Money Markets and Fixed Income securities: Project(30%)

Money Markets & Fixed Income Securities 3

Money Markets and Fixed Income Securities

  1. Using all available Government bond data to construct and present a yield curve, spot curve and forward curve

By use of the available government bond data, it was possible to construct yield curve, spot curve and forward curve as at the end of June 2015 and the end of December 2015. The spot curve and forward curve estimation were for a period of five years as illustrated below.

Figure 1. Spot curve and forward curve

Treasury Bonds

Treasury Bonds

Treasury Bonds

Treasury Bonds

Treasury Bonds

Treasury Bonds

Treasury Bonds

Treasury Bonds

Treasury Bonds

Treasury Bonds

Treasury Bonds

Treasury Bonds

Treasury Bonds

Treasury Bonds

Description

15-Jun-16
4.75%
Treasury Bond 130

15-Feb-17
6.00%
Treasury Bond 120

21-Jul-17
4.25%
Treasury Bond 135

21-Jan-18
5.50%
Treasury Bond 132

21-Oct-18
3.25%
Treasury Bond 141

15-Mar-19
5.25%
Treasury Bond 122

21-Oct-19
2.75%
Treasury Bond 143

15-Apr-20
4.50%
Treasury Bond 126

21-Nov-20
1.75%
Treasury Bond 146

15-May-21
5.75%
Treasury Bond 124

15-Jul-22
5.75%
Treasury Bond 128

21-Apr-23
5.50%
Treasury Bond 133

21-Apr-24
2.75%
Treasury Bond 137

21-Apr-25
3.25%
Treasury Bond 139

6/15/2016

2/2/2017

7/21/2017

1/21/2018

10/21/2018

3/15/2019

10/21/2019

4/15/2020

11/21/2020

5/15/2021

7/15/2022

4/21/2023

4/21/2024

4/21/2025

Publication date

31-Dec-2015

31-Dec-2015

31-Dec-2015

31-Dec-2015

31-Dec-2015

31-Dec-2015

31-Dec-2015

31-Dec-2015

31-Dec-2015

31-Dec-2015

31-Dec-2015

31-Dec-2015

31-Dec-2015

31-Dec-2015

Series ID

FCMYZJUN16D

FCMYFEB17D

FCMYJUL17D

FCMYJAN18D

FCMYOCT18D

FCMYMAR19D

FCMYOCT19D

FCMYAPR20D

FCMYNOV20D

FCMYMAY21D

FCMYJUL22D

FCMYAPR23D

FCMYAPR24D

FCMYAPR25D

30-Jun-2015

42,369.000

MATURITY DATE

6/15/2016

2/2/2017

7/21/2017

1/21/2018

10/21/2018

3/15/2019

10/21/2019

4/15/2020

11/21/2020

5/15/2021

7/15/2022

4/21/2023

4/21/2024

4/21/2025

COUPON RATE%

END OF 30-JUN-2015

END OF 30-JUN-2015 [YEARS]

END OF 31-DEC-2015

END OF 30-DEC-2015 [YEARS]

Source: (Rba.gov.au, 2016).

The three concepts discussed above; yield curve, spot curve and forward curve are usually used to compare the yield of the bonds and are interrelated. The spot rate refers to present yield of a given term and is usually positively correlated with the maturity duration of a term (Spaulding, 2016; Tsai, 2012). When spot rates of various maturities are taken and calculated, then plotted on a graph, the resulting shape of the curve can be used to decide on the best course of strategy that is effective for certain bonds (Shiller, 1990). In addition, bond and market yield data helps to inform whether to invest in buying of bonds, since the derived yield helps us analyze bond holding associated returns with regard to bond maturity (Tsai, 2012). However, predictive accuracy is at times hampered by assumption of constant coupon rate of the bonds life because of various factors.

Spot yield curves on the other side or zero coupon yield curve can be calculated and plotted against maturity term by following models described in various literature reviews (Jarrow, 1996). This can be done mathematical when we make the assumption that there are annual coupon payments as demonstrated. The formula for calculation is:

Pd = ∑((c/(1+rst)^t)+((m/(1+rst)^t)

With rst being spot yield of the bond with maturity years t and 1/(1+rst) discounting factor corresponding to t years.

Lastly the forward yield curve plots forward rates in respect to maturity term. The equation for calculating forward yield curve is given as.

Pd = ∑ ((C/ (1+0rf1) + (C/ (1+0rf1) (1+1rf2)) +…..+ (M/ (1+0rf1)… (1+r1rfr))

Source: (Choudhry, Joannas, & Pereira, 2001).

Figure 2. Yield %, spot rates and forward rates as at the end of June 2015

END OF 30-JUN-2015

YEAR TO MATURITY

TREASURY YIELD (% pa)

SPOT RATES

FORWARD RATE %Pa

Source: (Rba.gov.au, 2016).

