Any Fixed Income ppl here? Need idea for my case study

I am now doing a course and was given a case study.

In the case study, I was given a zero coupon yield curve and a theoterical yield curve based on the company’s own model. And the question is how to I trade on the mispricing? Any comments will be appreciated.

Buy the cheapest one with the widest option adjusted spread

Take the capital that is used for the fixed income trade, and trade equities instead. There’s no money in fixed income with yields so compressed.

So, I am assuming the first yield curve is tradeable. In that case, you buy/sell the rates where the market curve is too high/low, based on your theoretical model. Easiest way is to do bullet bonds with the maturity that you want, but obviously, there are many ways.

The question seems kind of vague. For instance, if the first curve is tradeable, why is your theoretical curve not marked to market? Or what pnl should you recognize if the market is not the same as your “theoretical” level? What is the theoretical level based on anyway?

find a bond, and you want to be on the tangent to its curves.

Well if this is just a case study and one question, yeah, just trade the discrepancy on the first curve. You’re company says the 10yr should be yielding 200bps, you see it at 171bps on the first curve. So sell the 10 yr on the first curve, etc. or if it’s the shape of the curve, it’s probably just go long the steepener or flattener type of question.

Thanks all for the comments. Sorry I was vague in the last post.

I was given bond price from yr 0.5 to yr 26. I was able to bootstrap and get the zero coupon yield from yr 0.5 to yr 26.

I was given a modelled yield curve (using 3 factor affine model) but the predicted yield curve give rate for yr 1,2,3,4,5,6,7,8,9,10,15,25.

  1. I read the previous comments and some say trade on the yield curve directly. Is STRIPS the instrument to trade on the yield curve?

  2. I used another approach which is to price each of the bond using the modelled yield curve. However, as coupon is half-annually, I was unable to use the modelled yield curve to calculate the PV of coupon in between each whole year (e.g. 0.5, 1.5, 2.5). Is it okay to use linear interpolation to get the 0.5 year rate?

  3. I was thinking of using cubic spline to approximate the rate in between each whole year. For example, I use 1 yr, 2 yr, 3 yr and 4 yr to approximate the 2.5 yr rate. For 3.5 yr rate, I use 2 yr, 3 yr, 4 yr and 5 yr. How do I approximate 0.5yr, 1.5 yr rate?

  4. Is there any additional things I can do to get better marks for the project?

Thanks all for the comments.

When you mentioned cubic interpolation, i remembered the Fixed income module i did years ago. and although i don’t remember anything from it…there was some talk about a Nelson-Siegel model for fitting yield curves…maybe you can do that?

Thanks Alladin. Found the guide on how to do it in youtube Bionic turtle. Only now I understand why people use Bionic turtle for FRM. I told you I used schweser and passed both exam. But I do not understand anything about piecewise cubic interpolation and Nelson Siegel. But after I saw his video and spreadsheet I was super clear (BTW, I don’t even know it is inside FRM syllabus. Or did he produce it for other purposes?