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Document: JOB # MAY 221

Author: Stuart Thomas Save Date: 27/11/2013

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Money markets and fixed income securities

Report Submitted

By

Student Name

University Name



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Data from the RBA.GOV.AU

June 2011

Series Number Coupon Maturity

Closing

Yield

Gross

Price

Accrued

Interest

Capital

Price

TB123 5.75% 15 Apr 12 4.700 101.993 1.194 100.799

TB127 4.75% 15 Nov 12 4.715 100.635 0.594 100.041

TB118 6.50% 15 May 13 4.735 103.937 0.813 103.125

TB129 5.50% 15 Dec 13 4.745 101.956 0.225 101.731

Dec 2011

Series Number Coupon Maturity

Closing

Yield

Gross

Price

Accrued

Interest

Capital

Price

TB123 5.75%

15 Apr

12 3.930 101.692 1.194 100.498

TB127 4.75%

15 Nov

12 3.480 101.670 0.587 101.083

TB118 6.50%

15 May

13 3.285 105.091 0.804 104.287

TB129 5.50%

15 Dec

13 3.160 104.635 0.225 104.410



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Part 1:

A. Calculate the dirty price, clean price, modified duration and modified convexity of the

Government bonds as at as at the end of June 2011 and the end of December 2011.

The value is calculates based on the fact that it pays 4 times a year and it uses the 30/360 US

day count convention. These calculations are at the end of June 2011.

Term Value Value Value Value

Series Number TB123 TB127 TB118 TB129

Coupon Rate 5.75% 4.75% 6.50% 5.50%

Par Value $100 $100 $100 $100

Full Market Value $101.993 $100.635 $103.937 $101.956

Dirty Price 10.20 10.06 10.40 10.20

Accrued Interest 1.194 0.594 0.813 0.225

Flat Market Value $100.799 $100.041 $103.125 $101.731

Clear Price 10.08 10.00 10.31 10.18

Table - 1: Calculation of dirt price and clear price at the end of June 2011

These calculations are at the end of December 2011

Term Value Value Value Value

Series Number TB123 TB127 TB118 TB129

Coupon Rate 5.75% 4.75% 6.50% 5.50%

Par Value $100 $100 $100 $100

Full Market Value $101.692 $101.670 $105.091 $101.956



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Dirty Price 10.17 10.16 10.51 10.20

Accrued Interest 1.194 0.594 0.804 0.225

Flat Market Value $100.498 $101.083 $104.287 $104.410

Clear Price 10.05 10.10 10.31 10.44

Table - 1: Calculation of dirt price and clear price at the end of December, 2011

For TB123: Calculation of the modified duration and convexity

Bond Price $96.05 $95.15 If Yield Changes By 1.00%

Face Value

100 100

Bond Price Will Change

By -0.90 -0.93%

Coupon Rate 5.75% 6%

Life in Years 1

1

Modified Duration

Predicts -0.90 -0.94%

Yield 10.00% 11% Convexity Adjustment 0.01 0.01%

Frequency 2 2 Total Predicted Change -0.90 -0.93%

Macaulay

Duration

0.99

Actual New Price $95.15

Modified

Duration

0.94

Predicted New Price $95.15

Convexity

1.33

Difference

$0.00 +0.0000%

Period Cash Flow

PV Cash

Flow

Duration

Calc

Convexity

Calc

0 ($96.05)



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1

2.88

2.74

2.74

4.97

2

102.88

93.31

186.62

507.81

Total

189.36

512.78

Total

For TB127- Calculation of the modified duration and convexity


Face Value

100 100


By -0.89 -0.93%


Life in Years 1

1

Modified Duration

Predicts -0.90 -0.94%



Macaulay

Duration

0.99


Modified

Duration

0.94


Convexity

1.34

Difference

$0.00 +0.0000%



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Period Cash Flow

PV Cash

Flow

Duration

Calc

Convexity

Calc

0 ($95.12)

