Investment Management assignment- here I attached questions and calculations, could you please help on Q1 (c), Q2 (c), Q3 (c) ? I need graphs and explanations respectively

Finance Discipline Group UTS Business School 25721 Investment Management AssignmentPart II Autumn 2016 1. The assignment should be completed individually. 2. Help: For consultation times, please check UTSOnline and the subject outline. Note that email is not an efficient way for asking questions about the assignment; please post any questions on the UTSOnline Discussion Board. 3. Due date: A hard copy of the assignment should be brought and submitted in the assignment box marked \"Finance3\" located in Building 8, Level 5, by 5:00pm Friday 3rd June 2016. Late submissions will not be accepted and no soft copy is required. 4. Complete a cover sheet (available on UTSOnline) with your signature and attach it to a printout of your answers. 5. The assignment computations are to be done in Excel, but the solutions may be pasted into Word and formatted for submission. The final report, including all text, tables and figures should be printed out on A4 paper with a minimum font size of 12. Also, the final report (excluding the cover sheet) should not exceed 10 pages in length. Subject Coordinator: Lei Shi In this assignment you will be computing zero-coupon yields, durations and also implementing a hedging strategy for a stream of liabilities. In order to help you do this you will find an Excel workbook called AssignmentIIData.xlsx on UTSOnline. 1 Data Description In AssignmentIIData.xlsx, you can find the coupon rate, maturity and yield-to-maturity (YTM) on 22 semi-annual treasury bonds. You can also find the zero-coupon yields (ZCY) with different maturities. Note that both YTM and ZCY are annualised rates, however YTMs are semi-annually compounded whereas ZCYs are annually compounded. 2 Question 1 (Zero-coupon Yields - 5 marks) Upon graduation from the UTS Business School, you're now working for a superannuation fund. On your first day at work, your boss has asked you to calculate the prices of government bonds that are currently traded in the market and also to investigate the current term structure of interest rate. (a) Based on information provided for the treasury bonds, compute the bond prices (accurate to 4 decimal places). (1 mark) (b) Based on the current yield curve, calculate the following forward rates out of 6 months f0.5 to 1.0 , f0.5 to 1.5 , f0.5 to 2.0 , , f0.5 to 10.5 , f0.5 to 11.0 ; and also the following forward rates out of 1 year f1.0 to 1.5 , f1.0 to 2.0 , f1.0 to 2.5 , , f1.0 to 10.5 , f1.0 to 11.0 ; (3 marks) (c) Plot the forward rates out of 6 months, forward rates out of 1 year and the current interest rates together on a single graph with investment horizon T on the horizontal axis. According the market expectation theory, what are investors' expectations about future interest rates for different maturities? (1 mark) 3 Question 2 (Durations - 5 marks) After