The first step is to calculate historical returns of AAA bonds. Bond yields alone are insufficient, so we inevitably have to make some assumptions. Based on the magnitude of the drawdowns reported in the paper, I calculated monthly returns using the following assumptions:
- At the end of each month, we purchase a bond whose yield and coupon rate are equal to the AAA yield at the time. We further assume that the bond matures in 30 years. Since the yield and coupon rates are the same, the purchase price is simply 100.
- At the end of the next month, we sell the bond, whose yield has changed to the new AAA yield at the time. The selling price can be computed easily using the standard price-yield formula (let coupon rate = previous month-end AAA yield, maturity = 29 years 11 months, and yield = current month-end AAA yield).
- Given the starting price and ending price, it's simple algebra to calculate the return of the bond over the month. (Don't forget about the interest that has been accrued over the month!)
- We can repeat this for each month from 1920 through today (i.e., at the end of each month, we sell the old 29-year 11-month bond and buy a new 30-year bond).
Steps 2–3 above can also be approximated using the method outlined in this post.
These returns allow us to compute the drawdowns:
These are crude estimates, but allow you to get a good qualitative read into historical long bond performance. To calculate more precise drawdowns, you'll need properly constructed total return indices – instead of using hypothetical bonds, these indices buy and sell real cash bonds.
I should also mention that the actual drawdown experienced by fixed income investors can vary greatly. Because the average duration of the bond market has not been even remotely close to 30 years (as assumed by the paper), losses incurred by an average investor was not as bad as depicted by the paper. The picture below shows the drawdown of all Treasury notes and bonds over time (weighted by amount outstanding):