1

2.38

2.26

2.26

4.10

2

102.38

92.86

185.71

505.34

Total

187.98

509.45

Total

For TB 118- Calculation of the modified duration and convexity


Face Value

100 100


By -0.90 -0.93%


Life in Years 1

1

Modified Duration

Predicts -0.91 -0.94%



Macaulay

Duration

0.98


Modified

Duration

0.94


Convexity

1.33

Difference

$0.00 +0.0000%



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Period Cash Flow

PV Cash

Flow

Duration

Calc

Convexity

Calc

0 ($96.75)

1

3.25

3.10

3.10

5.61

2

103.25

93.65

187.30

509.66

Total

190.40

515.28

Total

For TB129 - Calculation of the modified duration and convexity


Face Value

100 100


By -0.89 -0.93%


Life in Years 1

1

Modified Duration

Predicts -0.90 -0.94%



Macaulay

Duration

0.99


Modified

Duration

0.94


Convexity

1.34

Difference

$0.00 +0.0000%



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Period Cash Flow

PV Cash

Flow

Duration

Calc

Convexity

Calc

0 ($95.82)

1

2.75

2.62

2.62

4.75

2

102.75

93.20

186.39

507.20

Total

189.01

511.95

Total

B. Calculate the holding period return for each of the bonds over the period from end June

2011 end December 2011.

For TB 123

Holding period yield

Bond

value

$96.05

Par value (redemption

value)

97.19

Coupon rate (annual)

5.75%

Years till maturity

0.5

Today

30-06-

2011 Maturity 31-12-2011


6.55%



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For TB 127


Bond

value

$95.12


value)

96.25


4.75%

Years till maturity

0.5

Today

30-06-

2011 Maturity 31-12-2011


5.56%

For TB 118


Bond

value

$95.12


value)

97.90


6.50%

Years till maturity

0.5

Today

30-06-

2011 Maturity 31-12-2011


8.21%

For TB 129



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Bond

value

$95.12


value)

96.96


5.50%

Years till maturity

0.5

Today

30-06-

2011 Maturity 31-12-2011


6.70%

C. Calculate the modified duration, modified convexity and holding period return for an

equally-weighted portfolio of the bonds at both dates. Report on your findings. Compare and

contrast the return and volatility of the portfolio and the separate bonds at both dates.

At the end of June 2011

Macaulay Duration 0.99

Modified Duration 0.97

Convexity 1.43

Holding Return = 5.63 %

At the end of December, 2011

Macaulay Duration 0.91

Modified Duration 0.89

Convexity 1.31

Holding Return = 5.93 %

The calculated values suggests that for the equally weighted portfolio the the holding return get

increases for the end of the December 2011 because of the longer period than June 2011.



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Part 2:

A. Use all available Government bond data (ie not just the bonds in your portfolio) to construct and

present a yield curve, spot curve and forward curve as at the end of June 2011 and the end of

December 2011. Your spot curve and forward curve estimation should go out no more than 5

years. Present and discuss your findings.

Suppose we have the following Treasury yields (based roughly on rba.gov.com) The face

value is taken as $100 for the maturity years of 5.

Maturity (yrs) Coupon Price 32nds Yield

0.25 0 $99.46 2.17

0.50 0 $98.82 2.38

1.00 2.250 $99.66 99 21/32 2.61

1.50 2.250 $99.28 99 9/32 2.76

2.00 2.500 $99.15 99 5/32 2.96

2.50 2.875 $99.63 99 20/32 3.05

3.00 3.000 $99.53 99 17/32 3.19

3.50 3.125 $99.64 99 20/32 3.26

4.00 3.500 $100.58 100 19/32 3.37

4.50 3.375 $99.64 99 20/32 3.49

5.00 3.500 $99.77 99 25/32 3.58

Table: Value taken initially for the bonds for next 5 years and calculation of yield value



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Fig: Curve represents the yielding curve for the given bond and coupan rate

The above curve reflects the yield for current securities with certain maturities.

