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### Money markets and_fixed_income_securities essay sample from assignmentsupport.com essay writing services

1. 1. Money markets and fixed income securities Report Submitted By Student Name University Name Document: JOB # MAY 221 Author: Stuart Thomas Save Date: 27/11/2013 Page 1 of 22
2. 2. Data from the RBA.GOV.AU June 2011 Closing Gross Accrued Capital Series Number Coupon Maturity Yield Price Interest Price TB123 5.75% 15 Apr 12 4.700 101.993 1.194 100.799 TB127 4.75% 15 Nov 12 4.715 100.635 0.594 100.041 TB118 6.50% 15 May 13 4.735 103.937 0.813 103.125 TB129 5.50% 15 Dec 13 4.745 101.956 0.225 101.731 Closing Gross Accrued Capital Yield Price Interest Price 3.930 101.692 1.194 100.498 3.480 101.670 0.587 101.083 3.285 105.091 0.804 104.287 3.160 104.635 0.225 104.410 Dec 2011 Series Number Coupon Maturity 15 TB123 5.75% 12 15 TB127 4.75% 6.50% 5.50% May 13 15 TB129 Nov 12 15 TB118 Apr 13 Dec Document: JOB # MAY 221 Author: Stuart Thomas Save Date: 27/11/2013 Page 2 of 22
3. 3. Part 1: A. Calculate the dirty price, clean price, modified duration and modified convexity of the Government bonds as at as at the end of June 2011 and the end of December 2011. The value is calculates based on the fact that it pays 4 times a year and it uses the 30/360 US day count convention. These calculations are at the end of June 2011. Term Value Value Value Value Series Number TB123 TB127 TB118 TB129 Coupon Rate 5.75% 4.75% 6.50% 5.50% Par Value \$100 \$100 \$100 \$100 Full Market Value \$101.993 \$100.635 \$103.937 \$101.956 Dirty Price 10.20 10.06 10.40 10.20 Accrued Interest 1.194 0.594 0.813 0.225 Flat Market Value \$100.799 \$100.041 \$103.125 \$101.731 Clear Price 10.08 10.00 10.31 10.18 Table - 1: Calculation of dirt price and clear price at the end of June 2011 These calculations are at the end of December 2011 Term Value Value Value Value Series Number TB123 TB127 TB118 TB129 Coupon Rate 5.75% 4.75% 6.50% 5.50% Par Value \$100 \$100 \$100 \$100 Full Market Value \$101.692 \$101.670 \$105.091 \$101.956 Document: JOB # MAY 221 Author: Stuart Thomas Save Date: 27/11/2013 Page 3 of 22
4. 4. Dirty Price 10.17 10.16 10.51 10.20 Accrued Interest 1.194 0.594 0.804 0.225 Flat Market Value \$100.498 \$101.083 \$104.287 \$104.410 Clear Price 10.05 10.10 10.31 10.44 Table - 1: Calculation of dirt price and clear price at the end of December, 2011 For TB123: Calculation of the modified duration and convexity Bond Price \$96.05 \$95.15 If Yield Changes By 1.00% Bond Price Will Change Face Value 100 100 Coupon Rate 5.75% By 6% Modified -0.90 -0.93% Duration Life in Years 1 1 Predicts -0.90 -0.94% Yield 10.00% 11% Convexity Adjustment 0.01 0.01% Frequency 2 2 Total Predicted Change -0.90 -0.93% 0.99 Actual New Price \$95.15 Duration 0.94 Predicted New Price \$95.15 Convexity 1.33 Difference \$0.00 Macaulay Duration Modified PV Period Cash Flow 0 Flow Cash Duration Calc +0.0000% Convexity Calc (\$96.05) Document: JOB # MAY 221 Author: Stuart Thomas Save Date: 27/11/2013 Page 4 of 22
5. 5. 1 2.88 2.74 2.74 4.97 2 102.88 93.31 186.62 507.81 Total 189.36 512.78 Total For TB127- Calculation of the modified duration and convexity Bond Price \$95.12 \$94.23 If Yield Changes By 1.00% Bond Price Will Change Face Value 100 100 Coupon Rate 4.75% By 5% Modified -0.89 -0.93% Duration Life in Years 1 1 Predicts -0.90 -0.94% Yield 10.00% 11% Convexity Adjustment 0.01 0.01% Frequency 2 2 Total Predicted Change -0.89 -0.93% 0.99 Actual New Price \$94.23 Duration 0.94 Predicted New Price \$94.23 Convexity 1.34 Difference \$0.00 Macaulay Duration Modified +0.0000% Document: JOB # MAY 221 Author: Stuart Thomas Save Date: 27/11/2013 Page 5 of 22
