Bond Problems And Solutions PdfBy StГ©phanie C. In and pdf 20.03.2021 at 20:27 3 min read
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- Problems and Solutions 1 CHAPTER 1—Problems
- Valuation Concepts
Students please refer to the attached document for quick to learn study notes and practice question database for CA Final SFM. Also refer to the other links for handwritten class notes and answers to the questions in the question banks.
Solution 1. Exercise 1. What is the number of bonds he will buy? He has two choices: either invest in a US corporate bond denominated in euros or in a French corporate bond with same maturity and coupon.
Are the two bonds comparable? First, the coupon and yield frequency of the US corporate bond is semiannual, while it is annual for the French corporate bond. To compare the yields on the two instruments, you have to convert either the semiannual yield of the US bond into an equivalently annual yield or the annual yield of the French bond into an equivalently semiannual yield.
Second, the two bonds do not necessarily have the same rating, that is, the same credit risk. Third, they do not necessarily have the same liquidity. What is the effective annual interest rate?
Solution 2. Exercise 2. What is the yield to maturity of this bond? We suppose that the zero-coupon curve increases instantaneously and uniformly by 0.
What is the new price and the new yield to maturity of the bond? What is the impact of this rate increase for the bondholder? We suppose now that the zero-coupon curve remains stable over time. You hold the bond until maturity. What is the annual return rate of your investment?
Why is this rate different from the yield to maturity? With a flat curve at a 4. An investor buys these two bonds and holds them until maturity. Compute the annual return rate over the period, supposing that the yield curve becomes instantaneously flat at a 5.
What is the rate level such that these two bonds provide the same annual return rate? In this case, what is the annual return rate of the two bonds? We consider that the investor reinvests its intermediate cash flows at a unique 5.
The annual return rate of the two bonds is equal to 5. What is the 6-month forward rate in six months? What is the 1-year forward rate in six months? R2 0, 1. Extract the zero-coupon yield curve from the bond prices.
We anticipate a rate increase in one year so the prices of strips with residual maturity 1 year, 2 years and 3 years are respectively What is the zero-coupon yield curve anticipated in one year?
Solution 3. The 1-year zero-coupon rate denoted by R 0, 1 is equal to 3. The 1-year, 2-year and 3-year zero-coupon rates become respectively 4. Compute the par yield curve. Compute the forward yield curve in one year.
Draw the three curves on the same graph. What can you say about their relative position? The graph of the three curves shows that the forward yield curve is below the zero-coupon yield curve, which is below the par yield curve. This is always the case when the par yield curve is decreasing.
So risk premia are infinite. It is as if their investment habitat were strictly con- strained, exclusive. So, there exists a certain level of risk premia from which they are ready to change their habitual investment maturity. Their investment habitat is, in this case, not exclusive.
Same question when you know the year and year zero-coupon rates that are respectively equal to 8. Solution 4. We need to know the value for the 5-year and the 8-year zero-coupon rates. We have to estimate them and test four different methods. We use a linear interpolation with the zero-coupon rates.
Find R 0, 5 , R 0, 8 and the corresponding values for B 0, 5 and B 0, 8. We use a linear interpolation with the discount factors. Find B 0, 5 , B 0, 8 and the corresponding values for R 0, 5 and R 0, 8. The table below summarizes the results obtained using the four different meth- ods of interpolation and minimization — Rates Interpol.
DF Interpol. Rates Min. DF Min. The table shows that results are quite similar according to the two methods based on rates. Differences appear when we compare the four methods.
In par- ticular, we can obtain a spread of 7. We conclude that the zero- coupon rate and discount factor estimations are sensitive to the method that is used: interpolation or minimization.
Exercise 4. The other parameters are fixed. Solution 5. We assume that the compounding frequency is semiannual. Use the modified duration to find the approximate change in price if the bond yield rises by 15 basis points. He wishes to be hedged against a rise in interest rates. YTM stands for yield to maturity. We suppose that the YTM curve increases instantaneously by 0.
For a small move of the YTM curve, the quality of the hedge is good. For a large move of the YTM curve, we see that the hedge is not perfect because of the convexity term that is no more negligible see Chapter 6.
Compounding frequency is assumed to be annual. Solution 6. The straight line is the one-order Taylor estimation. Coupon frequency and compounding frequency are assumed to be annual. What is the Macaulay duration of this bond? What does convexity measure? Why does convexity differ among bonds? What happens to convexity when interest rates rise? What is the exact price change in dollars if interest rates increase by 10 basis points a uniform shift? Use the duration model to calculate the approximate price change in dollars if interest rates increase by 10 basis points.
Incorporate convexity to calculate the approximate price change in dollars if interest rates increase by 10 basis points. Convexity measures the change in modified duration or the change in the slope of the price-yield curve. Holding maturity constant, the higher the coupon, the smaller the duration.
Hence, for low duration levels the change in slope con- vexity is small. Alternatively, holding coupon constant, the higher the maturity, the higher the duration, and hence, the higher the convexity.
When interest rates rise, duration sensitivity of prices to changes in interest rates becomes smaller. Hence, we move toward the flatter region of the price-yield curve. Therefore, convexity will decrease parallel to duration.
Problems and Solutions 1 CHAPTER 1—Problems
Established and comprehensive evaluated pricing coverage, quality, independence and delivery in fixed income markets. Python for Data Science Cheat Sheet. Convertible Bond Analysis Process. Free code editor for Windows. Heston Model Github. Midpoint, Trapezoidal, Simpson approximation for integrals and Bond pricing functions.
Yield to maturity YTM is the annual return that a bond is expected to generate if it is held till its maturity given its coupon rate, payment frequency and current market price. Yield to maturity is essentially the internal rate of return of a bond i. Yield to maturity of a bond can be worked out by iteration, linear-interpolation, approximation formula or using spreadsheet functions. The iteration method of calculating yield to maturity involves plugging in different discount rate values in the bond price function till the present value of bond cash flows right-hand side of the following equation matches the bond price left-hand side :.
Question 1. Explain the formation of a chemical bond. This can occur in two ways; by transfer of one or more electrons from one atom to other or by sharing of electrons between two or more atoms. Question 2.
What is the value of the bond, if the discount rate is 15 percent by factor formula and table? Coupons are paid semi annually, what is the price of this debt by general floating equation? What is the price of this bond? Coupons are paid semi-annually, what is the price of this bond? Coupons are paid semiannually and the next coupon payment is exactly six months away.
A financial security refers to an instrument such as a stock or bond that represents a financial claim against assets. For example, as was covered in Chapter One, bonds typically have a fixed cash flow stream over a finite time horizon while stocks typically have a variable cash flow stream over a potentially infinite time horizon. Stocks also tend to be riskier than bonds, which results in investors demanding higher rates of return to compensate for the additional risk. While financial securities may have different characteristics, the concept of valuation is essentially the same regardless of the specific security. While the definition above is more conceptual, we can easily turn it into an applied process to value all stocks, bonds, or other investment opportunities.
Если он скажет да, его подвергнут большому штрафу, да к тому же заставят предоставить одну из лучших сопровождающих полицейскому комиссару на весь уик-энд за здорово живешь. Когда Ролдан заговорил, голос его звучал уже не так любезно, как прежде: - Сэр, это Агентство услуг сопровождения Белен. Могу я поинтересоваться, кто со мной говорит.
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Надо идти за ними, думал. Они знают, как отсюда выбраться. На перекрестке он свернул вправо, улица стала пошире.