Spot Curve

The one year spot rate is easily found by equalizing the cash flows.

y is the yield to maturity, z1 and z2 are the two zero rates (6mo and 1yr):

C1/(1+y/2) + (100+C2)/(1+y/2)^2 = C1/(1+z1/2) + (100+C2)/(1+z2/2)^2

1.1105 + 98.5364 = 1.1118 + 101.1250/(1+Z2/2)^2

Solving for z2, the 1yr zero rates:

99.6469 = 1.1118 + 101.1250/(1+Z2/2)^2

98.5351 = 101.1250/(1+Z2/2)^2

(1+Z2/2)^2 = 1.02628364

1+Z2/2 = 1.013056583 (Square root)

Z2/2 = 0.013056583

Z2 = 2.6113 Percent

In this case, the 1 year spot rate matches the yield; that isn't always the case.



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Maturity (yrs) Coupon Price 32nds Yield Spot Rate

0.25 na $99.46 2.17 2.17

0.50 na $98.82 2.38 2.38

1.00 2.250 $99.66 99 21/32 2.61 2.6113

1.50 2.250 $99.28 99 9/32 2.76 2.7440

2.00 2.500 $99.15 99 5/32 2.96 2.9448

2.50 2.875 $99.63 99 20/32 3.05 3.0359

3.00 3.000 $99.53 99 17/32 3.19 3.1784

3.50 3.125 $99.64 99 20/32 3.26 3.2497

4.00 3.500 $100.58 100 19/32 3.37 3.3651

4.50 3.375 $99.64 99 20/32 3.49 3.4889

5.00 3.500 $99.77 99 25/32 3.58 3.5835

Table: Calculation of the spot value and yield value based on the previous result.

Fig: Plotting of the regular yield curve (in blue) versus the spot curve.

This above figure represents the spot curve in yellow line that signifies that the spot curve is almost

follow the yield curve slop.

Forward Curve



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The 6mo forward rate in 6 months can be though of as what we could borrow/lend at for 6 months,

6 months from now. By the law of no arbitrage, investing our money now for 1 year or now for

6months, with the next 6mo rate locked in, must result in the same present value. y is the yield to

maturity, z1 is the 6mo spot rate, and f1 is the 6mo forward rate 6months from now.

C1/(1+y/2) + (100+C2)/(1+y/2)^2 = C1/(1+z1/2) + (100+C2)/(1+z1/2)(1+f1/2

1.1105 + 98.5364 = 1.1118 + 101.1250/((1+z1/2)(1+f1/2))

Solving for f1:

99.6469 = 1.1118 + 101.1250/((1+z1/2)(1+f1/2))

98.5351 = 101.1250/((1+2.38/2)(1+f1/2))

98.5351 = 99.9357644 /(1+f1/2)

(1+f1/2) = 1.014214487

f1/2 = 0.014214487

f1 = 2.8429

Maturity (yrs) Coupon Price 32nds Yield Spot Rate 6mo Fwd Rate

0.00 2.17 2.38

0.50 na $98.82 2.38 2.38 2.8429

1.00 2.250 $99.66 99 21/32 2.61 2.6113 3.0209

1.50 2.250 $99.28 99 9/32 2.76 2.7440 3.5997

2.00 2.500 $99.15 99 5/32 2.96 2.9448 3.4176

2.50 2.875 $99.63 99 20/32 3.05 3.0359 3.9537

3.00 3.000 $99.53 99 17/32 3.19 3.1784 3.6984

3.50 3.125 $99.64 99 20/32 3.26 3.2497 4.2473

4.00 3.500 $100.58 100 19/32 3.37 3.3651 4.5875



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4.50 3.375 $99.64 99 20/32 3.49 3.4889 4.5123

5.00 3.500 $99.77 99 25/32 3.58 3.5835

Table: Calculation of the Yield, spot and forward values

Fig: Yield Curve (Blue Line), Spot Curve (Yello Line) and Forward curve for sex months

(in Red color)

B. Review the predictive ability of the yield, spot and forward curves with comprehensive

reference to the relevant academic literature. Discuss the curves that you have estimated in Part

2A with reference to this literature. Does the June 2011 forward curve predict the 6 month spot

rate for December 2011? Comment.