6. 6. PV Period Cash Flow 0 2 Convexity (\$95.12) 1 Cash Duration Flow Calc Calc 2.38 2.26 2.26 4.10 102.38 92.86 185.71 505.34 Total 187.98 509.45 Total For TB 118- Calculation of the modified duration and convexity Bond Price \$96.75 \$95.85 If Yield Changes By 1.00% Bond Price Will Change Face Value 100 100 Coupon Rate 6.50% By 7% Modified -0.90 -0.93% Duration Life in Years 1 1 Predicts -0.91 -0.94% Yield 10.00% 11% Convexity Adjustment 0.01 0.01% Frequency 2 2 Total Predicted Change -0.90 -0.93% 0.98 Actual New Price \$95.85 Duration 0.94 Predicted New Price \$95.85 Convexity 1.33 Difference \$0.00 Macaulay Duration Modified +0.0000% Document: JOB # MAY 221 Author: Stuart Thomas Save Date: 27/11/2013 Page 6 of 22
7. 7. PV Period Cash Flow 0 2 Convexity (\$96.75) 1 Cash Duration Flow Calc Calc 3.25 3.10 3.10 5.61 103.25 93.65 187.30 509.66 Total 190.40 515.28 Total For TB129 - Calculation of the modified duration and convexity Bond Price \$95.82 \$94.92 If Yield Changes By 1.00% Bond Price Will Change Face Value 100 100 Coupon Rate 5.50% By 6% Modified -0.89 -0.93% Duration Life in Years 1 1 Predicts -0.90 -0.94% Yield 10.00% 11% Convexity Adjustment 0.01 0.01% Frequency 2 2 Total Predicted Change -0.89 -0.93% 0.99 Actual New Price \$94.92 Duration 0.94 Predicted New Price \$94.92 Convexity 1.34 Difference \$0.00 Macaulay Duration Modified +0.0000% Document: JOB # MAY 221 Author: Stuart Thomas Save Date: 27/11/2013 Page 7 of 22
8. 8. PV Period Cash Flow 0 2 Convexity (\$95.82) 1 Cash Duration Flow Calc Calc 2.75 2.62 2.62 4.75 102.75 93.20 186.39 507.20 Total 189.01 511.95 Total B. Calculate the holding period return for each of the bonds over the period from end June 2011 end December 2011. For TB 123 Holding period yield Bond value \$96.05 Par value (redemption value) 97.19 Coupon rate (annual) 5.75% Years till maturity 0.5 30-06Today 2011 Holding period yield Maturity 31-12-2011 6.55% Document: JOB # MAY 221 Author: Stuart Thomas Save Date: 27/11/2013 Page 8 of 22
9. 9. For TB 127 Holding period yield Bond value \$95.12 Par value (redemption value) 96.25 Coupon rate (annual) 4.75% Years till maturity 0.5 30-06Today 2011 Holding period yield Maturity 31-12-2011 5.56% For TB 118 Holding period yield Bond value \$95.12 Par value (redemption value) 97.90 Coupon rate (annual) 6.50% Years till maturity 0.5 30-06Today 2011 Holding period yield Maturity 31-12-2011 8.21% For TB 129 Document: JOB # MAY 221 Author: Stuart Thomas Save Date: 27/11/2013 Page 9 of 22
10. 10. Holding period yield Bond value \$95.12 Par value (redemption value) 96.96 Coupon rate (annual) 5.50% Years till maturity 0.5 30-06Today 2011 Maturity 31-12-2011 Holding period yield 6.70% C. Calculate the modified duration, modified convexity and holding period return for an equally-weighted portfolio of the bonds at both dates. Report on your findings. Compare and contrast the return and volatility of the portfolio and the separate bonds at both dates. At the end of June 2011 Macaulay Duration Modified Duration Convexity Holding Return 0.99 0.97 1.43 = 5.63 % At the end of December, 2011 Macaulay Duration Modified Duration Convexity Holding Return 0.91 0.89 1.31 = 5.93 % The calculated values suggests that for the equally weighted portfolio the the holding return get increases for the end of the December 2011 because of the longer period than June 2011. Document: JOB # MAY 221 Author: Stuart Thomas Save Date: 27/11/2013 Page 10 of 22
