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Fixed Income Securities And Critical Analysis
  • 4

  • Course Code: BAFI1065
  • University: RMIT University
  • Country: Australia

TASK

Assessment 2 is an individual project. Each student will choose four Australian Commonwealth Government Securities (you must choose at least two bonds with the remaining maturity time longer than 5 years). Refer to the Excel file "Australian government bond code and yield.xlsx" for the government bond information and daily yield. The RBA website (http://www.rba.gov.au) provides the bond data for the yield information of less than one year. 

govbondinfoanddailyyieldexcelfile

Required
Part 1: 
    A. Calculate the dirty price, clean price, modified duration, and convexity of the chosen government bonds on 31st January 2023 and 31st July 2023. Discuss the results. 
    Consider pricing during the coupon period and dealing with the partial period for duration and convexity
    Discuss the relationship of the coupon, term to maturity, and yield to maturity in each bond. 
    Compare and contrast the four bonds (based on the calculation of dirty price, clean price, modified duration and modified convexity).   
    
    B. Calculate each bond's holding period return from 31st January 2023 to 31st July 2023. Discuss the results. 

    Capital gain/loss of each bond
    Compare the changes in yield to the return movement of each bond
    Compare the return of the bonds
    
    C. Calculate the modified duration and convexity for an equally weighted portfolio of the four bonds at both dates. Estimate the holding period return for the portfolio over the six months between the two dates—report on your findings. Compare and contrast the return and volatility of the portfolio and the separate bonds at both dates. Discuss the results. 

Part 2: 

    A. Use all available Government bond data to construct and present a yield, spot, and forward curve on 31st January 2023 and 31st July 2023. Estimate the spot curve and forward curve for 5 years. Present and discuss the findings. 
    
  You need to consider “all” available government bond data. This means not using only the chosen four bonds to estimate the par coupon curve. 
    There are “many” assumptions that you can make to get the par coupon curve.
    Calculate the spot and forward rate curves based on the par coupon curves.
    Compare those three curves and discuss the trend of the curve.
    
    B. Review the yield, spot, and forward curves' predictive ability with a comprehensive reference to the relevant academic literature. Discuss the curves you have estimated in Part 2 (A) regarding this literature. Consider the COVID-19 pandemic, recent interest rate movement, and other significant events. Does the Jan 2023 forward curve predict the six-month spot rates in July 2023? Comment and explain.

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PART A

Ans 1

Based on above results it may be inferred that yield has inverse relationship with price and yield of bonds are higher than the coupon rate which caused bonds to trade at discount. The convexity of bond increases with time frame and so is the duration of bonds. The dirty price is higher than the clean price of the bond.

For AUG02750424=31-01-2023
 

Period Coupon DF PV Convexity PV * period
0.5 1.375 0.98 1.35 0.01 0.68
1 1.375 0.97 1.33 0.03 1.33
1.5 101.375 0.95 96.61 3.53 144.91
Bond Price- Clean 99.29   146.92
Convexity 3.57  
Macaulay Duration 1.48  
MD 1.43  
Bond Price- Dirty   99.83  
    10/21/2022 1/31/2023 102.00  


For AUG02750424=31-07-2023

Period Coupon DF PV Convexity PV * period
0.5 1.375 0.980 1.347 0.010 0.673
1 101.375 0.960 97.272 1.880 97.272
           
Bond Price 98.62   97.95
Convexity 1.890  
Macaulay Duration 0.993  
MD 0.962  
Bond Price- Dirty   99.15  
    5/21/2023 7/31/2023 71.00  


For AUG00251124==31-01-2023

Period Coupon DF PV Convexity PV * period
0.5 0.125 0.98 0.12 0.00 0.06
1 0.125 0.97 0.12 0.00 0.12
1.5 0.125 0.95 0.12 0.00 0.18
2 100.125 0.94 94.02 5.51 188.04
Bond Price- Clean 94.38   188.40
Convexity 5.51  
Macaulay Duration 2.00  
MD 1.93  
Bond Price- Dirty   94.38  
    10/21/2022 1/31/2023 102.00  


