In this research, the researcher has considered four different types of Government bond and considered their corresponding data from the government websites. The research will focus on relation between the bond price and other variants. The research is expected to assist future investors. In addition to this, the learner of bond finance shall get a clear evidence of approach. Thus, the researcher shall recommend to abide by all the processing mentioned here.
Contents
Introduction.
Part A..
Dirty price, clean price and modified duration of the bonds.
Holding period comparison.
Convexity analysis.
Part B:
Various chart Analysis.
Conclusion:
If a company is willing to invest in a business but lacking proper capital for the investment. Then the company issues bond or stock. It promises to pay the liquidity equivalent of the investor's capital. The investors were willing to enjoy the liquidity risk and trust the company policy purchases the stock of the organization. However, the condition is different in Australia. Here, the government offers a bond to the public. The public is assured with a fixed rate of interest and they need to undergo for a locking period. In this time the value of the bond can go up and down. Any other investor can invest during the period. However, it can affect the liquidity of government. Therefore, to manage this cash flow, the government changes the interest rate according to the bond price. If the bond price is low then the government offers high interest. Huang and Petkevich (2016) mentioned that low bond price means people are not willing to purchase the product. Offering a high interest draws the attention of people to increase their demand. Similarly, the fund value increases if the interest is lowered.
Here, the researcher has taken four bonds namely Treasury Bond 151, 126, 124 and 146. The data will be collected from the government website or the rba website only as mentioned by the professor. The dirty price, clean price and charts will be presented to find any similarity or dissimilarity among these data. The report analysis will be completely based on mathematical fact and no presumption other than cash flow will be made here.
The clean price of any bond is defined as the offered price of the bond when the acquired interest has been excluded from it (Li et al 2017). Apart from that, the clean price is an indicator of the dirty price of the bond. The relation between a clean price and the dirty price is
(Babatunde and Perera, 2017)
Here, accrued interest is calculated as
Accrued interest = C * Day since last clearing / (total number of days * period of consideration) (Li, Abraham and Cai, 2017)
Here, the author is considering government bonds of the category with different maturity and coupon interest. Based on the clean price of each, the author shall calculate the dirty price, clean price and other variables associated with each bond.
Treasury bond 126
Here the coupon interest is 4.50%
Maturity period is 15^{th} April 2020
The bond started on 29^{th} April 2009
The last payment date has not been mentioned in the excel format. However, the researcher is considering 15^{th} October as the last date of payment. All the calculations will be based on the given period of half a year.
The par value of the bond is identified as 1000$.
Accrued interest = 4.50 * 77 / (365*0.5) = 1.89 %
Clean price is identified as the price at which the last sale has occurred. For example, the Treasury bond 126 was sold on 15^{th} October of 2019. Thus, the bond price on that particular date will be the clean price of the bond. Here the value is 0.680. Thus, the dirty price will be 0.680 + 1.89 = 2.57 $
The modified duration of the bond is dependent on the Macaulay expression. Here, the par value is 1000$ and coupon 4.5% yields the PV1 as 45$.
Thus, the Macaulay duration is = 1.95 approximately
Therefore, the Modified duration will be Mac Duration / (1+ Yd/D) (Li et al 2017)
Here, the Yd is 4.7% and a 1 % decrease in bond price is presumed.
Thus, Modified duration is (1.95 / (1+ (4.7/1)) = 1.87 approximately
The Treasury bond 146 was introduced in the year 2015 on 10^{th} April. It will last up to 21^{st} November 2020. The bond has a face value of 1000$. The coupon associated with the bond is 1.75% to be paid per annum. It was last paid the interest on 21^{st} November 2019. Therefore, the calculation will be similar for the Treasury bond 146 as mentioned for Treasury bond 126. The accrued interest is measured as 0.19 % from 21^{st} November to 31^{st} November. The clean value is 0.8. Therefore, the Dirty value is measured as 0.99. 1.75% coupon on 1000$ par value yields 17.5$. Hence, the Macaulay duration is measured as 1.93 approximately. However, the modified duration is calculated as 1.90. (See appendix)
Treasury bond 124 started on 11^{th} September 2007. The bond will last up to 15^{th} May of 2021. The coupon rate of interest is 5.75% paid semiannually. The interest is paid up to 15^{th} November of each year. Therefore, the last payment date was 15^{th} Nov 2019. Therefore the clean value is measured as on that value is 0.805. The accrued interest is calculated as 1.45 approximately. Apart from this, the dirty value is summed as 2.225. On 5.75% of 1000$ face value, the yield is 57.5$. Thus, the Mac duration is given by 1.97 approximately. Therefore, the researcher has calculated as 1.87. The value is calculated as semiannually and 1% decrease is identified approximately.