looking at the current term-structure of interest rates, your boss is also interested to know each treasury bond's risk exposure to changes in the interest rates and its own yield-to-maturity (YTM). (a) Compute the modified duration for each of the treasury bonds. (2 mark) (b) Compute the effective duration for each of the treasury bonds. (2 marks) (c) Plot the modified and effective durations together with maturity on the horizontal axis and explain the differences in the two durations. (1 mark) 4 Question 3 (Hedging interest rate risk - 5 marks) Your boss is impressed with your work efficiency and now the real challenging task comes - you need to implement a hedging strategy to ensure that the fund has enough capital to meet a liability. The superannuation fund will need to pay $100,000 semi-annually for the next 11 years. (a) Use the current yield curve to determine the present value and also the effective duration of the liability. (1 mark) (b) Now, in order to hedge interest rate risk, you want to invest in a bond portfolio which has the same effective duration as the liability. To accomplish this task, pick two of the treasury bonds currently traded in the market, Bond A and Bond B, and determine the dollar amount that should be invested in each bond. Note that you need to determine which two bonds are most suitable. Also, assume the effective duration of your bond portfolio is given by Dp = wA DA + wB DB , where wA and wB are the percentage weights invested in Bond A and Bond B respectively. (2 marks) (c) Now suppose the entire yield curve shifts down by 50 basis points. Calculate the percentage change in the present value of the liability in part (a) and also of the value of the bond portfolio in part (b). Comment on the effectiveness of the hedge. (2 marks) 5 Q1 (a) (b) Interval Code 1 GSBK16 2 GSBC17 3 GSBM17 4 GSBA18 5 GSBS18 6 GSBE19 7 GSBS19 8 GSBG20 9 GSBU20 10 GSBI21 11 GSBM22 12 GSBG23 13 GSBG24 14 GSBG25 15 GSBG26 16 GSBG27 17 GSBU27 18 GSBG29 19 GSBG33 20 GSBK35 21 GSBG37 22 GSBK39 FV 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 Yield 2.25% 1.78% 1.85% 1.83% 1.79% 1.77% 1.82% 1.84% 1.95% 1.96% 2.12% 2.21% 2.31% 2.36% 2.40% 2.48% 2.56% 2.63% 2.83% 2.97% 3.01% 3.06% Yield/2 0.01125 0.00889 0.00925 0.00915 0.00894 0.00886 0.00908 0.00918 0.00976 0.00982 0.01058 0.01104 0.01157 0.01180 0.01200 0.01239 0.01281 0.01316 0.01415 0.01485 0.01503 0.01528 Coupon Payment $ 2.3750 3.0000 2.1250 2.7500 1.6250 2.6250 1.3750 2.2500 0.8750 2.8750 2.8750 2.7500 1.3750 1.6250 2.1250 2.3750 1.3750 1.6250 2.2500 1.3750 1.8750 1.6250 Annnuit T Note y- YTM Prices $ 0.9889 101.2361 1.9737 105.0403 2.9454 105.3429 3.9102 109.8468 4.8686 107.0255 5.8184 114.3954 6.7527 108.3856 7.6796 116.3698 8.5763 106.5382 9.4807 126.2851 10.3326 128.6593 11.1815 129.6571 12.0057 115.3646 12.8352 119.6910 13.6529 127.8266 14.4338 133.0569 15.1901 119.6220 15.9349 124.5958 16.5583 135.8610 17.1941 122.1786 17.8946 132.0716 18.5649 128.6630 Maturity ZCB (yrs) yields 0.50 2.263% 1.00 1.778% 1.50 1.856% 2.00 1.835% 2.50 1.793% 3.00 1.774% 3.50 1.823% 4.00 1.845% 4.50 1.965% 5.00 1.988% 5.50 2.164% 6.00 2.266% 6.50 2.357% 7.00 2.413% 7.50 2.468% 8.00 2.563% 8.50 2.626% 9.00 2.713% 9.50 2.981% 10.00 3.090% 10.50 3.163% 11.00 3.201% Forward Forward Rates out of Rates out ZCB Prices $ 6 months of 1 year 98.9008 98.3058 1.21% 97.3376 1.61% 2.00% 96.5275 1.63% 1.84% 95.7243 1.65% 1.79% 94.9957 1.62% 1.73% 93.9570 1.72% 1.83% 93.1082 1.74% 1.83% 91.6886 1.91% 2.01% 90.8977 1.89% 1.98% 89.2148 2.08% 2.18% 87.7672 2.20% 2.29% 86.1430 2.33% 2.43% 84.8814 2.38% 2.48% 83.6480 2.42% 2.52% 82.1125 2.51% 2.60% 80.4994 2.61% 2.70% 78.9390 2.69% 2.78% 76.2008 2.94% 3.04% 74.1272 3.08% 3.19% 72.6341 3.13% 3.24% 71.1883 3.18% 3.28% Q2 (a) (b) Coupon/ Denominato $1 ZCB Code Interval 2 Yield Yield/2 LHS Numerator r Denominator price GSBK16 1 0.0238 2.25% 0.0113 89.8889 1.0238 0.01152 1.00 0.9888 GSBC17 2 0.0300 1.78% 0.0089 113.5492 1.0511 0.00942 1.97 0.9824 GSBM17 3 0.0213 1.85% 0.0092 109.1666 1.0453 0.00984 2.94 0.9727 GSBA18 4 0.0275 1.83% 0.0091 110.3494 1.0826 0.01016 3.85 0.9641 GSBS18 5 0.0163 1.79% 0.0089 112.8568 1.0455 0.00968 4.85 0.9563 GSBE19 6 0.0263 1.77% 0.0089 113.9305 1.1132 0.01028 5.65 0.9483 GSBS19 7 0.0138 1.82% 0.0091 111.1928 1.0418 0.00997 6.73 0.9384 GSBG20 8 0.0225 1.84% 0.0092 109.9918 1.1158 0.01088 7.44 0.9291 GSBU20 9 0.0088 1.95% 0.0098 103.5115 1.0007 0.01055 8.69 0.9157 GSBI21 10 0.0288 1.96% 0.0098 102.8849 1.1992 0.01276 8.94 0.9058 GSBM22 11 0.0288 2.12% 0.0106 95.5180 1.2105 0.01411 9.72 0.8885 GSBG23 12 0.0275 2.21% 0.0110 91.5797 1.2086 0.01491 10.54 0.8737 GSBG24 13 0.0138 2.31% 0.0116 87.4678 1.0400 0.01378 12.01 0.8589 GSBG25 14 0.0163 2.36% 0.0118 85.7458 1.0741 0.01470 12.68 0.8457 GSBG26 15 0.0213 2.40% 0.0120 84.3333 1.1508 0.01616 13.14 0.8323 GSBG27 16 0.0238 2.48% 0.0124 81.7428 1.1942 0.01755 13.71 0.8161 GSBU27 17 0.0138 2.56% 0.0128 79.0945 1.0289 0.01613 15.29 0.8016 GSBG29 18 0.0163 2.63% 0.0132 77.0167 1.0689 0.01746 15.82 0.7852 GSBG33 19 0.0225 2.83% 0.0142 71.6714 1.1728 0.02103 15.92 0.7558 GSBK35 20 0.0138 2.97% 0.0149 68.3401 0.9929 0.01956 17.59 0.7369 GSBG37 21 0.0188 3.01% 0.0150 67.5336 1.0932 0.02193 17.68 0.7203 GSBK39 22 0.0163 3.06% 0.0153 66.4450 1.0366 0.02172 18.71 0.7063 Modified Effective P* Duration Duration 102.45 0.4944 0.4889 106.14 0.9770 0.9684 104.53 1.4561 1.4426 108.55 1.9067 1.8893 103.90 2.4015 2.3799 110.97 2.8001 2.7751 103.00 3.3331 3.3025 110.21 3.6881 3.6537 98.36 4.3042 4.2612 117.00 4.4273 4.3819 116.86 4.8107 4.7556 115.68 5.2113 5.1475 100.27 5.9358 5.8612 102.60 6.2660 6.1836 108.16 6.4919 6.4015 110.53 6.7733 6.6721 96.99 7.5483 7.4360 99.11 7.8052 7.6808 104.38 7.8472 7.6971 91.05 8.6677 8.5023 96.49 8.7103 8.5276 92.03 9.2131 9.0179 Q3 (a) Interval Code Coupon M FV Yield Yield/2 ZCB yield ZCB Yield/2 PV per period 1 GSBK16 0.0475 0.5 100 0.0225 0.0113 0.0226 0.0113 2 GSBC17 0.06 1 100 0.0178 0.0089 0.0178 0.0089 3 GSBM17 