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# Money market and fixed income 作业代写

**Money market and fixed income**

**PART A**

**Background information**

Money market and fixed income 作业代写

There are two kinds of commonwealth government securities outstanding in the market: the treasury fixed coupon bonds and treasury capital indexed bonds, with the former bonds having the largest face value issued in the market and the latter one being linked with the inflation rate. The issuer of commonwealth government securities is authorized to Australian Office of Financial Management (AOFM). The maturities for treasury fixed coupon bonds are 1, 2, 3, 4, 5, 7, 9, 10, 11 and 12 years, and capital indexed bonds 5, 10, 15 years. Besides these two outstanding securities, the Australia government also issues short-dated securities named Treasury Notes with their maturities in months.

For fixed coupon bonds, the interests are paid on six months or semi-annual basis. The amount of the coupon is calculated by the face value timing the coupon rate, with the face value of each bond $100. The interests are paid in the forms of checks or sending to the bank account directly. For capital indexed bonds, the coupon is paid by quarterly basis. Unlike the fixed coupon bonds, both the face value and the interests paid are continuously recalculated every time and adjusted in accordance with the inflation rates. So the capital indexes bonds are also called the inflation linked bonds which provide the investors the protections from depreciation caused by the increasingly inflation rate (http://www.australiangovernmentbonds.com/types-of-bonds/).

**Bond price volatility**

The bond price is usually deducted by the following formula: . Through the equation, it can be seen that there are a few factors affecting the bond prices: the coupon, the maturity and the market required rate. These three factors are also the determinants affecting the interest rate sensitivity of the bond. The so-called interest rate sensitivity is the index measuring the price percentage changes when the yield changed 1%. Generally, there are some characteristics for the interest rate sensitivity. Firstly, the interest rate sensitivity is negative related with the coupon rate. The higher the coupon rate is, the less changes of the bond prices are. Secondly, the sensitivity is positive related with the maturity, and with the longer the maturity is, the less acceleration is of the sensitivity. Thirdly, the sensitivity is asymmetric changed to the yield. The price changing range is lower caused by the rising up of the yield than that caused by the same scale decreasing of the yield. The measurements indicating the interest rate sensitivity include: price value basis point, duration and convexity (Peterson, Steven P, Hoboken, N.J., 2012).

The bond duration is the time weighted discounted value of the future cash flows including both the coupon and the principal. The most often used duration is as following: , and the modified duration is .

However, the duration is still not the perfect measuring index for the interest rate sensitivity because it changes with the yield. Stanley and Diller (1984) brought the concept of convexity. Duration indicates the slope of the price-yield curve, and convexity indicates the degree of the crook of the curve. It can be calculated through the following formula:, or (Frank J. Fabozzi, 1995).

**Presumptions**

The report chooses four on the run commonwealth securities as at the date Jun. 2012 and Dec. 2012 as the research object. Their information is listed in the following table:

Table 1. Bond prices and yields 6 June 2012

(sources:http://www.australiangovernmentbonds.com/blog/category/bond-prices-and-rates/page-2/)

And before calculating conduction, some assumptions are given in advance and discussed for the convenience of calculation. Firstly, the required interest rates or the discount rate for the investors are assumed to be 10% annually. Its reasons are (1) the discount rate is the required interest rate by investors and should be equal to the value when investors investing this amount of money elsewhere. So generally, this rate should equal to the risk-free rate plus the risk premium. Usually, the banks’ overnight indexed swaps of 30 days are taken as the risk-free rates. Table 2 listed these rates in 2012. The mean interest rate is about 3.63% in 2012. (2) according to Zvi Bodie’s research (2009), it is shown that the global risk premium in the capital market is about 6%-8%. (3) hence the 10% annual required interest is the reasonable assumption and convenient for the calculation.

Table 2. the 2012 banks overnight indexed swaps

(Sources: http://www.rba.gov.au/statistics/tables/index.html#interest_rates)

**Question 1.**

The calculation of duration for these four bonds is shown in the appendices respectively. hence the dirty price, clean price, modified duration and modified convexity of the Government bonds as at as at the end of June 2012 and the end of December 2012 can be deducted based on duration. The results are shown in the following table.

Table 3. calculation results at June 2012

Money market and fixed income 作业代写

Table 4. calculation results at Dec. 2012

**Question 2.**

The holding period return (HPR) is a simple and important index to measure the investment performances on the portfolio or an asset. It is percentage value of total revenues including dividends, interests and capital gains to the purchasing prices. In can be calculated by the following formula:. The HPR for the four bonds are listed in the following table.

