1,000 par value bonds paying a 7% semi-annual coupon with 15 years to maturity. The bonds were originally issued at par value. a. What was the original yield to maturity on the bonds? They were issued at par…so the YTM = Coupon rate: 7% b. If the current price of the bonds is $875, what is the yield to maturity of the bonds TODAY? 1000 FV .07(1000)÷2= PMT (15-7)*2 = N -875 PV I/Y = 4.623*2 = 9.25% c. If the yield to maturity computed in part b remains constant, what will be the price of the bonds three years from today? Leave everything the same, just change N to (8 – 3)*2 = 10 PV = $911.70 2. You are looking to invest some money and identify two $1,000 par bonds with the same risk, both with 12 years to maturity and paying semi-annual coupons. Each of the bonds has a required return of 7%, but one bond is priced at $839.42 and the other at $1,120.44. Compute the annual coupon rates for each bond. 1000 FV Only difference is price for second one 12*2 N -1120.44 PV 3.5 I/Y -839.42 PV PMT = 42.5*2 = 85 PMT = 25*2 = 50 C. Rate = 85/1000 = .085 = 8.5% C . Rate = 50/1000 = .05 = 5% 3. A $1,000 par bond has a 5% semi-annual coupon and 12 years to maturity. Bonds of similar risk are currently yielding 6.5%. a. What should be the current price of the bond? 1000 FV .05(1000)÷2= PMT 12*2 = N 6.5/2 = I/Y PV = $876.34 b. If the bond’s price five years from...
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...Bond prices, interest rates, spot rates Ex: a bond gets issued at $1000 par value, with a coupon rate of 10%. The bond will expire in 5 years. We know that the coupon payments are $100 (10% of par value). The payments happen at the end of each year. So at the end of year 1, the bondholder gets $ Now, the interest rate goes up. WHY WOULD THE INTEREST RATE GO UP? IS IT THE CENTRAL BANK THAT DETERMINES THAT THIS INTEREST RATE MOVE UP? IS THIS INTEREST RATE (FOR ONLY ONE PERIOD) THE SAME AS THE SPOT RATE? ALSO, UNTIL BEFORE WE STARTED TALKING ABOUT SPOT RATES WE ALWAYS ASSUMED THAT “INTEREST RATES WERE THE SAME EACH YEAR”. DOES THIS MEAN THAT THE TERM STRUCTURE OF INTEREST RATES IS FLAT? What happens to the bond? The coupon payments are still going to be the same ($100 at the end of each year). But the yield to maturity changes. What is the YTM? * It is the total return you will receive if you hold the bond until maturity * The rate of return anticipated on a bond if held until the end of its lifetime. * It’s considered a long-term bond yield expressed as an annual rate. * The YTM calculation takes into account the bond’s current market price (PV of all of the bond’s cash flows), par value, coupon interest rate, and time to maturity. * It assumes that all coupon payments are reinvested at the same rate as the bond’s current yield (WHAT DOES THIS ACTUALLY MEAN? IF YOU SELL IT BEFORE IT MATURES, THEN YOU DON’T GET THAT ACTUAL YIELD? IS IT BECAUSE SINCE...
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...calculate the convexity for the two bonds you selected for the Module Two Assignment. Conduct an analysis of their duration and convexity and expound on the difference between the two concepts. Since I did not choose two bonds in Module Two Assignment, I considered the following bonds: **Using the dollar value of the bond and a $1000 face value, I considered a bond that has the following: Coupon rate-5 % Years remaining to maturity-5 Priced to yield- 4% Semi-annual interest Effective Duration: Yield 3% 4% 5% Value 109.222 104.491 100.000 Effective duration = (109.22218 – 100)/(2*104.49129*0.01) = 4.41289 The approximate change in price if the yield increases from 4% to 5% is: 4.41289 x 0.01 x –1 = –4.41289% Considering a bond that has the following: Coupon rate-5 % Years remaining to maturity-10 Priced to yield-4% Semi-annual interest Running Head: Calculate Convexity Effective duration: Yield 3% 4% 5% Value 117.168 108.175 100.000 Effective duration = (117.16864 - 100)/(2 (108.17572) (0.01)) = 7.935533 The approximate change in price if the yield increases from 4% to 5%: 7.935533 x 0.01 x –1 = –7.935533% Considering a bond that has the following: Coupon rate-10% Years to maturity-5 Yield 9% 10% 11% Value 103.956 96.231 100.000 Effective Duration = (103.956-96.231)/ 2(100)(0.01)= 77.25/20=3.8625 Effective duration= 3.8625 years Considering three different bonds that may have different convexity: Bond 1 2 3 Coupon 5 percent 10 percent 10...
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...Problem 5-1 Current market price Given: Interest paid annually $1,000 par value 12 years to maturity Coupon rate of 8% Yield to maturity of 9% Using a financial calculator phone app PMT=80 FV=1000 I=9% N=12 Current market price=$928.39 Problem 5-2 Yield to Maturity Given: Interest paid annually $1,000 par value 12 years to maturity Coupon rate of 10% Current price=$850 Using a financial calculator phone app PV=-850 PMT=100 FV=1000 N=12 Yield to Maturity=12.48% Problem 5-6 Market Risk Premium Given: Risk Free Rate=3% Inflation=3% for two years Current Yield=6.3% Current Yield=rRF+IP+MRP 6.3%=3%+3%+MRP MRP=.3% Problem 5-7 Current Price of the Bond Given: Interest paid semiannually $1,000 par value 8 years to maturity Coupon rate of 10% Yield to maturity of 8.5% Using a financial calculator phone app PMT=100 FV=1000 I=8.5% N=8 Current market price=$1085.80 Problem 5-13 Yield to Maturity Given: 5 years to maturity Par value of $1000 Coupon Rate=8% Current Yield=8.21% Using Excel =RATE(5,80,-974.42144,1000) Yield to Maturity= 8.65% Question 6-6 If a company’s beta were to double, would its expected return double? No, the expected return will increase but since the beta is multiplied by the market risk premium it will not double as the beta does. Problem 6-1 Portfolio Beta Given: $35,000 in stock1 Beta1=.8 $40,000 in stock2 Beta2=1.4 Portfolio beta= (.46667)(.8)+(.53333)(1.4)=1.12 Problem 6-2 ...
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