Essays on Money Markets and Fixed Income Securities Assignment

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The paper 'Money Markets and Fixed Income Securities ' is a great example of a Finance and Accounting Assignment. 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 Title 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 Treasury Bond 1304.75%15-Jun-16 Treasury Bond 1206.00%15-Feb-17 Treasury Bond 1354.25%21-Jul-17 Treasury Bond 1325.50%21-Jan-18 Treasury Bond 1413.25%21-Oct-18 Treasury Bond 1225.25%15-Mar-19 Treasury Bond 1432.75%21-Oct-19 Treasury Bond 1264.50%15-Apr-20 Treasury Bond 1461.75%21-Nov-20 Treasury Bond 1245.75%15-May-21 Treasury Bond 1285.75%15-Jul-22 Treasury Bond 1335.50%21-Apr-23 Treasury Bond 1372.75%21-Apr-24 Treasury Bond 1393.25%21-Apr-25 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 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 1.930 1.970 2.015 2.020 2.065 2.105 2.210 2.285 2.435 2.475 2.670 2.775 2.915 3.005 42,369.000 2.000 1.995 2.020 2.015 2.015 2.040 2.095 2.130 2.245 2.300 2.480 2.610 2.750 2.815 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% 4.75% 6.00% 4.25% 5.50% 3.25% 5.25% 2.75% 4.50% 1.75% 5.75% 5.75% 5.50% 2.75% 3.25% PAR                             END OF 30-JUN-2015 351 583 752 936 1,209 1,354 1,574 1,751 1,971 2,146 2,572 2,852 3,218 3,583 END OF 30-JUN-2015 [YEARS] 0.962 1.597 2.060 2.564 3.312 3.710 4.312 4.797 5.400 5.879 7.047 7.814 8.816 9.816 END OF 31-DEC-2015 167 399 568 752 1,025 1,170 1,390 1,567 1,787 1,962 2,388 2,668 3,034 3,399 END OF 30-DEC-2015 [YEARS] 0.46 1.09 1.56 2.06 2.81 3.21 3.81 4.29 4.90 5.38 6.54 7.31 8.31 9.31 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 the 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 help 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 the assumption of a constant coupon rate of the bond's life because of various factors. Spot yield curves on the other side of the zero-coupon yield curve can be calculated and plotted against maturity terms by following models described in various literature reviews (Jarrow, 1996).

This can be done mathematically 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 rest  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 with respect to maturity term.

The equation for calculating the forward yield curve is given. Pd = ∑ ((C/ (1+0rf1) + (C/ (1+0rf1) (1+1rf2)) +… ..+ (M/ (1+0rf1)… (1+r-1rfr)) 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                     BOND PAR $ 100                                                               YEAR TO MATURITY 0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.0 4.5 5.0 BOND PAR $ 100 $ 100 $ 100 $ 100 $ 100 $ 100 $ 100 $ 100 $ 100 $ 100 TREASURY YIELD (% pa) 1.800 1.900 1.970 2.010 2.020 2.030 2.070 2.100 2.250 2.300 SPOT RATES 1.89000 1.90005 1.97023 2.01040 2.02016 2.03022 2.07113 2.10100 2.25650 2.30221 FORWARD RATE %Pa 1.890 1.910 2.011 2.131 2.059 2.081 2.317 2.310 3.505 2.714 PV   0.941 1.942 2.956 3.940 4.925 5.995 7.054 8.587 9.789 Source: (Rba. gov. au, 2016). The data above represents the construct and presentation of a yield %, spot rates, and forward rates 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 Figures 3 and 4 below. Figure 3. Treasury yields as at end of June 2015.   Figure 4. The yield curve, spot curve, and forward curve as at the end of June 2015 Figure 5. Yield %, spot rates, and forward rates as at the end of December 2015 END OF 31-DEC-2015                     BOND PAR $ 100                                         YEAR TO MATURITY 0.500 1.000 1.500 2.000 2.500 3.000 3.500 4.000 4.500 5.000 BOND PAR 100.000 100.000 100.000 100.000 100.000 100.000 100.000 100.000 100.000 100.000 TREASURY YIELD (% pa) 2.000 1.995 2.020 2.015 2.015 2.030 2.080 2.120 2.200 2.280 SPOT RATES 1.890 1.996 2.021 2.015 2.015 2.030 2.081 2.122 2.204 2.281 FORWARD RATE %Pa 1.890 2.101 2.071 2.000 2.013 2.106 2.389 2.404 2.864 2.976 PV   0.988 1.991 2.964 3.931 4.925 6.024 7.122 8.397 9.704 Source: (Rba. gov. au, 2016). The data above represents the construct and presentation of a yield %, spot rates, and forward rates 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 are as shown in Figures 6 and 7 below. Figure 6. Treasury yields as at end of December 2015     Figure 7. Graph of the Yield curve, spot curve and forward curve as at the end of December 2015       Discussion The data above depicts normal basic shape with average yields since the slope gently rises with a rise in maturity; this is characteristic of the 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 riskier than their short term counterparts hence commanding higher rates in terms of interest (Ingersoll, 1987; Jarrow, 1996).   PART 2 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 a comprehensive reference to the relevant academic literature was 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 signifies the market expected to rise based on returns in the future which is consistent with financial models that describe the 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 in December 2015?  June 2015 forward curve predicts 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 0.5 1.0 1.5 2.0 BOND PAR   $                              100   $                        100   $                                    100   $                            100 TREASURY YIELD (% pa) 1.800 1.900 1.970 2.010 SPOT RATES 1.89000 1.90005 1.97023 2.01040 FORWARD RATE %Pa 1.890 1.910 2.011 2.131             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: [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: [Accessed 15 May 2016].

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