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I am interested in aggregated Amihud ratios measures over bond groups. For a large panel data set with daily bond prices and volumes I have calculated already Amihud ratios per ISIN/day.
Naive aggregation of the Amihud ratios over subgroups of bonds would yield biased results however, as daily returns appear to be increasing in Coupon rates.

The question is: Is there a computational way to immunize differences in coupon rates across bonds, i.e. is there an approach to construct daily zero coupon returns to increase comparability?

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Back when I had lots of free time, I used to publish a series of constant maturity par bond total return indices (http://hungrydummy.com/datacenter/). Because these are "par" bonds, they are immune to coupon effects. I briefly described the computational methodology on that page, which is copied below. The same methodology can be used to create constant maturity zero bond returns.

The Constant Maturity Total Return Indices are constructed using the Gurkaynak, Sack, and Wright’s fitted curves. More specifically, I assume the index rolls into a new par bond at the end of each month. This same bond is then held through the following month, with daily returns marked again with the GSW fitted curves. Note that the returns reported here are higher than the returns of comparable benchmark bond indices (annualized excess return of 1.5% for 10s since 1981). Here are a few reasons: 1) Bonds in my indices typically have higher durations than benchmark issues. For example, if 10-year notes are issued once a year, then 11 months after issuance, the bond in the benchmark index would have only 9.1 years to maturity. In my index, the bonds would have at least 9.9 years to maturity, since they are rolled into new 10-year bonds monthly. 2) Benchmark bonds tend to be rich at issuance, and gradually cheapen as they age, thus reducing their returns, all else equal. Hypothetical bonds created with fitted curves don’t suffer from this issue. It’s debatable whether it’s a good idea to use hypothetical bonds, since an index should ideally reflect actual investable performance. I devised these indices mainly because most bond indices do not have long enough a history and do not provide the kind of granularity I’m interested in. On the other hand, my indices more accurately reflect yield curve dynamics, instead of being plagued by other idiosyncratic factors. Furthermore, it sheds some light on possible return enhancement opportunities. For example, instead of rolling on-the-run issues, buying and holding cheaper off-the-run issues not trading special in the repo market may generate higher returns.

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  • $\begingroup$ Thanks haginile, I believe this comes close to the solution I came up finally. I am constructing a zero coupon yield curve per day using the Svensson model and reconstruct prices for each bond in a second step. $\endgroup$ – Luks Jul 31 '15 at 17:10
  • $\begingroup$ @Lukas, yep that's exactly the right approach! I needed super long time series, so I just used the Fed's for convenience. $\endgroup$ – Helin Jul 31 '15 at 17:30

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