## Friday, April 15, 2011

### Historical Bond Price and Total Returns from 10y Yield Series

Without access to Barclays or Merrill Bond Indicies to the 1970s or Ned Davis to 1950, studying historical bond returns is very difficult.  Here is a way to derive price and total returns on the 10 year US Treasury back to 1962.  I would like to extend to 1871, but monthly yields from Shiller and Fed are averages of the daily yields and not month-end values.  Applying this method to these month averages does not work.

 From TimelyPortfolio

R code:

require(RQuantLib)
require(quantmod)
require(PerformanceAnalytics)

getSymbols("DGS10",src="FRED") #load US Treasury 10y from Fed Fred

#Fed monthly series of yields is the monthly average of daily yields
#Shiller series also is monthly average
#to calculate returns monthly average does not work
#so we get daily, take monthend with to.monthly
#and unfortunately the series does not go back as far
DGS10<-to.monthly(DGS10)[,4]
DGS10pricereturn<-DGS10  #set this up to hold price returns

DGS10pricereturn[1,1]<-0
colnames(DGS10pricereturn)<-"PriceReturn"
#I know I need to vectorize this but not qualified enough yet
#Please feel free to comment to show me how to do this
for (i in 1:(NROW(DGS10)-1)) {
DGS10pricereturn[i+1,1]<-FixedRateBondPriceByYield(yield=DGS10[i+1,1]/100,issueDate=Sys.Date(),
maturityDate= advance("UnitedStates/GovernmentBond", Sys.Date(), 10, 3),
rates=DGS10[i,1]/100,period=2)[1]/100-1
}

#total return will be the price return + yield/12 for one month
DGS10totalreturn<-DGS10pricereturn+lag(DGS10,k=1)/12/100
colnames(DGS10totalreturn)<-"Total Return"

charts.PerformanceSummary(merge(DGS10pricereturn,DGS10totalreturn),ylog=TRUE,colorset=c("cadetblue","darkolivegreen3"),main="Simulated Returns from US10y Yield")
mtext("Source: Federal Reserve FRED",side=1,adj=0)

#### 6 comments:

1. I know this might sound antithetical to a bond guy, but won't the monthly series get you close enough?

2. Monthly averages smooth and disallow month-to-month decomposition of returns into price and interest. For historical review of drawdown, price return is necessary. I will run it in a post for everyone to see the impact.

3. well I was wrong; see my next post for clarification. Thanks Peter for the very useful comment.

4. hi,
just chanced upon this blog, nice !

Shouldnt you be using geometric returns instead of arithmetic returns in:
#total return will be the price return + yield/12 for one month
DGS10totalreturn<-DGS10pricereturn+lag(DGS10,k=1)/12/100

i.,e the second term should be something like:
((1 + lag(DGS10,k=1)/100)^(1/12) - 1)

5. since there is no reinvestment or geometric compounding I chose arithmetic. I think this is correct.

6. Hello thanks for this great job. I have a very basic question (sorry new) how can run this code? and possibly change it to have European bond or at least to update this to reflect the last 10 yrs?
Thanks a lot!!