giovedì 16 ottobre 2014

We exploit the Yield to Maturity in order to find the minimum in the bonds prices.

We show today, an efficient method to optimize the input on the ten-year AAA sovereign bonds, in order to obtain an outperformance of the portfolio without then having to rely on risky bonds to achieve the performance targets.
Observe a downhill bond below the parity, does not give us any indication of what are the minimum that could reach. The study of the yield to maturity, compared with the yield of the coupon, allows us to identify input levels historically very effective, both in trading activity and as a medium/long term.


Here, we only use high quality ten-year sovereign bonds; such as AAA, issued in 100 and in an usual market situation. However, these conditions are not always binding, which only allow us to eliminate some of the clauses of volatility as a lowering of the credit rating or a poor liquidity of the bond. In addition, the study was calibrated for this institution and explains the use of AAA bonds.


A bond with a very high rating (for example, an AAA) issued around 100 on the market and at a certain rate, provides us a long series of information and of relative certainties because of high quality; see mainly regular coupon payments already known and the redemption price at maturity, usually equal to 100. These certainties as well as the liquidity of the products, makes bonds attractive and suitable investments for intensive-capitals activities which cannot be committed, for example, in stocks. We are talking about millions of Euros.
The same bond, if it is traded on the market during its life, such as at 98, it obviously offers us an higher Yield to maturity and it is therefore, potentially more interesting at this particular time that it has been issued at a price of 100. However, for example, a price of 98, offers us a partial information which is not enough to evaluate and optimize an eventual investment because the Yield of a bond must be also, and perhaps more importantly, evaluated as a function of the variable time.
So, know that a bond, issued in 100, is equal to the less of the parity in a determined moment, it uniquely tells us that offers a Yield to maturity higher that the Yield of  the coupon, but not so much higher after all. We do not know how far it could go down, in order to optimize the intervention. It could downhill until 97 or 88.
Instead, we try today, to individuate a possible level of support, by reading almost exclusively, the average Yield to maturity of the bond.

Historical Study:

We analyzed 88 historical series of the German Ten-year (Dbr) with maturities ranging from 1996 to 2004. Some of the bonds are therefore, already expired.

Tab 1: Dbr maturity. Coupon: Yield %. Ytm max: historical maximum of the difference between the yield to maturity and the coupon. Ytmc: Ytm max / Coupon: %

Chart 1: example of reading the table:
Take the DBR 6 15/09/2003 (ISIN DE0001134914) and in the second column, we read that the coupon of the bond is equal to 6%. The following column shows that, historically, the average yield to maturity overcomes 1.764 percentage points (Bps) the yield of the coupon, which represents + 29.40%. In fact, the bond’s price joined a quote of 89.10 by the 5th January, 1995 for a yield to maturity of 7.764%. See chart 1.

We report data graphically as above: the highest ratios Ytmc and horizontal the maturities of Dbr. We calculated that the historical average of the values is 25% while we graphically observe, during the last years, some maximum levels comprehended in the area between 40 and 50%  approximately. With regard to the statistical analysis, the 2nd quartile (then the median) is equal to 26.08%, while the 3rd quartile is equal to the 43.09%.


From the data obtained, we observe therefore that, during the last 15 years, some high excursions levels emerge, between the yield of the coupon and its yield to maturity (ytmc), detectable in 25/50%. Obviously, the maxima peaks in the yields to maturity correspond to the minima of the prices.
We try, as a consequence, to exploit the yield to maturity in order to intervene on the bonds, at a very competitive prices.


We use the same bond of our previous example: Dbr 6 09/15/2003.
We look for a bond that has a ration between yield to maturity and yield of the coupon (Ytmc) comprehended between 25% and 50%, because higher levels could be due to a 0-coupon bond or Stressed-bonds and/or not high quality ones, but not only... Historically speaking, it is better to do not utilize a bond that offers a coupon less than 1%.
Once that our Ytmc ratio, will be in the area individuated above, we insert a simple moving average and we intervene in the bond purchase when our Ytmc ratio will pass under the simple moving average. The closing of the operation is relative. In fact, the bond can be held until the maturity because the yield to maturity has certainly been optimized.
Otherwise, the bond could be sold when the ratio will be taken over its simple moving average and under quote of 25% or 50%. This is the assumption that most interests us because it allows us to get a not indifferent over performance  with a simple moving average and in a relatively narrow.
The ratio Ytmc is therefore, calculated in this way: (( yield to maturity max- coupon)/coupon)*100
We look, now, at some examples and some variants, right after.


