Deutsche bank: Finding relative value trades

Aaron Cheong, Ivan Wu, Venkata Ghanta, Xueqi Zeng

W. P. Carey School of Business

Yield Curve: We have used the data points given in Exhibit 1 (Coupon rate, price and maturity date) to find out

the yield to maturity for all the securities. Taking the current date as 15-Aug-2003 we have calculated

the remaining maturity for all the securities in half yearly terms. After that we have used the YEILD

function in Excel to calculate the appropriate annual-yield to maturity rate for each of the treasury

securities.

The syntax of the function is: YIELD( settlement, maturity, rate, pr, redemption, frequency)

Settlement - The settlement date of the security (i.e. the date that the coupon is purchased).

Maturity - The maturity date of the security (i.e. the date that the coupon expires).

Rate - The security's annual coupon rate.

Pr - The security's price per $100 face value.

Redemption - The security's redemption value per $100 face value.

Frequency - The number of coupon payments per year. This must be one of the following:

o 1 - Annually

o 2 - Semi-Annually (As treasury securities pay interest semi-annually)

o 4 - Quarterly

For the security that matures in 6 months, we got yield as 0.882%, similarly for the security that matures

in 12 months, we got yield as 1.191% and so on.

Then we calculated the respective annualized spot rates / zero coupon yields by equating the discounted

cash flows to the price of security using different discount rates.

For example, for obtaining the zero coupon yield for 1-year treasury security we have used the

following approach:

($2.125/2)/(1+0.00882/2)1 + $102.125.0/(1+z2/2)2 = $100.9254, then we have z2 =1.193%.

Using this 0.5 year and 1 year zero coupon yield, we have obtained the zero coupon yield for 1.5-

year security using the same principles (i.e. sum of the cash flows discounted at the respective discount

rates should equal to the current price of the bond). The price of remaining securities is calculated in a

similar manner.

8/15/2003Maturity Rate (%) Price Years YTM Zero Coupon Yield (%)

2/15/2004 3.000% 101.05 0.5 0.882% 0.882 8/15/2004 2.125% 100.93 1 1.191% 1.193 2/15/2005 1.500% 99.89 1.5 1.572% 1.575 8/15/2005 6.500% 109.09 2 1.848% 1.873 2/15/2006 5.625% 108.44 2.5 2.141% 2.174 8/15/2006 2.375% 99.78 3 2.450% 2.471 2/15/2007 6.250% 111.72 3.5 2.717% 2.790 8/15/2007 3.250% 101.08 4 2.961% 3.008 2/15/2008 3.000% 99.17 4.5 3.200% 3.254 8/15/2008 3.250% 99.27 5 3.410% 3.480 2/15/2009 5.500% 109.77 5.5 3.530% 3.655 8/15/2009 6.000% 112.15 6 3.723% 3.882 2/15/2010 6.500% 114.91 6.5 3.883% 4.075 8/15/2010 5.750% 110.39 7 4.032% 4.220 2/15/2011 5.000% 105.29 7.5 4.171% 4.352 8/15/2011 5.000% 104.76 8 4.291% 4.487 2/15/2012 4.875% 103.44 8.5 4.386% 4.588 8/15/2012 4.375% 99.28 9 4.473% 4.664 2/15/2013 3.875% 95.03 9.5 4.525% 4.696 8/15/2013 4.250% 97.77 10 4.530% 4.711 2/15/2014 13.250% 174.33 10.5 4.355% 4.736 8/15/2014 12.500% 168.94 11 4.490% 4.928 2/15/2015 11.250% 157.06 11.5 4.753% 5.329 8/15/2015 10.625% 152.42 12 4.821% 5.383 2/15/2016 9.250% 140.01 12.5 4.925% 5.462 8/15/2016 7.500% 123.30 13 5.035% 5.520 2/15/2017 8.750% 136.06 13.5 5.036% 5.574 8/15/2017 8.875% 137.50 14 5.095% 5.663 2/15/2018 9.125% 140.79 14.5 5.108% 5.674 8/15/2018 9.000% 139.91 15 5.149% 5.717 2/15/2019 8.875% 138.74 15.5 5.203% 5.790 8/15/2019 8.125% 130.72 16 5.261% 5.830 2/15/2020 8.500% 135.29 16.5 5.271% 5.850 8/15/2020 8.750% 138.35 17 5.300% 5.902 2/15/2021 7.875% 128.50 17.5 5.347% 5.916 8/15/2021 8.125% 131.73 18 5.356% 5.930 2/15/2022 8.000% 130.47 18.5 5.379% 5.949 8/15/2022 7.250% 121.58 19 5.417% 5.956 2/15/2023 7.125% 120.17 19.5 5.434% 5.966 8/15/2023 6.250% 109.45 20 5.467% 5.951 2/15/2024 7.500% 125.46 20.5 5.427% 5.940 8/15/2024 7.500% 125.45 21 5.451% 5.979 2/15/2025 7.625% 127.15 21.5 5.463% 6.002 8/15/2025 6.875% 117.55 22 5.491% 5.996 2/15/2026 6.000% 106.36 22.5 5.503% 5.946 8/15/2026 6.750% 116.20 23 5.500% 5.982 2/15/2027 6.625% 114.71 23.5 5.502% 5.965 8/15/2027 6.375% 111.40 24 5.513% 5.960 2/15/2028 6.125% 108.04 24.5 5.522% 5.956 8/15/2028 5.500% 99.63 25 5.527% 5.913 2/15/2029 5.250% 96.29 25.5 5.523% 5.878 8/15/2029 6.125% 108.41 26 5.513% 5.905

Using the zero coupon yields calculated we have plotted the yield curve using various maturities and

their respective zero coupon yields. The yield curve is as shown below:

0 5 10 15 20 25 300.0

1.0

2.0

3.0

4.0

5.0

6.0

7.0

Yield Curve (Zero Coupon Yield)

Years

The yield curve is mostly normal with a slight inversion at the end after 24 years and a minor flat/hump

in the 8-10 year range.

