Investment Management Free Essays

UNIVERSITY OF TEXAS AT DALLAS SCHOOL OF MANAGEMENT FIN6310: INVESTMENT MANAGEMENT SOLUTIONS TO PROBLEM SET #1 PROF. ARZU OZOGUZ SPRING 2013 1. Calculate the value of the following two bonds. We will write a custom essay sample on Investment Management or any similar topic only for you Order Now Assume that coupon payments are made semi-annually and that par value is $1,000 for both bonds. Coupon rate Time to maturity Yield-to-maturity Bond A 5% 5 yrs 7. 2% Bond B 5% 25 yrs 7. 2% Recalculate the bonds’ values if the yield to maturity changes to 9. 4%. Which bond is more sensitive to the changes in the yield? Will this always be the case? When the yield-to-maturity is 7. %, the bond prices are, respectively, 1 1 1. 036 0. 036 1 1. 036 0. 036 1 1. 047 0. 047 1 1. 047 0. 047 25 1000 1. 036 1000 1. 036 908. 98 1 25 746. 58 When the yield-to-maturity is 9. 4%, the bond prices are, respectively, 1 25 1000 1. 036 1000 1. 047 827. 62 1 25 579. 01 Price of bond A decreases by 8. 95%, while price of bond B drops by 22. 45%. The longer term bond is more sensitive to a given change in the discount rate. This will always be the case. Mathematically, there are more terms in the equation for the longer-term bond that are influenced by the discount rate. Practically speaking, your money is tied up longer with a longer term bond and so you will experience greater capital losses and gains when interest rates change. 2. A bond with a coupon rate of 4. 7% is priced to yield 6. 30%. Coupon is paid is semi-annually; the par value is $1,000. The bond has 5 years remaining until maturity. Assuming that market rates stay the same over the next five years, calculate the value of the bond at the beginning of each year and the amount of change in the bond’s value from year to year. Describe the behavior of the bond’s value over time. At t = 0, at issue the price will be 1 1 1. 0315 0. 0315 1 1. 0315 0. 0315 1 1. 0315 0. 0315 1 1. 0315 0. 0315 1 1. 0315 0. 0315 23. 5 1000 1. 0315 932. 28 At the end of year 1, the price becomes 1 23. 5 1000 1. 0315 1000 1. 0315 1000 1. 0315 1000 1. 0315 944. 20 1 23. 5 956. 88 1 23. 5 970. 37 1 23. 5 1000 984. 73 The price change from year to year is ? ? ? ? ? 11. 92 12. 68 13. 49 14. 36 15. 27 The bond is selling at a discount today; its price will rise to move toward par value at maturity. The change in price increases as it gets closer to maturity. 3. Suppose that you purchased a 20-year bond that pays an annual coupon of $40 and is selling at par. Calculate the one –year holding period return for each of these three cases. a. The yield-to-maturity is 5. 5% one year from now. If the yield-to-maturity is 5. 5% one year from now, the bond will be selling for 1 1 1000 1. 055 40 825. 89 1. 055 0. 055 Hence, the holding-period-return (HPR) is: 825. 89 40 1000 13. 41% 1000 b. The yield-to-maturity is the same one year from today as it is today. In this case, the bond price will remain at par and therefore the holding period return equals to coupon rate 4% c. The yield-to-maturity is 2. 5% one year from now. 1 1000 1. 025 40 1224. 68 1. 025 0. 025 Hence, the holding-period-return (HPR) is: 1224. 68 40 1000 26. 47% 1000 1 4. Plot the yield curve implied by the data in the following table. Time to maturity 3 months 6 months 1 year 2 years 5 years 10 years 15 years 20 years Yield-tomaturity 2. 40% 2. 60% 3. 00% 4. 30% 4. 80% 5. 70% 6. 40% 5. 20% Based on the Expectations Hypothesis, what does the yield curve tell us about short-term rates 5 years from now? What does it tell us about short rates 15 years from now and 20 years from now? Since the yield curve is upward sloping through the fifth year, investors expect that short term rates will be higher during that period than they are today. That is, they expect the 3-month rate to be higher than 2. 4% when five years have passed. They also expect short term rates to be higher than current rates in 15 years. This is reflected in the slope of the yield curve which is positive through year 15. However, the expectation is that after 15 years, short term rates will begin to fall again. The downward slope in the yield curve is a sign of that expectation. That is, the 3-month rate that prevails 20 years from now is expected to be lower than the 3-month rate that prevails 15 years from now. 5. The current yield curve for default free zero-coupon bonds is as follows: Maturity (years) 1 2 3 Yield-tomaturity 10% 11% 12% a. What are the implied one year forward rates? The one-year forward rate for time 2 solves the following equation: 1. 11 1. 10 1 12. 