11. 11. Part 2: A. Use all available Government bond data (ie not just the bonds in your portfolio) to construct and present a yield curve, spot curve and forward curve as at the end of June 2011 and the end of December 2011. Your spot curve and forward curve estimation should go out no more than 5 years. Present and discuss your findings. Suppose we have the following Treasury yields (based roughly on rba.gov.com) The face value is taken as \$100 for the maturity years of 5. Maturity (yrs) Coupon Price 32nds Yield 0.25 0 \$99.46 2.17 0.50 0 \$98.82 2.38 1.00 2.250 \$99.66 99 21/32 2.61 1.50 2.250 \$99.28 99 9/32 2.76 2.00 2.500 \$99.15 99 5/32 2.96 2.50 2.875 \$99.63 99 20/32 3.05 3.00 3.000 \$99.53 99 17/32 3.19 3.50 3.125 \$99.64 99 20/32 3.26 4.00 3.500 \$100.58 100 19/32 3.37 4.50 3.375 \$99.64 99 20/32 3.49 5.00 3.500 \$99.77 99 25/32 3.58 Table: Value taken initially for the bonds for next 5 years and calculation of yield value Document: JOB # MAY 221 Author: Stuart Thomas Save Date: 27/11/2013 Page 11 of 22
12. 12. Fig: Curve represents the yielding curve for the given bond and coupan rate The above curve reflects the yield for current securities with certain maturities. Spot Curve The one year spot rate is easily found by equalizing the cash flows. y is the yield to maturity, z1 and z2 are the two zero rates (6mo and 1yr): C1/(1+y/2) + (100+C2)/(1+y/2)^2 = C1/(1+z1/2) + (100+C2)/(1+z2/2)^2 1.1105 + 98.5364 = 1.1118 + 101.1250/(1+Z2/2)^2 Solving for z2, the 1yr zero rates: 99.6469 = 1.1118 + 101.1250/(1+Z2/2)^2 98.5351 = 101.1250/(1+Z2/2)^2 (1+Z2/2)^2 = 1.02628364 1+Z2/2 = 1.013056583 Z2/2 = 0.013056583 Z2 = 2.6113 Percent (Square root) In this case, the 1 year spot rate matches the yield; that isn't always the case. Document: JOB # MAY 221 Author: Stuart Thomas Save Date: 27/11/2013 Page 12 of 22
13. 13. Maturity (yrs) Coupon Price 0.25 na 0.50 32nds Yield Spot Rate \$99.46 2.17 2.17 na \$98.82 2.38 2.38 1.00 2.250 \$99.66 99 21/32 2.61 2.6113 1.50 2.250 \$99.28 99 9/32 2.76 2.7440 2.00 2.500 \$99.15 99 5/32 2.96 2.9448 2.50 2.875 \$99.63 99 20/32 3.05 3.0359 3.00 3.000 \$99.53 99 17/32 3.19 3.1784 3.50 3.125 \$99.64 99 20/32 3.26 3.2497 4.00 3.500 \$100.58 100 19/32 3.37 3.3651 4.50 3.375 \$99.64 99 20/32 3.49 3.4889 5.00 3.500 \$99.77 99 25/32 3.58 3.5835 Table: Calculation of the spot value and yield value based on the previous result. Fig: Plotting of the regular yield curve (in blue) versus the spot curve. This above figure represents the spot curve in yellow line that signifies that the spot curve is almost follow the yield curve slop. Forward Curve Document: JOB # MAY 221 Author: Stuart Thomas Save Date: 27/11/2013 Page 13 of 22
14. 14. The 6mo forward rate in 6 months can be though of as what we could borrow/lend at for 6 months, 6 months from now. By the law of no arbitrage, investing our money now for 1 year or now for 6months, with the next 6mo rate locked in, must result in the same present value. y is the yield to maturity, z1 is the 6mo spot rate, and f1 is the 6mo forward rate 6months from now. C1/(1+y/2) + (100+C2)/(1+y/2)^2 = C1/(1+z1/2) + (100+C2)/(1+z1/2)(1+f1/2 1.1105 + 98.5364 = 1.1118 + 101.1250/((1+z1/2)(1+f1/2)) Solving for f1: 99.6469 = 1.1118 + 101.1250/((1+z1/2)(1+f1/2)) 98.5351 = 101.1250/((1+2.38/2)(1+f1/2)) 98.5351 = 99.9357644 (1+f1/2) = 1.014214487 f1/2 = 0.014214487 f1 = 2.8429 Maturity (yrs) Coupon Price /(1+f1/2) 32nds Yield Spot Rate 6mo Fwd Rate 2.17 2.38 2.38 2.38 2.8429 0.00 0.50 na \$98.82 1.00 2.250 \$99.66 99 21/32 2.61 2.6113 3.0209 1.50 2.250 \$99.28 99 9/32 2.76 2.7440 3.5997 2.00 2.500 \$99.15 99 5/32 2.96 2.9448 3.4176 2.50 2.875 \$99.63 99 20/32 3.05 3.0359 3.9537 3.00 3.000 \$99.53 99 17/32 3.19 3.1784 3.6984 3.50 3.125 \$99.64 99 20/32 3.26 3.2497 4.2473 4.00 3.500 \$100.58 100 19/32 3.37 3.3651 4.5875 Document: JOB # MAY 221 Author: Stuart Thomas Save Date: 27/11/2013 Page 14 of 22
