I'm recently reading a research paper on the yield curve by Salomon brothers and in it it states that when the forward curve is above the par yield curve, it is seen as cheaper. If for example, the years 9-12 of the forward rate curve lie above the par yield curve with the forward 12 year rate above the 9 year rate as well, it is recommended to buy the 12 year bond while selling the 9 year bond.

Unfortunately, I am unable to accurately grasp the concept behind this in relation to the par yield curve. Please help! Thank you!


First, it's not true that a market sector is cheap whenever the forward curve lies above the par curve. In fact, whenever the yield curve is upward sloping, the forward curve will always lie above the par curve. Conversely, when the yield curve is downward sloping, forwards will always lie beneath the par curve. In the example you quoted, Ilmanen chose a day on which the par curve is virtually flat to make a very specific point: forwards can amplify small misplacing.

To understand the rich/cheap signals, let's think through the shape of the yield curve first: the forward curve Ilmanen provided (we'll call it "Curve A") is not particularly smooth. But it can be argued that a sensible forward curve SHOULD be very smooth; after all, market participants can't possible have very differing views regarding short-term interest rate 10-years from today vs 11-years from today. So imagine that there is a "fair value" version of the forward curve that's super smooth (we'll call it "Curve B").

Now let's price bonds with the two curves. Because the forward rates on curve A (the wavy one) in the 12-year sector are particularly high, bond cash flows, when discounted with these high forward rates, will result in lower prices. By contrast, the forward rates on the fair value curve B will be much lower – because of the smoothness constraint, the curve can't swing up like that. Accordingly, the fair value of 12-year bonds, when priced using these lower forward interest rates, will be higher. This is why the 12-year sector can be perceived as cheaper than fair value.

In practice, it's probably easier to build a smooth forward curve and calculate spreads relative to this smooth curve, instead of depending on a wavy forward curve to detect rich/cheap signals.

  • $\begingroup$ Thank you for your excellent insight! Can't upvote you as I don't have 15 rep but I truly appreciate your comment. Cheers! $\endgroup$ – Timothy Ng Feb 27 '15 at 5:44
  • $\begingroup$ Hi sorry I've a follow up question. In the same paper on page 5 it states that selling a unit of the 2 year and buying a duration weighted 10y will produce negative carry. I don't quite understand this as doesnt the 10y provide higher yield returns compared to the 2y? $\endgroup$ – Timothy Ng Mar 6 '15 at 7:56
  • $\begingroup$ @TimothyNg 2-year note DV01 today is 1.96, while 10-year is 8.88. So for each unit of 10-year note you buy, you have to sell 4.53 units of the 2-year note. In yield terms, 2-year note carry over 3-months is 6.8bp, 10-year note carry over 3-month is 5.7bp, so -1.1bp net. But it gets worse, 2-year roll down over 3-months is 10.5bp, and 10-year roll down over 3-months is 2.3bp, -8.2bp net. Total roll and carry over three months for a 2s/10s flattener is therefore -9.3bp. $\endgroup$ – Helin Mar 6 '15 at 16:59
  • $\begingroup$ Thank you once again haginile. Excellent and easy to understand comments! Sorry i dont have any way to upvote your comment $\endgroup$ – Timothy Ng Mar 10 '15 at 5:49
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    $\begingroup$ @TimothyNg Extremely practical! At the end of the day, trading the yield curve boils down to understanding what's priced into the curve (which these seven papers are all about) and how your views differ. I've known people who short sell bonds just because they believe yields will rise. You'll never make this kind of mistake after reading these papers -- upward sloping forward curves already imply higher yields, and you only go short if you believe bonds will underperform forwards. All of these most important lessons are fully covered in these papers. $\endgroup$ – Helin Mar 11 '15 at 4:34

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