009%. Similarly, the one-year forward rate for time 3 solves That is, the equation: 1. 12 That is, 14. 0271% 1. 11 1 b. Assume that the expectations hypothesis of the term structure is correct. If market expectations are accurate, what will the yields to maturity on one year and two year zero coupon bonds be next year? We have already computed the forecast for the one year rate next year. We must now compute the expectation for the 2-years to maturity. This must equate the strategy that consists of investing for 3 years at the current 3-year spot rate with the strategy of investing at the one-year spot rate and then rolling over the profits into a two-year bond one year from now: 1. 10 1 1. 12 13. 0136%. Hence, the forecast for the one-year yield is This implies that 12. 09%, and forecast for the two-year yield is 13. 0136%. c. If you purchase a two year zero coupon bond now, what is the expected total rate of return over the next year? What if you purchase a three year zero coupon bond? You can assume that the par value is $100. We need to compute the forecasted price of the two-year zero-coupon bond at the end of the first year. Notice that by that time this has become a one-year bond. Hence its price is 1000 1. 12009 892. 79 Today the price of this bond is simply 892. 79 811. 62 does not pay any coupons, its return is given by: 1 1 10% . 11. 62. Since this bond Similarly, if you purchase a three-year zero coupon bond today, the forecasted price a year later is 1000 1. 130136 Today, this bond’s price is simply expected holding period return is 78. 295 71. 178 1 78. 295 . 71. 178. Therefore, the 10% 6. Consider the following three bonds. You are investigating how the bonds would react to changes in interest rates. Bond A Face value Years to maturity Coupon rate Yield-to-maturity $1,000 3 5. 5% 4. 80% Zero-coupon bond $1,000 2. 85 0 4. 80% Bond B $1,000 3 8. 75% 4. 80% Assume that coupons are paid once a year. . Find the duration of each bond. Bond A Time 1 2 3 Price ZCB Time 2. 85 Price Bond B Time 1 2 3 Price Cash Flow 87. 5 87. 5 1087. 5 Present value 83. 49 79. 67 944. 81 1107. 97 Weight 0. 075 0. 072 0. 853 Cash Flow 1000 Present value 874 . 92 874. 92 Weight 1. 000 Cash Flow 55 55 1055 Present value 52. 48 50. 08 916. 58 1019. 13 Weight 0. 051 0. 049 0. 899 Hence, the durations are: 0. 051 0. 075 1 1 0. 049 0. 072 2 2 0. 899 0. 853 3 3 2. 85 2. 78 2. 85 b. Calculate the modified duration of each bond. The modified durations are ? ? 2. 85 2. 72 1. 048 2. 78 2. 5 1. 048 c. Calculate the estimated percentage change in price of each bond due to a 0. 50% change in yield to maturity. The percentage change in the price of each bond due to a change in the yield? ? ? to-maturity is ? ? ? 2. 72 2. 65 0. 5% 1. 36% 1. 33% 0. 5% d. What can you conclude about the reactions of the bonds? Specifically, compare the percentage price changes of the bonds with similar durations and the bonds with similar maturities. Bonds with equal durations are more alike than bonds with equal maturities in their reactions to changes in yields. 7. Suppose that your insurance company has issued a Guaranteed Investment Contract (GIC) that matures in three years and promises to pay an interest rate of 23. 36%. The amount invested in GIC today is $150,000. You have decided to immunize your position by purchasing a bond that has a par value of $150,000, a coupon rate of 23. 36%, and four years to maturity. The bond is selling currently at par value. a. What is the future value of your company’s obligation? The future value of the obligation is $150,000 1. 2336 $281,588. 13 b. Assume that the interest rate stays at 23. 36%. At the date at which each payment is received, compute the accumulated value of reinvested coupons and the proceeds from the bond sale. How close will you come to your meeting your obligation? The bond pays a coupon of $150,000 23. 36% $35,040. If the market rates remain unchanged, at the end of year three it will be possible to sell the bond still at par. With this information, we can construct the following table: Year 1 2 3 3 Total future value Cash flow 35,040 35,040 35,040 150,000 Accumulated value 53,322. 78 43,225. 34 35,040 150,000 281,588. 13 That is, you will be able to repay your obligation in full. How to cite Investment Management, Essay examples Investment Management Free Essays 24/02/2013 1 25721 INVESTMENT MANAGEMENT Lecturers: Sean Anthonisz Nadima El-Hassan Jianxin Wang Brandon Zhu Subject Coordinator: Jianxin Wang Objectives 2 ? ? ? ? Why do you take this subject? What do you expect to learn? How much did you pay for this subject? Is this a good investment? Investment Decisions 3 ? ? How much should I invest in risky assets? How much should I invest in different risky assets? ? ? How many risky assets should I hold? When not to diversify? ? How to determine mispricing? Fair value today? Expected return next year? ? How well do asset pricing models work? ? ? 