15. 15. 4.50 3.375 \$99.64 99 20/32 3.49 3.4889 5.00 3.500 \$99.77 99 25/32 3.58 4.5123 3.5835 Table: Calculation of the Yield, spot and forward values Fig: Yield Curve (Blue Line), Spot Curve (Yello Line) and Forward curve for sex months (in Red color) B. Review the predictive ability of the yield, spot and forward curves with comprehensive reference to the relevant academic literature. Discuss the curves that you have estimated in Part 2A with reference to this literature. Does the June 2011 forward curve predict the 6 month spot rate for December 2011? Comment. Yield curve analyses the term to maturity for the particular bond given. The measurement of the differences of the interest rate which also has the different term to maturity are being done in this yield curve for the given bond rate, face value and discount rate. The maturity effect on the bond is estimated using the yield curve. (Cox et al, 1993) For example, in case of Australian treasury bills the yield curve is estimated based on the various debt security and term to the maturity. Mostly it is found that the yield curve as upward sloping. (Tuckman, B, 2002) This describes that the upward sloping is basically signifies that the short term to maturity generally estimated as the low interest rates and on the other hand the longer term to maturity is estimated as the higher interest terms. Document: JOB # MAY 221 Author: Stuart Thomas Save Date: 27/11/2013 Page 15 of 22
16. 16. Based on the literature it can be explained that the for maximization of the investment return will only be happen when the investment will be done for the longer term means higher yields. (M. Felton, 1994) In this case there is no immediate liquidity requirement and the yield curve shape and its level will be continuous and constant that means it will not change. The shape and the level of the yield curve are used to develop the interest rate of forecast with the use of the mathematical expectations theory model. The expectations theory that is applied for the yield curve generation explains that the for a longer time the interest rate on the yield curve can be calculated as the multiplication of the all interest rate of the shorter time intervals that is comprised for the longer time to maturity. (De Boor, 1978) If the increasement is done to the investment yield for the longer period then the yield curve shapes like a flat curve this means throughout same rate for all kind of maturities, if the shorter period has the high interest rate and the longer period have the low interest rate than the slop will be downward, and if there is upward sloping and as well as flat sloping combining in a one yield curve then this yield curve is called as humped yield curve. For the pricing bond generally the spot rate curve is estimated. It is also called spot rate treasury curve. These spot curves can be constructed from on the run or off the run or combination of both treasuries. (Hull, 2005) Based on the coupon strips for treasury the spot treasury curve can be calculated. There number of bond which have the multiple cash flows or say coupon rates at number of points in the bonds lives. Therefore, it is not the correct evaluation of the maturity and bonds based on the single interest rate because there are different interest rates based on the discounted cash flows. Therefore while making the fair bond valuation there is need to have the good practice to matching the discount to the each payment for the corresponding treasury spot rate for the present value of the each bond price. Based on the forward curve, the valuation of time value of money is estimated. This curve represents the price at which the market is ready to transact the future price. (James, J, 2000) It explains the forward rate of the price for the bonds or treasury bonds. But still there is one issue as found in the earlier researches that forward curve doesn’t represent the actual future price. Based on Document: JOB # MAY 221 Author: Stuart Thomas Save Date: 27/11/2013 Page 16 of 22
