My Finance

Introduction. We combine the old analysis of four bond rates and six spreads (with extended and updated data, using autoregression and annual volatility , abbreviated later as VAP) with our new tool, the Yeo-Johnson transform (abbreviated later as YJX). We wish to answer whether switch to IID Gaussian innovations can be done using YJX not VAP.

Data. We take augmented December annual average rate data, all available in Github repository. All data is taken from the usual website, Federal Reserve Economic Data. These are:

• Short-term Treasury rates, 1920-now
• Long-term Treasury rates, 1925-now (from 1960 this corresponds to 10-year Treasury rates)
• Moody’s AAA and BAA corporate bond rates, 1919-now

The data series which we analyze are:

• ln(BAA), ln(AAA), ln(Long)
• BAA-AAA, BAA-Long, AAA-Long
• BAA-Short, AAA-Short, Long-Short
• ln(BAA) – ln(AAA), ln(BAA) – ln(Long), ln(AAA) – ln(Long)
• ln(BAA-AAA), ln(BAA-Long)
• ln(ln(BAA) – ln(AAA)), ln(ln(BAA) – ln(Long))

Analysis. We take data which is either rate or spread, with or without logarithms.

1. We run autoregression
2. We test and using Ljung-Box tests for 5 or 10 lags, and we accept IID only if all four tests give us value greater than 5%.
3. We apply the Shapiro-Wilk and Jarque-Bera tests for and we accept Gaussianity only when both tests give us value greater than 5%.
4. We divide and apply Steps 2-3 again.
5. We apply the Yeo-Johnson transform to and fit the autoregression
6. We test much like we tested in Steps 2-3.
7. We divide and apply Steps 2-3 again.

Results: Unfortunately, success in making these IID Gaussian is achieved using YJX only for spreads BAA-AAA, BAA-Long and some combinations of logarithms. But not for the rates themselves. Thus we cannot model bond markets without VAP.