For AUG00251124==31-07-2023

Period Coupon DF PV Convexity PV * period
0.5 0.125 0.98 0.12 0.00 0.06
1 0.125 0.96 0.12 0.00 0.12
1.5 100.125 0.94 94.17 3.41 141.25
           
Bond Price 94.41   141.43
Convexity 3.42  
Macaulay Duration 1.50  
MD 1.45  
Bond Price- Dirty   94.46  
    5/21/2023 7/31/2023 71.00  

For AUG01751132=31-01-2023
 

Period Coupon DF PV Convexity PV * period
0.5 0.875 0.98 0.86 0.01 0.43
1 0.875 0.97 0.84 0.02 0.84
1.5 0.875 0.95 0.83 0.03 1.24
2 0.875 0.93 0.82 0.05 1.63
2.5 0.875 0.92 0.80 0.07 2.00
3 0.875 0.90 0.79 0.09 2.36
3.5 0.875 0.88 0.77 0.12 2.71
4 0.875 0.87 0.76 0.15 3.04
4.5 0.875 0.85 0.75 0.18 3.36
5 0.875 0.84 0.73 0.21 3.67
5.5 0.875 0.82 0.72 0.25 3.97
6 0.875 0.81 0.71 0.29 4.25
6.5 0.875 0.80 0.70 0.33 4.52
7 0.875 0.78 0.68 0.37 4.79
7.5 0.875 0.77 0.67 0.42 5.04
8 0.875 0.75 0.66 0.46 5.28
8.5 0.875 0.74 0.65 0.51 5.51
9 0.875 0.73 0.64 0.56 5.74
9.5 0.875 0.72 0.63 0.61 5.95
10 100.875 0.70 70.94 75.87 709.38
Bond Price- Clean 84.94   775.72
Convexity 80.58  
Macaulay Duration 9.13  
MD 8.82  
Bond Price- Dirty   84.94  
    10/21/2022 1/31/2023 102.00  


For AUG01751132=31-07-2023

 

Period Coupon DF PV Convexity PV * period
0.5 0.875 0.98 0.86 0.01 0.43
1 0.875 0.96 0.84 0.02 0.84
1.5 0.875 0.94 0.82 0.03 1.24
2 0.875 0.92 0.81 0.05 1.62
2.5 0.875 0.90 0.79 0.07 1.98
3 0.875 0.89 0.78 0.09 2.33
3.5 0.875 0.87 0.76 0.12 2.66
4 0.875 0.85 0.75 0.14 2.98
4.5 0.875 0.84 0.73 0.17 3.29
5 0.875 0.82 0.72 0.21 3.58
5.5 0.875 0.80 0.70 0.24 3.86
6 0.875 0.79 0.69 0.28 4.13
6.5 0.875 0.77 0.67 0.32 4.38
7 0.875 0.76 0.66 0.36 4.63
7.5 0.875 0.74 0.65 0.40 4.86
8 0.875 0.73 0.64 0.44 5.08
8.5 0.875 0.71 0.62 0.49 5.29
9 0.875 0.70 0.61 0.53 5.49
9.5 100.875 0.68 68.94 66.54 654.94
           
Bond Price 82.03   713.60
Convexity 70.496  
Macaulay Duration 8.699  
MD 8.400  
Bond Price- Dirty   82.37  
    5/21/2023 7/31/2023 71.00  



For AUG04500433==31-01-2023

 

Period Coupon DF PV Convexity PV * period
0.5 2.25 0.980 2.205 0.016 1.103
1 2.25 0.961 2.161 0.042 2.161
1.5 2.25 0.942 2.118 0.077 3.178
2 2.25 0.923 2.076 0.121 4.153
2.5 2.25 0.904 2.035 0.172 5.087
3 2.25 0.886 1.995 0.232 5.984
3.5 2.25 0.869 1.955 0.298 6.842
4 2.25 0.852 1.916 0.371 7.664
4.5 2.25 0.835 1.878 0.450 8.450
5 2.25 0.818 1.841 0.534 9.203
5.5 2.25 0.802 1.804 0.624 9.922
6 2.25 0.786 1.768 0.718 10.608
6.5 2.25 0.770 1.733 0.817 11.264
7 2.25 0.755 1.698 0.920 11.889
7.5 2.25 0.740 1.665 1.027 12.485
8 2.25 0.725 1.632 1.136 13.053
8.5 2.25 0.711 1.599 1.249 13.593
9 2.25 0.697 1.567 1.365 14.106
9.5 2.25 0.683 1.536 1.482 14.593
10 102.25 0.669 68.421 72.814 684.212
           
