Modify yield data set to price data set

Several financial data sources I mentioned in my previous post offer yield data series. But yield data series are often unpractical as we want to know how much money we would make if we invest in some bond fund or index. There exists one simple way how to change yield data series into price data series.

Imagine yield data set with monthly granularity and following first few entries:

31. jan. 1926   2,5 %
28. feb. 1926   3,3 %
31. mar. 1926  3,7 %

We would now like to change this yield data set to price data set with desired duration. We can start with price data set entry 1 on 31.1.1926 and then calculate entry for price data set for february 1926 as:

(price entry on january 1926) * (1 + (yield entry on january 1926) / 12 + [ (yield entry on january 1926)-(yield entry on february 1926) ] * (index duration) )

So we could calculate price index for february 1926 as interest gain for one month and gain or loss caused by change in interest rates multipled by our index duration. We could imagine that yields from example are for 10 year interest rates (bond index will then have duration around 7). Then we would calculate our price data set entry as:

1 * (1 + 2,5%/12 + (2.5% - 3,3%)*7)  = 0.946

It is very handy to have price data series as we could then use them as a proxy for bond funds in our money management and portfolio management calculations.