0.0425 1.5 100 0.0185 0.0092 0.0186 0.0093 4 GSBA18 0.055 2 100 0.0183 0.0091 0.0183 0.0092 5 GSBS18 0.0325 2.5 100 0.0179 0.0089 0.0179 0.0090 6 GSBE19 0.0525 3 100 0.0177 0.0089 0.0177 0.0089 7 GSBS19 0.0275 3.5 100 0.0182 0.0091 0.0182 0.0091 8 GSBG20 0.045 4 100 0.0184 0.0092 0.0184 0.0092 9 GSBU20 0.0175 4.5 100 0.0195 0.0098 0.0197 0.0098 10 GSBI21 0.0575 5 100 0.0196 0.0098 0.0199 0.0099 11 GSBM22 0.0575 5.5 100 0.0212 0.0106 0.0216 0.0108 12 GSBG23 0.055 6 100 0.0221 0.0110 0.0227 0.0113 13 GSBG24 0.0275 6.5 100 0.0231 0.0116 0.0236 0.0118 14 GSBG25 0.0325 7 100 0.0236 0.0118 0.0241 0.0121 15 GSBG26 0.0425 7.5 100 0.0240 0.0120 0.0247 0.0123 16 GSBG27 0.0475 8 100 0.0248 0.0124 0.0256 0.0128 17 GSBU27 0.0275 8.5 100 0.0256 0.0128 0.0263 0.0131 18 GSBG29 0.0325 9 100 0.0263 0.0132 0.0271 0.0136 19 GSBG33 0.045 9.5 100 0.0283 0.0142 0.0298 0.0149 20 GSBK35 0.0275 10 100 0.0297 0.0149 0.0309 0.0154 21 GSBG37 0.0375 10.5 100 0.0301 0.0150 0.0316 0.0158 22 GSBK39 0.0325 11 100 0.0306 0.0153 0.0320 0.0160 PV of the liability 98,887.52 98,253.16 97,279.49 96,428.82 95,653.32 94,860.25 93,872.39 92,948.87 91,614.85 90,626.99 88,893.87 87,419.38 85,948.80 84,630.26 83,290.96 81,674.77 80,225.95 78,589.00 75,649.39 73,764.11 72,107.67 70,709.20 y ZCB Y+ y 0.01% 0.0227 0.01% 0.0179 0.01% 0.0187 0.01% 0.0184 0.01% 0.0180 0.01% 0.0178 0.01% 0.0183 0.01% 0.0185 0.01% 0.0198 0.01% 0.0200 0.01% 0.0217 0.01% 0.0228 0.01% 0.0237 0.01% 0.0242 0.01% 0.0248 0.01% 0.0257 0.01% 0.0264 0.01% 0.0272 0.01% 0.0299 0.01% 0.0310 0.01% 0.0317 0.01% 0.0321 PV* per period 98,882.68 98,243.50 97,265.17 96,409.88 95,629.83 94,832.30 93,840.13 92,912.37 91,574.42 90,582.57 88,846.03 87,368.11 85,894.24 84,572.43 83,230.02 81,611.09 80,159.54 78,520.17 75,579.64 73,692.60 72,034.32 70,633.88 1,913,329.01 PV*1 of the liability 1,912,314.92 Effective Duration 5.30011337 Q3 (b) D1(GSBM23 D2(GSBG24 Effective d PV of the li 5.2113 from Q2 5.9358 from Q2 5.3001 from Q3 (a) 1,913,329.01 from Q3 (a) P1 P2 1,678,845.99 234,483.02 Q3 (C) y2 y-y2 0.50% 0.50% 0.50% 0.50% 0.50% 0.50% 0.50% 0.50% 0.50% 0.50% 0.50% 0.50% 0.50% 0.50% 0.50% 0.50% 0.50% 0.50% 0.50% 0.50% 0.50% 0.50% PV*2 D1(GSBM23) D2(GSBG24) Deff1 PV p1 pv2 ZCB 1.76% $ 99,130.15 1.28% $ 98,738.22 1.36% $ 98,000.22 1.33% $ 97,382.75 1.29% $ 96,838.09 1.27% $ 96,272.20 1.32% $ 95,503.73 1.34% $ 94,796.80 1.47% $ 93,664.00 1.49% $ 92,881.55 1.66% $ 91,325.21 1.77% $ 90,028.31 1.86% $ 88,728.50 1.91% $ 87,579.86 1.97% $ 86,403.35 2.06% $ 84,931.16 2.13% $ 83,626.53 2.21% $ 82,117.41 2.48% $ 79,229.34 2.59% $ 77,439.10 2.66% $ 75,881.61 2.70% $ 74,589.47 1965087.56711 5.2113 from Q2 5.9358 from Q2 5.3001 from Q3(a) 1,965,087.57 from q3 (C 1,724,261.41 ZCB-0.5% 2.26% 1.78% 1.86% 1.83% 1.79% 1.77% 1.82% 1.84% 1.97% 1.99% 2.16% 2.27% 2.36% 2.41% 2.47% 2.56% 2.63% 2.71% 2.98% 3.09% 3.16% 3.20% 1.76% 1.28% 1.36% 1.33% 1.29% 1.27% 1.32% 1.34% 1.47% 1.49% 1.66% 1.77% 1.86% 1.91% 1.97% 2.06% 2.13% 2.21% 2.48% 2.59% 2.66% 2.70% p2 240,826.16