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hw12 - ORIE 4630 D Ruppert Homework#12 Friday Note Students...

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ORIE 4630 — D. Ruppert Homework #12 — Friday, Nov 19, 2010 Note: Students are required to work independently on homework. On Black Monday the return on the S&P 500 was - 22.8%. Ouch! This homework assignment attempts to answer the question “what was the conditional probability of a return this small or smaller on Black Monday?” “Conditional” means given the information available the previous trading day. Run the following R code: library(Ecdat) library(fGarch) data(SP500,package="Ecdat") returnBlMon = SP500$r500[1805] x = SP500$r500[(1804-2*253+1):1804] plot(x,ylim=c(-.23,.04)) points(507,returnBlMon,col="red",pch="*",cex=2) results = garchFit(~arma(1,0)+garch(1,1),data=x,cond.dist="std") dfhat = as.numeric([email protected]$par[6]) forecast = predict(results,n.ahead=1) The S&P500 returns are in the dataset SP500 in the Ecdat package. The returns are the variable r500 . (This is the only variable in this dataset.) Black Monday is the 1805th return in this dataset. This code fits an AR(1)/GARCH(1,1) model to the last two years of data before Black Monday, assuming 253 trading days/year. The conditional distribution
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