Table 5. HPR from the period as at Jun. 2012

Money market and fixed income 作业代写

**Question 3.**

The duration for a portfolio is the average effective maturity of the portfolio. It is the weighted average duration of each bond with the weight to be the value of that bond to the total value of the portfolio. The following tables show the results for these four bonds as at the two dates:

Table 6. portfolio duration as at Jun 2012

Table 7. portfolio duration as at Dec. 2012

**Part B.**

**Question 2.**

The yield curve shows the yield level of securities with the same risks except the risks in different terms to maturities. It reflects the relationships between of yield to maturity and terms structure. Generally, there are four kinds of yield curves: positive ones with the higher yield to the longer maturities, negative ones with higher yield to shorter maturities, even ones with the same yield and camel back ones with higher yield at the middle of the period (Jessica James & Nick Webber, 2001).

The spot curve is the curve with the spot rate of zero-coupon bonds. However, in the real market, there are rarely zero-coupon bonds issued. In order to acquire the spot rate, it usually chooses the bootstrap method. The formula adapting to calculate the spot rate is as following:, where z is the spot rate.

And the forward rate can be concluded through the following formula: , where ri is the forward rate. And the following tables show the results of calculating the spot rate and the forward rate.

Table 8. Spot rate and forward rate at Jun. 2012

Table 9. Spot rate and forward rate at Dec. 2012

And the following figures illustrate the yield curve, spot curve and forward curve respectively.

Figure 1-3 yield curve, spot curve and forward curve as at Jun. 2012 and Dec. 2012

Figure 1. yield curve

(Sources: http://www.rba.gov.au/fin-services/bond-facility/prices/2013/bp-mar13.html)

**Figure 2.**

**Figure 3.**

**Question 2.**

**Literature review**

**The yield curve and economy growth**

Researchers explain that the interest rate in short term will influence people’s expectation, and the expectation will arouse the changes of long term interest rates. Furthermore, the long term interest rate will have influence on consumption, investment and so on; hence directly affect the economy growth. So the growing trend of the national economy can be predicted from the yield curve.

Besides, the yield curve reflects the present monetary policy, which is made based on the consideration of the future economic prospects. Hence the yield curve reflects the future economic trend (Estrella.AandG.A.Hardouvel, 1991).

**The yield curve and the inflation rate**

The fact that Inflation can be predicted based on the yield curve is attributed to people’s psychological expectation. The Fisher Formula is: nominal rate=real interest rate+inflation rate. When the inflation rate in the short term is relatively lower, thereby with the lower nominal rate, people tend to form the expectation that the long term inflation rate will increase. At this moment, they are usually to ask the bonds having the higher yield. In short, the increasing spread indicates the rising inflation expectation. And when the short term inflation rate is relatively higher, market participant tend to form a decreasing long term inflation rate expectation, thereby they are willing to buy the bonds at a rate lowering than the current bond yield. In short, the narrowing interest rate gap including the decreasing inflation rate expectation (Fama.F.Eugen,1975).

**The yield curve and the forward interest rate**

Based on the assumptions that the market participants are risk neutral and hold the same expectations, the bond market are highly effective and there is no transaction costs, the expectation theory holders believed that the forward interest rate changing expectation is the only factor that decided the yield curve and realized through the arbitrage forces. If expectation believed that the future short term interest rates rise up, then the yield curve will have a positive slope, and vice verse (Fama.F.Eugen, 1990).

Figure 1 shows that the yield curve both at the date Jun. 2012 and Dec. 2012 have the positive slope. Based on the discussions above, it can be concluded that standing at the point of these two dates, the Australian long term interest rate is expected to rise in the future. Hence consumptions, investment, etc would be compressed. The economy is expected to have a slow growth. And in order to maintain the economy growing, the central bank is better to implement the expansionary monetary policy. And the Australians hold the expectations that the inflation rate in the long term will rise up, hence they require a higher long term yield to make up the loss of investment caused by inflation. At last, according to expectation theory, the Australians believe that the short term interest rate in the future is likely to rise up.

From figures 2 and figure 3, it can be seen that the one-year spot rate curve and one-year forward curve have the same movement direction. And the decreasing speed for spot rate is lower than the forward curve. And based on the table, we can see that one year forward rate at Jun. 2012 is the spot rate on Dec. 2012, hence it can be concluded that the June 2012 forward curve does predict the 6 month spot rates at December 2012.

**References:**

http://www.australiangovernmentbonds.com/types-of-bonds/

Peterson, Steven P, Hoboken, N.J.(2012). Investment theory and risk management. Wiley

Frank J. Fabozzi (1995). Duration, Convexity, and Other Bond Risk Measures. John Wiley & Sons

Zvi Bodie (2009). Investments. The McGraw Hill Companies, 7

^{th}ed.

Jessica James & Nick Webber (2001).

*Interest Rate Modelling*. John Wiley & Sons

Fama.F.Eugene (1976). Short term interest rates as predietors of inflation. The Americaneconomiereview.

Estrella. A and G. A. Hardouvelis (1991). The term structure as a predietors of real economic activity. The journal of finance.

Fama.F.Eugene (1990). Term structure forecasts of interest rates，inflation and real returns. journal of monetary economics.

**Appendices**

Money market and fixed income 作业代写

Calculation process of duration

Appendix 2. calculation of spot rate and forward rate

Money market and fixed income 作业代写