Treasury bond 151 was introduced in 18th January 2017 and it will be matured by 21^{st} December 2021. However, the rate of the coupon is measured as 2.0% as compounded semiannually. The face value is identified as 1000$ and the term of the year is measured as 4 years. The bond pays annual interest on 21^{st} December of each year. Therefore, the bond has paid its annual interest on 21^{st} December 2019. Hence, the effective days of 10. The clean price is measured by 0.875. Thus, the accrued interest is measured as 0.11. Therefore, the dirty price of the bond as on 31^{st} December is 0.985. To calculate the Macaulay duration and modified duration is calculated by considering a 1% annual decrease. In addition to this, the yield is considered as 5.95%. The researcher has calculated the Macaulay duration as 1.94 and Modified duration as 1.89. Based on the given values, the researcher shall calculate the convexity graph.
Each bond analyzed in this assignment has a different holding period. ) mentioned that a holding period is a time for which an investor invests in a bond. Here, the researcher is considering a fixed investment period of 1^{st} July to 31^{st} December. Here, the researcher may identify the return of investment for each value. To ease the calculation the researcher is considering a null income condition to compare the return on investment for each bond.
It has an initial value on 1^{st} July at 1.025. While the fund value reached 0.900 on 31^{st} December. Therefore, the difference between them is 0.125. Therefore, the percent change in return is 0.125/1.025 = 12.2% (Approximately). Thus, if a person purchases 1000 stocks yields 1025 at the beginning. The return of the person on 31^{st} December will be identified as 900. It makes a 125$ loss for the person to invest in this bond. Thus, it accounted that the person may have been suffering from a loss percentage of value 12.2 approximately.
The same period of holding will be considered in this case. ) mentioned that if we are to compare between the bonds. Then we should compare them within a standard holding period. In this research, the instructor has restricted the holding period from 1^{st} July to 31^{st} December 2019. Therefore, it will provide a justifiable comparison among these. However, the bond 146 has an initial value of 1.010 as in 1^{st} of July. The end value of the fund in 31^{st} December is identified as 0.930. Therefore, the return can be calculated as (1.010 - 0.930) / 0.930 = 8.6% loss half yearly. Thus, if a person invests 1000$ in the fund on 1^{st} July and the value is reduced to 914$ at the end of six months. However, the loss per cent is small compared to fund 126.
The convexity graph showed a very little variation in the initial and final value of the bond 151. Therefore, it is expected it can be a good investment option for investors. Najafi and Mehrdoust (2017) stated that the convexity graph is always an indicator of return. Many investors do not compare mathematical facts. Instead of that, they check for the convexity graph of them. Here, the researcher has identified 0.975 as the initial value. The researcher has further identified the final value of the fund on 31^{st} December 2019 was 0.920. Therefore, the calculated return is (0.975 – 0.920) / 0.920 = 5.6% loss half yearly. Among the other three bonds, it shows the least possible loss. That means if a person invests 1000$ in the bond on 1^{st} July then the valuation of money on 31^{st} December will be 944$. Causing a 56 dollar loss for 1000$ investment. This is the lowest possible risk investment policy (Najafi and Mehrdoust, 2017). It further justifies the conventional convexity graph theory. As it seemed it is the most reliable bond among these four. Also, the theory is established by mathematical calculations.
As mentioned in the convexity analysis, the bond 124 looked very much similar to bond 151. In fact, the researcher mentioned it as a carbon copy of bond 151. Hence, it is expected that this bond will be low loss bond among the others. On 1^{st} July 2019, the bond value is measured as 0.980. The same bond value reached 0.925 on 31^{st} December, 2019. Therefore, it is the investors have experienced loss in this bond. The rate of loss is (0.980 – 0.925) / 0.980 = 5.61% Loss half yearly. Thus, it is quite relevant the bond is exactly similar to the bond 151. Besides, their rate of loss is almost exactly similar. If a person invests 1000$ amount in this fund on 1st July then the person would have received 943.9$ at the end. It causes a loss of 44.1$ per thousand.
From the above comparison, it has been found that all the bonds are providing loss to an investor. However, the Treasury bond 151 has the least loss ratio with 5.6% half yearly loss. The Treasury bond 126 has been the most loss bond among all with 12.2 % loss half yearly. The Treasury bond 126 is the second least affected bond with almost 5.61% loss half yearly. The Treasury bond 126 and 151 are very similar to each other.
The bond convexity is a phenomenon where the bond yields increase with a decreasing interest rate. The formula to measure the bond yield is dependent on coupon rate and year of maturity. As the interest rate has increased by a substantial amount the bond price is reduced. The chart below shows the convexity in bond price
The convexity graph in between June and December is not very satisfying. The interest rate has been found very fluctuating during this part. In between October, the yield reached the bottom-most point. However, the fund recovered thereafter. It expected that the promised return on investment may get affected due to this fluctuation. Serena and Moreno. (2016) mentioned that if the fund fails to reach the yield value in six months then an annual one per cent decrease can affect as 2% if compounded annually. Among all these bonds, it has not any sharp growth or any sharp declination. Therefore, it has shown a flat line through these 130 days.
The bond 146 is compounded annually rather semiannually. The advantage of annual compounding is if a decrease occurs then it fails to make any proper impact in the fund. Therefore, the stability of such funds is always improved than others. The theory can be justified here as well. The bond 151 has not shown fluctuations such as bond 126. Therefore, the convexity graph is depicted here to compare its plot with the others. The best thing is at the end, the bond has already reached the value of initial. Thus, it can be presumed it is a low growth but low risked bond.