1° example:

The chart 3 is really clear about:
20th January 1995: Buy bond at 90.19
19th February 1996: Sell Bond at 99.69
Numbers of days: 389
Coupon: 6%
The result of the operation in this period is of +6.48% of the coupon for 13 months to which occurs add +10.53% of augmentation of the bond’s price which takes to the total amount of +17,01%..
For that reason, we bought a ten-year bond with the rating AAA and we kept it for 13 months, gaining +17,01%. This is almost 3 times the yield of a coupon.
Our goal is then, to intervene on safe bonds and to optimize the profitability in order to get high yields in few time. In this way, observing the Ytmc and using a simple moving average, we are able, in many cases, to individuate great intervention’s levels.
Doing so, we have a safe portfolio which offers us an extra yield.

Chart 3: above, in black, we see the bond’s price. Under, in blue, the yield to maturity of the bond, is represented. In the central section, in red, the ratio Ytmc and the average level of 25% underlined in Chart 2, together with a simple moving average, are represented.

2° example:

Bond Dbr 4 07/04/2009 (Isin DE0001135119).

3rd December 1999: Buy Bond at 91.75
16th December 1999: Sell Bond at 91.22
Number of days: 13
Coupon: 4%
Yield of the coupon: +0.14%
Yield of the price: -0.57%
Total Yield of the period: -0.43%

2° operation:
22nd February 2000: Buy Bond at 89.86
11th April 2001: Sell Bond at 94.69
Number of days: 409
Coupon: 4%
Yield of the coupon: +4.54%
Yield of the price: +5.37%
Total Yield of the period: +9.91%
We lost while the first operation, but we could keep the bond for a little more time because, generally, it is difficult to lose money when we buy a bond that offers a yield to maturity of more than 30% to the yield of the coupon, like in this case. A magic formula does not exist, but indeed, some methods that work in most cases, do exist.
In the second operation, we kept the bond for less than 14 months, gaining almost 2.5 times more of the yield of the coupon. We are always talking about a AAA rating bond.

Chart 4: the chart shows the bond Dbr 4 07/04/2009 with intervention signals.

3° example:

We use a bond not yet expired: Dbr 2.25 09/04/2020 (Isin DE0001135416).

29th April 2001: Buy Bond at 92.69
24th November 2011: Sell bon at 102.29
Number of Days: 205
Coupon: 2.25%
Yield of the coupon: +1.28%
Yield of the price: +10.36%
Total Yield of the period: +11.64%

In this case too, we gained 5 times the annual yield of the coupon of the bond, in less than 7 months.

Chart 5: the graphic shows the bond Dbr 2.25 09/04/2020 with intervention signals.


1° variant:

We use an American Tnotes: T 1.625 11/15/22 (Isin US912828TY62)

In some cases, the ratio Ytmc is very high and remains inside levels higher than 50% for a long term. It is also the case of the English ten-year UK TSY 1.75% 2022 (Isin GB00B7L9SL19).
In these occasions, every intersection between the Ytmc downward and its moving average, provides an opportunity to purchase the bond. As we can see in the chart below, the 13th September, 2013, the Ytmc breaks down its moving average for the first time, generating a buy signal and a second time, generating an increment signal in January 13th, 2004.
In both cases, the Ytmc is kept over the 50% and provides purchase and increase signals. The closing, will be verified when the Ytmc will be taken over the moving average, while it will be below 50% (or 25%).