17. 17. the above curve yield, spot and forward curve, it can be explained easily that the yield curve has the upward slope so in this case the possibility is of having the longer period with higher interest rate and the shorter period with the low interest rate. (W. H., Flannery, 1992) For the treasury curve called as spot curve, it can be seen that its slope is almost same as the yield price slope. The conclusion can be drawn for the spot rate that based on the multiple cash flows and similar as the yield value the slope of the curve is same. In the last figure, there have been constructed the entire three yield, spot and forward curve. It can be seen from the figure that the forward is much higher for the larger term to maturity but also in between it goes down and then up. Document: JOB # MAY 221 Author: Stuart Thomas Save Date: 27/11/2013 Page 17 of 22
18. 18. Part 3: A: Describe the shape and level of the current Yield Curve in Australian Commonwealth Government Securities (i.e.: at the time of your dealing sessions – use data gathered from the trading system in the FMTS, plot the curve and discuss it). Maturity (yrs) Coupon 1 2 3 5 7 9 10 11 15 Price 6.5 6.25 6.25 6 5.25 5.75 5.75 5.5 4.75 32nds \$99.46 \$98.82 \$110.48 \$112.26 \$112.61 \$119.18 \$123.78 \$123.80 \$118.01 Yield 2.17 2.38 2.61 2.76 2.96 3.05 3.19 3.26 3.37 110 15/32 112 8/32 112 5/8 119 6/32 123 25/32 123 13/16 118 Table: Data calculation for the current trading system in the FMTS and the yield and bond price Fig: Treasury Yields curve for the current trading system in the FMTS As shown in the figure the yield curve is on the upward side which means the longer term maturity has the higher interest rate and the shorter term maturity has the lower interest rate. As seen from the above graph that the maturity for the 15 years and so the coupon rate is higher as 6.00 on an average for the complete maturity period. In case of the fixed interest fund managers the implication of this yield curve will lower down the maturity period because for the fixed interest the maturity period will be lower if the fixed rate is greater than the average of the yield rate otherwise reverse will be true. Document: JOB # MAY 221 Author: Stuart Thomas Save Date: 27/11/2013 Page 18 of 22
19. 19. Based on your view of the yield curve, and other sources, what is your view on Interest Rates in Australia for the following time horizons?  6 Months – The interest rate in Australia for the six months time horizons is lower.  12 Months – For 12 months time horizon the interest rate in Australia will be higher. As the curve suggests that for the shorter period the interest rate will be lower and for the longer period the interest rate will be higher. B: (4 Marks) With respect to your trading portfolio: 1. Report on your Portfolio composition in Market Value Terms and Face Value Terms: (a) At the commencement of trading At commencement of trading the Face Value is less than the market value which means the original price is less than the actual price during the investment this means the investment value is in profit. (b) After Dealing Session 2 After the dealing of the session 2, the face value is again lower the actual market value, so it shows that the invested money to the stock market is still in profit. 2 What is the level of interest rate risk in your portfolio, as measured by? (a) Portfolio Modified Duration at the commencement of trading The level of interest rate risk at the commencement of the trading is lower but increases soon after the trading starts. (b) Portfolio Modified Duration after Dealing Session 2 After the dealing session 2, the level of the interest rate goes increases and after some time it becomes medium risk for the investment. Document: JOB # MAY 221 Author: Stuart Thomas Save Date: 27/11/2013 Page 19 of 22