1 24/02/2013 Investment Decisions 4 ? Passive versus active investing ? ? Is market efficient? Why not? What does it take to beat the market? How to hedge and how much to hedge? Derivative pricing Trading cost, liquidity, private information ? How should I manage risk? ? ? ? How should I trade? ? ? Sources of my performance? What Do We Learn in This Subject? 5 ? ? ? ? A theoretical framework for portfolio construction. A theoretical framework for the pricing of equities and bonds. Some practical applications of asset pricing models and portfolio analysis. We will write a custom essay sample on Investment Management or any similar topic only for you Order Now Issues relating to market efficiency and investor behaviour. Course Structure 6 Funds Management Information Portfolio Theory Risk and Return Markets and Investing CAPM Factor Models APT Options Fixed Income Equities Futures 2 24/02/2013 Investment Electives 7 ? ? ? ? ? ? 25705 Financial Modelling and Forecasting 25728 Bond Portfolio Management 25729 Applied Portfolio Management 24731 International Finance 25762 Synthetic Financial Products A whole range of subjects for Quant Fin majors: technical analysis, numerical analysis, fin econometrics, stat methods, derivative pricing, interest rate modelling. Prerequisite 8 ? ? 25742 Financial Management Basic math and statistics Basic calculus and optimization Probability and distributions ? Mean, variance, standard deviation, covariance ? Linear regression by ordinary least square (OLS) ? ? ? Read the online Quantitative Review ? A very brief review next week What Is Expected – in class 9 ? Lectures are primarily aimed at Identifying and explaining key concepts and issues Highlighting the links to practice ? Completing selected problems from text ? ? ? Questions are encouraged and rewarded. ? Discussion is better than lecture Mutual respect and encouragement; Potential problems: repeated late arrivals, chatting during lecture, academic honesty Code of behavior ? ? 3 24/02/2013 What Is Expected – outside class 10 ? Address some details within the course reading materials. ? Group study is more effective ? ? Workload is about 7-8 hours per week on average (albeit uneven), including course readings, practices, and assignments. Multiple learning channels: ? ? Multiple levels of learning: ? Web-bas ed learning support Lecture material, textbook, and Excel sheets Approach to Learning 11 ? ? ? Read relevant chapters prior to lectures Attempt to identify and understand the key messages: Concepts? Issues? Connections? Ask questions during lecture. ? You paid $$$ for the opportunity ? ? Think reflect; don’t just summarize memorize. Practice using back-of-chapter questions. Approach to Learning — I listen and I forget; I see and I remember; I do and I understand. —Xun Zi Just Do It! —Nike 12 4 24/02/2013 Textbook and Readings 13 ? Bodie, Kane, Marcus, Investments, 9th Ed, McGraw-Hill/Irwin, 2011. ? You take full responsibility if using an earlier edition. ? ? ? ? Harvard Business School case study 9202-024 â€Å"Strategic Capital Management†. R. A. Haugen, Modern Investment Theory, 5th Ed, Pearson Higher Education, 2001. J. H. Cochrane, 2006, Investments Notes. Other fun books on financial markets. Assessments 14 ? Weekly online quizzes: 10 marks ? ? ? ? ? 15 MC questions in 1 hour Unlimited tries with the best mark kept Monday morning to next Wednesday midnight Once closed, quizzes cannot be reopened Best 10 marks for the semester Group-based case report Online group registration Report due 5pm Friday March 29 Late submissions carry point deduction ? Case study in lecture 6: 10 marks ? ? ? ? Assessments 15 ? Mid-session exam: 40 marks ? ? ? ? Cover lectures 1 – 6, including the case study Multiple-choice (20 marks) Short-answer questions (20 marks) No formula sheet Cover lectures 7 – 13, excluding lecture 8 Multiple-choice (20 marks) Short-answer questions (20 marks) A short list of formulas will be identified and provided during the final exam. ? Final exam: 40 marks ? ? ? ? 5 24/02/2013 Online Group Registration 16 ? ? ? ? ? ? Log in the online course website Click on â€Å"Groups† in the left panel Group names contain â€Å"1m†, â€Å"2m†, â€Å"3m†, â€Å"4m†, indicating max members = 1, 2, 3, 4, respectively. The first member is the group leader. Registration closes after 5pm on March 10. Changing group only in the most extreme circumstances. What’s Required? 