Yield curve analyses the term to maturity for the particular bond given. The measurement of the

differences of the interest rate which also has the different term to maturity are being done in this

yield curve for the given bond rate, face value and discount rate. The maturity effect on the bond is

estimated using the yield curve. (Cox et al, 1993) For example, in case of Australian treasury bills

the yield curve is estimated based on the various debt security and term to the maturity. Mostly it is

found that the yield curve as upward sloping. (Tuckman, B, 2002) This describes that the upward

sloping is basically signifies that the short term to maturity generally estimated as the low interest

rates and on the other hand the longer term to maturity is estimated as the higher interest terms.



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Based on the literature it can be explained that the for maximization of the investment return will

only be happen when the investment will be done for the longer term means higher yields. (M.

Felton, 1994) In this case there is no immediate liquidity requirement and the yield curve shape and

its level will be continuous and constant that means it will not change.

The shape and the level of the yield curve are used to develop the interest rate of forecast with the

use of the mathematical expectations theory model. The expectations theory that is applied for the

yield curve generation explains that the for a longer time the interest rate on the yield curve can be

calculated as the multiplication of the all interest rate of the shorter time intervals that is comprised

for the longer time to maturity. (De Boor, 1978) If the increasement is done to the investment yield

for the longer period then the yield curve shapes like a flat curve this means throughout same rate

for all kind of maturities, if the shorter period has the high interest rate and the longer period have

the low interest rate than the slop will be downward, and if there is upward sloping and as well as

flat sloping combining in a one yield curve then this yield curve is called as humped yield curve.

For the pricing bond generally the spot rate curve is estimated. It is also called spot rate treasury

curve. These spot curves can be constructed from on the run or off the run or combination of both

treasuries. (Hull, 2005) Based on the coupon strips for treasury the spot treasury curve can be

calculated. There number of bond which have the multiple cash flows or say coupon rates at

number of points in the bonds lives. Therefore, it is not the correct evaluation of the maturity and

bonds based on the single interest rate because there are different interest rates based on the

discounted cash flows. Therefore while making the fair bond valuation there is need to have the

good practice to matching the discount to the each payment for the corresponding treasury spot rate

for the present value of the each bond price.

Based on the forward curve, the valuation of time value of money is estimated. This curve

represents the price at which the market is ready to transact the future price. (James, J, 2000) It

explains the forward rate of the price for the bonds or treasury bonds. But still there is one issue as

found in the earlier researches that forward curve doesn’t represent the actual future price. Based on



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the above curve yield, spot and forward curve, it can be explained easily that the yield curve has the

upward slope so in this case the possibility is of having the longer period with higher interest rate

and the shorter period with the low interest rate. (W. H., Flannery, 1992) For the treasury curve

called as spot curve, it can be seen that its slope is almost same as the yield price slope. The

conclusion can be drawn for the spot rate that based on the multiple cash flows and similar as the

yield value the slope of the curve is same. In the last figure, there have been constructed the entire

three yield, spot and forward curve. It can be seen from the figure that the forward is much higher

for the larger term to maturity but also in between it goes down and then up.



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Part 3:

A:

Describe the shape and level of the current Yield Curve in Australian Commonwealth Government

Securities (i.e.: at the time of your dealing sessions – use data gathered from the trading system in

the FMTS, plot the curve and discuss it).

Maturity (yrs) Coupon Price 32nds Yield

1 6.5 $99.46 2.17

2 6.25 $98.82 2.38

3 6.25 $110.48 110 15/32 2.61

5 6 $112.26 112 8/32 2.76

7 5.25 $112.61 112 5/8 2.96

9 5.75 $119.18 119 6/32 3.05

10 5.75 $123.78 123 25/32 3.19

11 5.5 $123.80 123 13/16 3.26

15 4.75 $118.01 118 3.37

Table: Data calculation for the current trading system in the FMTS and the yield and bond price

Fig: Treasury Yields curve for the current trading system in the FMTS

As shown in the figure the yield curve is on the upward side which means the longer term maturity

has the higher interest rate and the shorter term maturity has the lower interest rate. As seen from

the above graph that the maturity for the 15 years and so the coupon rate is higher as 6.00 on an

average for the complete maturity period. In case of the fixed interest fund managers the implication

of this yield curve will lower down the maturity period because for the fixed interest the maturity

period will be lower if the fixed rate is greater than the average of the yield rate otherwise reverse

will be true.