20. 20. 3. How has the interest rate risk profile of your portfolio changed? What are the implications for your portfolio in the current yield curve environment? The interest rate of risk profile for the portfolio goes increasing with the maturity time but soon after some time the level of interest risk goes down and the risk reduces. In the current yield curve environment the portfolio signifies that the investment return will be higher over the time. As the yield is on average of 3.50% which means the return will be almost 30 percent higher of the invested money. So the current yield curve environment is in favour of the investment. 4. Comment on whether you achieved your set objectives with regard to interest rate risk:  If you achieved your objective, what trading actions/strategy contributed to your success? Yes the set objectives achieved because of the balanced portfolio and using the options of forwarding rate which shows the yield rate was higher for the given maturity period.  If you did not achieve your objective, what would you do differently? In case the objectives were not achieved then the investment need to revise based on the forward rate and should wait for the right time for investment.  Was your trading consistent with the market view developed in Part 2? Yeah, little bit it seems from the part -2 yield graph that the trading was consistent as the yield rate was almost similar to the earlier rate except of some places where it was higher than the previous. C: Compare and contrast your performance from one dealing session to another. Discuss what you could do to improve future dealing sessions. What lessons did you learn and how did you perform as a team? In one dealing session it was normally slow but in another dealing session it got improved because of the higher rate of return of interest. For future dealing session it is needed to more focus on the longer period of maturity instead of the shorter period of maturity. The longer period always gives Document: JOB # MAY 221 Author: Stuart Thomas Save Date: 27/11/2013 Page 20 of 22
21. 21. the fair result than the shorter period. From this I learnt lot of things like how to make the portfolio, how to invest money, how to buy government bonds and how to perform yield curve, stop curve, and forward curve based on the coupon rate for the multiple time intervals. Based on overall conclusion the performance as a team, it was quite satisfactory. Document: JOB # MAY 221 Author: Stuart Thomas Save Date: 27/11/2013 Page 21 of 22
22. 22. References: 1. Cox, Raymond A. K., and Daniel E. Vetter. "Money Market Returns and Risk, 19381989." Journal of Midwest Finance 22 (1993): 50-54. 2. M. Felton. "Performance from Riding the Yield Curve, 1980-1992." Journal of Business and Economic Perspectives 20 (1994): 128-32. 3. De Boor, C.: A Practical Guide to Splines, Springer Verlag (1978). 4. Hull, J.: Options, Futures and Other Derivatives Prentice Hall (2005). 5. James, J., and Webber, N.: Interest Rate Modelling, Wiley (2000). 6. W. H., Flannery, B. P., Teukolsky, S. A., and Vetterling, V. T.: Numerical Recipes in C: The Art of Scientiﬁc Computing, Cambridge University Press (1992). 7. Tuckman, B.: Fixed Income Securities, Wiley (2002). Document: JOB # MAY 221 Author: Stuart Thomas Save Date: 27/11/2013 Page 22 of 22