The data above represents the construct and presentation of a yield %, spot rates and forward rates as at the end of June 2015 of the available government bond data. The corresponding construct yield curve, spot curve and forward curve as at the end of June 2015 from the above data is as shown in figure 3 and 4 below.

Figure 3. Treasury yields as at end of June 2015.

Money Markets and Fixed Income securities: Project(30%)

Figure 4.Yield curve, spot curve and forward curve as at the end of June 2015

Money Markets and Fixed Income securities: Project(30%) 1

Figure 5. Yield %, spot rates and forward rates as at the end of December 2015

END OF 31-DEC-2015

YEAR TO MATURITY

TREASURY YIELD (% pa)

SPOT RATES

FORWARD RATE %Pa

Source: (Rba.gov.au, 2016).

The data above represents the construct and presentation of a yield %, spot rates and forward rates as at the end of December 2015 of the available government bond data. The corresponding construct yield curve, spot curve and forward curve as at the end of December 2015 from the above data is as shown in figure 6 and 7 below.

Figure 6. Treasury yields as at end of December 2015

Money Markets and Fixed Income securities: Project(30%) 2

Figure 7. Graph of Yield curve, spot curve and forward curve as at the end of December 2015

Money Markets and Fixed Income securities: Project(30%) 3

Discussion

The data above depicts normal basic shape with average yields since the slope gently rises with rise in maturity; this is characteristic of behavior of average return on yield when data is plotted on a graph of bonds return overtime (Ingersoll, 1987). This observation is consistent with literature that indicates as described by the liquidity preference theory that investments with longer maturity are deemed more risky than their short term counterparts hence commanding higher rates in terms of interest (Ingersoll, 1987; Jarrow, 1996).

  1. The review of the predictive ability of the yield, spot and forward curves

The review of the predictive ability of the yield, spot and forward curves with comprehensive reference to the relevant academic literature were considered with regard to estimates in Part 2A with reference to the available data. The Government bonds are characterized by liquidity and risk free and hence the reasons we adopt traded yield curve and spot data in order to come up with implied forward rates that can be used to predict future market bond yields (Elliott and Echols, 1977: Nyholm and Rebonato, 2008). The shape of the yield curve depicts long term yield expected and as shown above the positive yield curve signify market expectation to rise based on returns in the future which is consistent with financial models that describe behavior of bonds for long-term returns. A study by Livingston and Jain (1982) states that “empirically observed bond yield to maturity curves have consistently been found to become flat for long maturities, as evidenced by the empirical work of various government securities”.

Does the June 2015 forward curve predict the 6 month spot rates at December 2015?

June 2015 forward curve predict the 6 months spot rates at December 2015, and this can be expressed mathematically which tally’s with observed data as shown below;

Figure 8. Summary

YEAR TO MATURITY

TREASURY YIELD (% pa)

SPOT RATES

FORWARD RATE %Pa

Six months rate after six months

(1+y1, 12/200)2 = (1+y0, 6/200) (1+f6, 12/200)

(1+1.90005/200)2 = (1+1.8/200) (1+f6, 12/200)

1.01909075 = 1.009(1+f6, 12/200)

=2.000148

References

Elliott, J, & Echols, M. 1977. Expected Yield Curve Movements and Rational Term Structure Expectations: An Empirical Note, Journal Of Money, Credit & Banking (Ohio State University Press), 9:1. Business Source Premier, EBSCOhost, viewed 15 May 2016.

Choudhry, M., Joannas, R., Pereira, R. 2001. Capital markets instruments analysis and valuation. Prentice Hall, New York.

Ingersoll, J. 1987. Theory of financial decision making. Bowman & Littlefield, California.

Jarrow, R. 1996. Modelling fixed income securities and interest rate options. McGraw-Hill, NewYork.

Livingston, M, & Jain, S. 1982. Flattening of Bond Yield Curves for Long Maturities’, Journal Of Finance, 37, 1, pp. 157-167, Business Source Premier, EBSCOhost, viewed 18 May 2016.

Nyholm, K, & Rebonato, R. 2008. Long-horizon yield curve projections: comparison of semi-parametric and parametric approaches, Applied Financial Economics, 18:20. Business Source Premier, EBSCOhost, viewed 15 May 2016.

Rba.gov.au. 2016. Historical data. [online] Available at: <http://www.rba.gov.au/statistics/historical-data.html> [Accessed 15 May 2016].

Shiller, R. 1990. The term structure of interest rates. Handbook of monetary economics, North-Holland. London.

Tsai, S. 2012. Liquidity and Yield Curve estimation. Emerging Markets Finance & Trade, 48: 5. Business Source Premier, EBSCOhost, viewed 15 May 2016.

Spaulding, W. 2016. Spot Rates, Forward Rates, and Bootstrapping. [online] Available at: <http://thismatter.com/money/bonds/spot-rates-forward-rates-bootstrapping.htm> [Accessed 15 May 2016].