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Based on your view of the yield curve, and other sources, what is your view on Interest Rates in

Australia for the following time horizons?

6 Months – The interest rate in Australia for the six months time horizons is lower.

12 Months – For 12 months time horizon the interest rate in Australia will be higher.

As the curve suggests that for the shorter period the interest rate will be lower and for the longer

period the interest rate will be higher.

B: (4 Marks)

With respect to your trading portfolio:

1. Report on your Portfolio composition in Market Value Terms and Face Value Terms:

(a) At the commencement of trading

At commencement of trading the Face Value is less than the market value which means the

original price is less than the actual price during the investment this means the investment value

is in profit.

(b) After Dealing Session 2

After the dealing of the session 2, the face value is again lower the actual market value, so it shows

that the invested money to the stock market is still in profit.

2 What is the level of interest rate risk in your portfolio, as measured by?

(a) Portfolio Modified Duration at the commencement of trading

The level of interest rate risk at the commencement of the trading is lower but increases soon

after the trading starts.

(b) Portfolio Modified Duration after Dealing Session 2

After the dealing session 2, the level of the interest rate goes increases and after some time it

becomes medium risk for the investment.



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3. How has the interest rate risk profile of your portfolio changed? What are the implications for

your portfolio in the current yield curve environment?

The interest rate of risk profile for the portfolio goes increasing with the maturity time but soon

after some time the level of interest risk goes down and the risk reduces. In the current yield curve

environment the portfolio signifies that the investment return will be higher over the time. As the

yield is on average of 3.50% which means the return will be almost 30 percent higher of the

invested money. So the current yield curve environment is in favour of the investment.

4. Comment on whether you achieved your set objectives with regard to interest rate risk:

If you achieved your objective, what trading actions/strategy contributed to your success?

Yes the set objectives achieved because of the balanced portfolio and using the options of

forwarding rate which shows the yield rate was higher for the given maturity period.

If you did not achieve your objective, what would you do differently?

In case the objectives were not achieved then the investment need to revise based on the forward

rate and should wait for the right time for investment.

Was your trading consistent with the market view developed in Part 2?

Yeah, little bit it seems from the part -2 yield graph that the trading was consistent as the yield

rate was almost similar to the earlier rate except of some places where it was higher than the

previous.

C:

Compare and contrast your performance from one dealing session to another. Discuss what you

could do to improve future dealing sessions. What lessons did you learn and how did you perform

as a team?

In one dealing session it was normally slow but in another dealing session it got improved because

of the higher rate of return of interest. For future dealing session it is needed to more focus on the

longer period of maturity instead of the shorter period of maturity. The longer period always gives



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the fair result than the shorter period. From this I learnt lot of things like how to make the portfolio,

how to invest money, how to buy government bonds and how to perform yield curve, stop curve,

and forward curve based on the coupon rate for the multiple time intervals. Based on overall

conclusion the performance as a team, it was quite satisfactory.



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References:

1. Cox, Raymond A. K., and Daniel E. Vetter. "Money Market Returns and Risk, 1938-

1989." Journal of Midwest Finance 22 (1993): 50-54.

2. M. Felton. "Performance from Riding the Yield Curve, 1980-1992." Journal of Business and

Economic Perspectives 20 (1994): 128-32.

3. De Boor, C.: A Practical Guide to Splines, Springer Verlag (1978).

4. Hull, J.: Options, Futures and Other Derivatives Prentice Hall (2005).

5. James, J., and Webber, N.: Interest Rate Modelling, Wiley (2000).

6. W. H., Flannery, B. P., Teukolsky, S. A., and Vetterling, V. T.: Numerical Recipes in C:

The Art of Scientific Computing, Cambridge University Press (1992).

7. Tuckman, B.: Fixed Income Securities, Wiley (2002).

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