Bond Price 103.604   849.549
Convexity 84.46  
Macaulay Duration 8.20  
MD 7.92  
Bond Price- Dirty   104.47892  
    5/21/2023 7/31/2023 71.00  



For AUG04500433==31-07-2023
 

Period Coupon DF PV Convexity PV * period
0.5 2.25 0.980 2.205 0.016 1.103
1 2.25 0.961 2.161 0.042 2.161
1.5 2.25 0.942 2.118 0.077 3.178
2 2.25 0.923 2.076 0.121 4.153
2.5 2.25 0.904 2.035 0.172 5.087
3 2.25 0.886 1.995 0.232 5.984
3.5 2.25 0.869 1.955 0.298 6.842
4 2.25 0.852 1.916 0.371 7.664
4.5 2.25 0.835 1.878 0.450 8.450
5 2.25 0.818 1.841 0.534 9.203
5.5 2.25 0.802 1.804 0.624 9.922
6 2.25 0.786 1.768 0.718 10.608
6.5 2.25 0.770 1.733 0.817 11.264
7 2.25 0.755 1.698 0.920 11.889
7.5 2.25 0.740 1.665 1.027 12.485
8 2.25 0.725 1.632 1.136 13.053
8.5 2.25 0.711 1.599 1.249 13.593
9 2.25 0.697 1.567 1.365 14.106
9.5 2.25 0.683 1.536 1.482 14.593
10 102.25 0.669 68.421 72.814 684.212
           
Bond Price 103.604   849.549
Convexity 84.46  
Macaulay Duration 8.20  
MD 7.92  
Bond Price- Dirty   104.47892  
    5/21/2023 7/31/2023 71.00  

 

Answer 2

The holding period of each bond has been computed as under:
 

Bond 31-Jan 31-Jul Coupon Return
AUG02750424= 99.83 99.15 1.375 0.70%
AUG00251124= 94.38 94.46 0.125 0.21%
AUG01751132= 84.94 82.37 0.875 -2.00%
AUG04500433= 108.16 104.48 2.25 -1.32%


Based on above computation, it may be inferred that holding period return of bond is lower than anticipated on account of increase in yield of bonds over the time period. The results are positive for two bonds and negative for other two. 

Ans 3

In case of equal weighted portfolio, it may be seen that MD is lower for portfolio than 2 bonds and higher than other two bonds. The same result holds for convexity. Further, holding period return is negative for the portfolio and thus equal weighted portfolio shall not provide negative return on an overall basis.

Bond MD Convexity HPR
AUG02750424= 1.433 3.569 0.70%
AUG00251124= 1.935 5.513 0.21%
AUG01751132= 9.132 80.583 -2.00%
AUG04500433= 8.279 96.657 -1.32%
Portfolio 5.195 46.581 -0.60%

 

Bond MD Convexity HPR
AUG02750424= 0.96 1.89 0.00%
AUG00251124= 1.45 3.42 0.00%
AUG01751132= 8.40 70.50 0.00%
AUG04500433= 8.20 84.46 0.00%
Portfolio 4.753 40.067 0.00%

 

Part B

Ans 1

Forward curve has been forecasted for 5 years considering the current year bond as base. The forward curves at two different dates are as under:
   

  31-01-2023 31-07-2023
  Forward Rate Forward Rate
1 Year 3.094% 3.967%
2 Year 3.118% 3.832%
3 Year 3.208% 3.809%
4 Year 3.283% 3.809%
5 Year 3.353% 3.867%


The curve are as under:

forwardcurve
 

Yield curve is presented as under:

yield curve
 

Answer 2

Predictive ability of yield , spot and Forward curves

A graph representing the yields of bonds with various maturities is called a yield curve ( CFI Team, 2022). One of the most crucial instruments in economics and finance, it is frequently employed to forecast future economic activity.