Treasury bond 124 is similar to other bonds. As the interest rate increased during the first twenty days of observation, the value of a bond is decreased. The interest value seems to be constant for the next 20 days. However, the interest value gets lowered for the next 20 days. It gave rise in the yield of the bond. Apart from this, the fund value reduced for the next 30 days. Thus the interest rate was high during the time. Also, the value of bond showed positive growth in 70^{th} to 90^{th} day of observation. However, the fund value started to grow for the next 20 days. The fund value is lower than its first value. However, it has not reached the mark from where it started.
As the government rate of interest varies the chart depicts similar changes in yield in a given period. It proves the convexity theory of bond. Treasury bond 151 is a carbon copy of Treasury bond 124. Here, the interest is almost similar and compounded half yearly. The fund started to decrease at first. However, the fund value raised in between 40^{th} day to 50^{th} day. Here, it shows sharp growth in increase. Apart from this, for the next 25 days, it showed a sharp degradation. However, the fund value remained almost constant between 85^{th} day to 120^{th} day of observation. As mentioned in bond 124, bond 151.
Treasury Bond 151 may have the least loss of return during the holding period. However, the volatility of the Treasury bond 126 is lowest to be found by comparing the graph above. It has been found that 151 is the most volatile among all. Hence, we cannot predict the outcome as the graph changes its course every moment. While treasury bond 126 maintains a smooth flow. The researcher further reports that due to similar behaviour among bond 124 and 151. The Bond 124 is also considered as a volatile Bond. Thus, if an investor invests in any of the Bond due to the least rate of loss then it is similar to playing gamble.
The researcher has plotted the Treasury bond 124 and Treasury bond 126 graphs to identify the cash flow and forward chart and discounted function chart. In addition to the backwards chart. Thereafter, the researcher has plotted other characteristics of the plotting. The main thing that researcher identified that is the Bond 126 and bond 151 showed a similar plotting as mentioned above. However, the plotting
Irrespectively the graph shows an improper flat line as cash flow remained the same for the given period. The author considered fixed cash due to the irrelevant nature of the graph. The spot rate also showed constant behaviour. The discounted function showed a variance than others. At first, it decreased and then increased and remained at a fixed value. The forward rate seemed to be very professional as it maintained a ramp type graph. Apart from this,
With interest value 1.75% and low duration estimation the analysis is similar to other government funds. As the fund is progressing with static cash flow and ramp-like forward flow. However, the cash flow made the spot rate static.
The chart is almost similar to the previous one but it has cash flow interruption. As one can see due to the steady behaviour of the Bond, the researcher presumed a change in cash flow. As the cash flow increased the forward chart changed its behaviour. But maintained a very similar nature like the behaviour of treasure bond 124.
The researcher has found a trend among these curves. Since they are all government fund and driven by government data. Hence, they all more or less similar. However, different cash flow has been considered for each and their period of a compound is also different (Najafi and Mehrdoust, 2017). Therefore, some basic change has been observed. It can be said chart 126 and chart 146 shows in disciplinary plotting. While chart 124 and 151 are most accurate and provides a better result. In addition to this, it can be presumed that all the bonds indicate loss percentage as the degradation of yields continued during the term.
The dirty value or clean value or accrued interest are dependent on each other. Therefore, each indicates the quality of a bond return. Based on the facts found from these statistics one investor should find one's best bond. Apart from that, there are certain thing that often some investors consider. For example, many of them check for the convexity graph for an immediate conclusion. The process is very effective as it is supported by the return on a holding period calculation. However, the researcher believes that the return of a holding period cannot predict the volatile nature during a period. Therefore, the forward, backward and cash flow graph should be considered. But these methods require ample time and the research was limited to a certain time. The researcher expects more proficient result if given more time. The researcher is recommending to undergo a complete analytical procedure before investment. As the volatile nature cannot be understand by the general mathematical formula. However, the backward chart may point out the variance associated with growth of the bond. Thus, considering one tool should not be the doing of a wise man rather considering all should be the concept behind this.
Babatunde, S. O., and Perera, S. (2017). Barriers to bond financing for public-private partnership infrastructure projects in emerging markets. Journal of Financial Management of Property and Construction.
Huang, K., and Petkevich, A. (2016). Corporate bond pricing and ownership heterogeneity. Journal of Corporate Finance, 36, 54-74.
Li, S., Abraham, D., and Cai, H. (2017). Infrastructure financing with project bond and credit default swap under public-private partnerships. International Journal of Project Management, 35(3), 406-419.
Najafi, A. R., and Mehrdoust, F. (2017). Bond pricing under mixed generalized CIR model with mixed Wishart volatility process. Journal of Computational and Applied Mathematics, 319, 108-116.
Rebonato, R. (2018). Bond Pricing and Yield Curve Modeling: A Structural Approach. Cambridge University Press.
Serena, J. M., and Moreno, R. (2016). Domestic financial markets and offshore bond financing. BIS Quarterly Review September.
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