17 ? ? ? Materials covered in the chapters listed in the lecture program, except certain subsections are explicitly excluded. The midsession and the final exams will focus on materials covered during lectures, with at most 3-4 multiple-choice questions in each exam on materials not covered in lectures. Materials not covered in lectures will be heavily featured in the online quizzes. Administrative Issues 8 ? Name sign: â€Å"Open† for the business of learning ? Take it out at the start of every lecture It’s good to make the lecturer know your name ? Come to consultation hours ? ? ? Other times by appointment Email for straightforward questions Complex questions are best answered through interactive discussion ? Emails will be answered before or during the next consultation hours ? 6 24/02/2013 Learning Support â €“ Postgraduate ? ? ? ? ? Need help with your postgraduate studies at UTS Business School? Are you new to university / postgraduate education? Not sure to how develop your academic skills in writing, reading, critical thinking etc.? Not sure how to complete assignments or achieve your best? Ask for help from the Learning Support Coordinator ? ? ? ? ? ? Make appointments for confidential individual help Lots of ‘online study resources’ to recommend / hardcopy study resources to share Attend the Study Skills Workshops all semester / or download them / Help by email / phone support / Email: learningsupport@uts. edu. au www:http://www. business. uts. edu. au/teaching/student/resources/studen t-learning. tml Join us on facebook UTSBlearningsupport ? Asset Classes 20 ? ? ? ? ? ? The money market The bond market The equity market The real estate market Currency markets Derivative markets ? Financial and commodities ? Others? Trading Platforms 21 ? Organized exchanges Dealership markets Auction markets ? Electronic trading ? ? ? ? OTC – NASDAQ Alternative trading systems (ATS) ? ECNs, dark pools, internal crossi ngs. ? Algorithm/high frequency trading 7 24/02/2013 High Frequency Trading 22 ? Menkveld (2011): a HFTer on Chi-X Dutch stocks from Jan 2007 to June 2008 Trades 1400 times per stock per day ? Gross profit per trade â‚ ¬0. 88 ? ? ? ? ? â‚ ¬1. 55 profit on the spread net of fees â‚ ¬0. 45 profit on positions 5 seconds â‚ ¬1. 13 loss on positions = 5 seconds Max capital committed ? â‚ ¬2 million per stock ? Implied annualized Sharpe ratio = 9. 35! ? ? Sharpe ratio for SP500 over the period = -0. 16 ? Chi-X is in Australia. Costs of Trading 23 ? Commission: fee paid to broker for making the transaction ? Exchange members/subscribers? ? Spread: Bid and ask prices Spread: ask – bid ? P89, #14 ? Market versus limit orders ? ? ? Price impact of large trades Stock Margin Trading 24 ? ? ? ? Borrow (from brokers) to purchase shares Initial margin Maintenance margin – minimum level the equity margin can be Margin call ? Call for more equity funds ? Margin arrangements differ for stocks and derivatives 8 24/02/2013 Margin Trading – Initial Conditions 25 ? ? ? ? ? X Corp: P = $70 Initial Margin = 50% Maintenance Margin = 40% 1000 Shares Purchased Initial Position: Stock $70,000 Borrowed Equity $35,000 $35,000 Maintenance Margin 26 ? ? Stock price falls to $60 per share New Position ? $60,000=$35,000(Borrowed) + 25,000(Equity) ? Margin = $25,000/$60,000 = 41. 67% How far can the price fall before a margin call? ? ? (1000P – $35,000) / 1000P = 40% P = $58. 33 ? P88, #9 Short Sale 27 ? ? Purpose: Profit from a price fall Mechanics Borrow stock through a dealer/broker Sell it and deposit proceeds and margin in an account ? Any dividend is passed back to the lender ? Closing out the position ? ? ? ? Buy back the stock and retu rn it to the lender Profits can be deposited into your own account ? Naked versus covered short sale 9 24/02/2013 Short Sale – Initial Conditions 28 Z Corp Initial Margin Maintenance Margin Initial Price Sale Proceeds Margin Account Balance 100 Shares 50% 30% $100 $10,000 $ 5,000 $15,000 Short Sale – Maintenance Margin 29 ? Stock Price Rises to $110 Stock owed Net equity ? Margin % (4000/11000) ? ? $11,000 $ 4,000 36% ? ? How much can the stock price rise before a margin call? ($15,000 – 100P) / (100P) = 30% P = $115. 38 P89, #12 Summary 30 ? Course introduction and requirements ? Think, reflect, and participate ? ? Financial markets and assets Trading of financial assets Trading platforms Transaction costs ? Margin trading and short selling ? ? 10 How to cite Investment Management, Essay examples