The current market yield for bonds with different maturities is represented by the spot yield curve. Based on the state of the market, the forward yield curve displays the anticipated future rates for bonds with various maturities.

The prediction capacity for yield curve's has been the subject of extensive academic study. There is a strong ability for the yield curve to predict future economic growth, inflation, and recessions, as per majority of studies.

A recession is strongly predicted by an inverted yield curve, which occurs when short-term rates are greater than long-term yields (Kose, 2022). This is one of the most well-known discoveries in the literature. Since the 1970s, every recession in the US has been foreshadowed by an inverted yield curve.

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The COVID-19 epidemic and recent changes in interest rates have made it difficult for the yield curve to anticipate future events.

A severe economic downturn brought on by the epidemic prompted unprecedented global monetary policy measures by central banks. The yield curve has been altered by these measures, making it more challenging to decipher its forecast indications.
 
Predicting the future form of the yield curve has become more challenging as a result of the recent quick increase in interest rates.

Predictive ability of the spot and forward rates in the context of the given yield rates 

The yield curve in the example is upward sloping, which is a typical shape for yield curves. This shows that the market anticipates future economic expansion and increased inflation.
 
The forward curve demonstrates that the market anticipates a small increase in short-term interest rates during the following six months. This is consistent with the interest rates' recent sharp climb.

Does the Jan 2023 forward curve predict the six-month spot rates in July 2023?

The six-month spot rate is expected to be around 4.5% in July 2023, according to the forward curve. The forward curve is only a forecast, therefore it's crucial to keep in mind that the actual market rate in July 2023 can be higher or lower than 4.5% (Agmon, 2023).

Various factors that could ultimately affect the spot rate in the month of July 2023 ,which comprised :
•    The outlook of the economy
•    Expectations for inflation
•    Central banks' decisions about monetary policy
•    Unforeseen occurrences like the COVID-19 epidemic (Dheeraj Vaidya, 2023)

Overall, the forward curve indicates that the market anticipates a small increase in short-term interest rates during the next six months. However, there is a lot of uncertainty over the direction that interest rates will take in the future, so the actual market rate in July 2023 could be either higher or lower than 4.5%.

Also Read - Financial Economics Assignment Help

Overall Conclusion

A useful instrument for forecasting future economic activity is the yield curve. But the COVID-19 pandemic and subsequent changes in interest rates have made it difficult for the yield curve to anticipate the future.

Given that the yield curve is upward sloping, it appears that the market anticipates future economic expansion and rising inflation. The forward curve demonstrates that the market anticipates a small increase in short-term interest rates during the following six months.

The forward curve is only a forecast, therefore it's crucial to keep in mind that the actual market rate in July 2023 can be higher or lower than 4.5%. The spot rate in July 2023 may be impacted by a number of variables, including as the state of the economy, inflation expectations, central bank monetary policy choices, and unforeseen occurrences.

References

CFI Team, 2022. What is the Yield Curve?. [Online] 
Available at: https://corporatefinanceinstitute.com/resources/fixed-income/yield-curve/
[Accessed 28 September 2023].
Agmon, T., 2023. The forward exchange rate and the prediction of the future spot rate: Empirical evidence. [Online] 
Available at: https://www.sciencedirect.com/science/article/abs/pii/0378426681900364#:~:text=The%20results%20show%20that%20the,all%20the%20examined%20forecast%20leads
[Accessed 28 September 2023].
Dheeraj Vaidya, C. F., 2023. Spot Exchange Rate. [Online] 
Available at: https://www.wallstreetmojo.com/spot-exchange-rate/
[Accessed 28 September 2023].
Kose, S. C. a. M. A., 2022. Recession: When Bad Times Prevail. [Online] 
Available at: https://www.imf.org/external/pubs/ft/fandd/basics/recess.htm
[Accessed 28 September 2023].

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