18th September 2013: Buy Bond at 91.30 (Yield to maturity mid = 2.62%)
13th January 2014: Buy Bond at 91.20 (Yield to maturity mid = 2.70%)
Number of days until the 2014 may 15: 237 (1° buy) and 122 ( 2° buy)
Coupon: 1.625%
First buy. +1.07% coupon and +3.18% price: total +4.25%
Second Buy: +0.55% coupon and +3.28% price: total +3.84%

In both cases we bought near the minima in the prices of bonds with yields to maturity much higher than the yield of the coupon. In addition, until May 15th, 2014 the first purchase took advantage of +4.25%, while the second one of +3.84%. This is not bad, considering we are talking about an AAA bond with a coupon of 1.625%...

Chart 6: the chart shows the American ten-year T 1.625 11/15/22 with the signals of Buy and Increase. The Buy Signal should generate itself in few weeks/months.

2° Variant

We use the Finnish ten-year: FINNISH GOV’T RFGB 1 ½ 04/23 (Isin FI4000062625)
In the previous variant we saw that we can make several purchases when the Ytmc ratio is maintained above 50% for a long term. The same technique can be applied in case of permanence above the 25%.
Now, we see how to exploit the sagging downward by the Ytmc ratio of the thresholds of 50% and 25%.
We observe that in mid-September 2013, the Finnish ten-year, with a coupon of 1.50% it is very depreciated until having a yield to maturity of 2.30% (the 10th September 2013), exceeding, therefore, the 50% in the ratio Ytmc. In this occasion we can get a buy signal of the bond in case of return below the 50% and, we can decide if we close a transaction for trading purchases or if we increase the position to be in the medium/long term. In both cases, the result is definitely satisfying.

1° case: closing at 25%
Profit of the coupon at 1,50% for 127 days: +0.53%
Profit of the price: +3.43%
Total amount of the operation: +3.96% for 127 days, while the coupon yields 1.5% for one year.

2°case: increase up to 25% with a counting until the 15th of May 2014. The bond was quoted at 100.57 that day.
First purchase the 12th of September 2013: profit of the coupon at 1.50% for 243 days: +1.02% plus the profit in the price: +7.26%. Total Profit: +8.28%
Second purchase (increase) the 29th of January 2014: Profit of the coupon at 1.50% for 116 days: +0.48% plus the profit in the price: +3.70%. Total Profit +4.18%

In both cases, we got important yields in reduced time, by using a sovereign bond with an AAA rating and the coupon at 1.50%.

Chart 7: the chart shows here above, the price of the Finnish ten-year RFGB 1 172 04/23 and the Ytmc ratio with levels of 25% and of 50%, on below.


The exploitation of the ratio between the yield to maturity and the coupon (Ytmc) included between the 25% and 50% with the use (or not) of a simple moving average, does not allow us to easily individuate the minima in the bonds’ prices. The levels of 25% and 50% have been calculated on the German ten-year and should be reasonably optimized over the investments. However, the 15%25% and 40%/50% areas are generally very adapted for the purpose. See chart. 8.
The intervention on these minima, allows us, in case of trading, to get some very important over performances on the bonds with AAA ratings, in few weeks/months, while, for a medium/long term’s investor, it offers us a valid point of intervention allowing us to pick the bond in a favorable moment of its life, with a yield to maturity definitely higher than the return of a coupon.
With this simple but historically efficient method, an institutional can maintain a bond portfolio, obtaining an extra yield offered by the market. The extra yield has been obtained by optimizing the inputs on AAA bond and not by running greater risks of some speculative instruments such as derivates or non investment grade bonds. Consideration, should be given to preserving the capital invested before we even try to earn. As written above, we are talking about millions of Euros.
We analyzed the German ten-year, but the same methodology can therefore, be applied to the English ten-year ones (Ukt) and to the American Tnotes, as we saw in the variants or on any other Sovereign bond. Obviously, the study works on corporate bonds with lower ratings, too.

Chart 8: we observe the Ytmc Ratio relative to 40 ten-year maturities of the American Tnotes and it immediately results two interesting areas: one up to 40% and the other one up to 20%. For statistics, the ratio’s average is, in this case, 22% while the 3rd quartile is 32%. On the horizontal line, we see the maturities of the bonds.

Translated by Alice Albani.

Best Rgds
Giovanni Maiani