Finding Relative Value Trades:

After we have calculate zero coupon yield for all the securities, we compared the zero coupon yields

with the Deutsche bank yields. If Deutsche bank yields were higher than zero coupon yields, then the

bonds are cheap in Deutsche bank’s perspective and we should buy them as the expected yield i.e. the

return is more. If Deutsche bank yields are lower than zero coupon yields then the bonds are rich in

Deutsche bank’s perspective. So the security is expensive and we shouldn’t buy that security. In ideal

case Deutsche bank should short such bonds based on their belief, but it is very risky to short bonds

based on liquidity and a host of other reasons. We should neither buy nor sell these rich bonds.

After comparing all the 13 securities, we have identified 3 securities to be cheap, 8 securities to be rich

and 2 securities to be fairly valued from Deutsche bank. But of the securities that have some mispricing,

some of the securities offer higher profit potential compared to the others. In the cheap basket of

securities 1-year and 25-year treasury offers the highest profit potential at 5.1 and 1.8 bps. Some of the

remaining cheap category securities have very low mispricing, that the effective cost of trading will

neutralize the mispricing.

8/15/2003Maturity Rate (%) Price Years YTM Zero Coupon Yield (%) DB Rates Delta (Bps) Recommendation

2/15/2004 3.000% 101.05 0.5 0.882% 0.882 NA8/15/2004 2.125% 100.93 1 1.191% 1.193 1.244% 5.13 Cheap2/15/2005 1.500% 99.89 1.5 1.572% 1.575 NA8/15/2005 6.500% 109.09 2 1.848% 1.873 1.873% N2/15/2006 5.625% 108.44 2.5 2.141% 2.174 NA8/15/2006 2.375% 99.78 3 2.450% 2.471 2.411% 6.01 Rich2/15/2007 6.250% 111.72 3.5 2.717% 2.790 NA8/15/2007 3.250% 101.08 4 2.961% 3.008 2.967% 4.19 Rich2/15/2008 3.000% 99.17 4.5 3.200% 3.254 NA8/15/2008 3.250% 99.27 5 3.410% 3.480 3.445% 3.45 Rich2/15/2009 5.500% 109.77 5.5 3.530% 3.655 NA8/15/2009 6.000% 112.15 6 3.723% 3.882 3.856% 2.60 Rich2/15/2010 6.500% 114.91 6.5 3.883% 4.075 NA8/15/2010 5.750% 110.39 7 4.032% 4.220 4.200% 2.07 Rich2/15/2011 5.000% 105.29 7.5 4.171% 4.352 NA8/15/2011 5.000% 104.76 8 4.291% 4.487 4.468% 1.88 Rich2/15/2012 4.875% 103.44 8.5 4.386% 4.588 NA8/15/2012 4.375% 99.28 9 4.473% 4.664 4.653% 1.12 Rich2/15/2013 3.875% 95.03 9.5 4.525% 4.696 NA8/15/2013 4.250% 97.77 10 4.530% 4.711 4.711% N2/15/2014 13.250% 174.33 10.5 4.355% 4.736 NA8/15/2014 12.500% 168.94 11 4.490% 4.928 NA2/15/2015 11.250% 157.06 11.5 4.753% 5.329 NA8/15/2015 10.625% 152.42 12 4.821% 5.383 NA2/15/2016 9.250% 140.01 12.5 4.925% 5.462 NA8/15/2016 7.500% 123.30 13 5.035% 5.520 NA2/15/2017 8.750% 136.06 13.5 5.036% 5.574 NA8/15/2017 8.875% 137.50 14 5.095% 5.663 NA2/15/2018 9.125% 140.79 14.5 5.108% 5.674 NA8/15/2018 9.000% 139.91 15 5.149% 5.717 5.716% 0.07 Rich2/15/2019 8.875% 138.74 15.5 5.203% 5.790 NA8/15/2019 8.125% 130.72 16 5.261% 5.830 NA2/15/2020 8.500% 135.29 16.5 5.271% 5.850 NA8/15/2020 8.750% 138.35 17 5.300% 5.902 NA2/15/2021 7.875% 128.50 17.5 5.347% 5.916 NA8/15/2021 8.125% 131.73 18 5.356% 5.930 NA2/15/2022 8.000% 130.47 18.5 5.379% 5.949 NA8/15/2022 7.250% 121.58 19 5.417% 5.956 NA2/15/2023 7.125% 120.17 19.5 5.434% 5.966 NA8/15/2023 6.250% 109.45 20 5.467% 5.951 5.952% 0.04 Cheap2/15/2024 7.500% 125.46 20.5 5.427% 5.940 NA8/15/2024 7.500% 125.45 21 5.451% 5.979 NA2/15/2025 7.625% 127.15 21.5 5.463% 6.002 NA8/15/2025 6.875% 117.55 22 5.491% 5.996 NA2/15/2026 6.000% 106.36 22.5 5.503% 5.946 NA8/15/2026 6.750% 116.20 23 5.500% 5.982 NA2/15/2027 6.625% 114.71 23.5 5.502% 5.965 NA8/15/2027 6.375% 111.40 24 5.513% 5.960 NA2/15/2028 6.125% 108.04 24.5 5.522% 5.956 NA8/15/2028 5.500% 99.63 25 5.527% 5.913 5.932% 1.87 Cheap2/15/2029 5.250% 96.29 25.5 5.523% 5.878 NA8/15/2029 6.125% 108.41 26 5.513% 5.905 NA