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We can use extend.data function to extend time series using historical proxy. For example: ‘EEM = extend.data(EEM, VEIEX, scale=T)`

The same procedure can be applied to extend leverage series. For example ProShares Ultra 20+ Year Treasury (UBT) can be extended using properly leveraged iShares 20+ Year Treasury Bond (TLT) series.

Let’s look at few examples:

# Load historical data

tickers = spl('TMF,UBT,TLT')

data = new.env()
getSymbols(tickers, src = 'yahoo', from = '1970-01-01', env = data, auto.assign = T)   

TLTx2 = create.leveraged(data$TLT, leverage=2)    
proxy.test(list(UBT=data$UBT, TLTx2=TLTx2),price.fn=Ad)

plot of chunk plot-2

TLTx2   99%
Mean 22.5% 22.2%
StDev 30.6% 30.1%

The create.leveraged function simply multiplies out the daily series returns by the given leverage factor.

Another example is Direxion Daily 20+ Yr Trsy Bull 3X ETF (TMF); it is based on a different bond index than iShares 20+ Year Treasury Bond (TLT), so it is not a perfect proxy, but will do for our testing purposes.

TLTx3 = create.leveraged(data$TLT, leverage=2)    
proxy.test(list(TMF=data$TMF, TLTx3=TLTx3),price.fn=Ad)

plot of chunk plot-3

TLTx3   100%
Mean 17.2% 22.9%
StDev 31.0% 47.2%

Finally let’s plot the evolution of extended 1x, 2x, 3x leverage treasury bond ETFs.

UBT = extend.data(data$UBT, create.leveraged(data$TLT, leverage=2), scale=T)
TMF = extend.data(data$TMF, create.leveraged(data$TLT, leverage=3), scale=T)    

proxy.test(list(TLT=data$TLT, UBT=UBT, TMF=TMF),price.fn=Ad)

plot of chunk plot-4

TLT   100% 100%
TMF     100%
Mean 8.7% 24.9% 17.4%
StDev 13.8% 41.9% 27.4%

(this report was produced on: 2015-03-24)