Section 2 TFs

# Section 2 TFs - Stat 107 Section #2 February 10, 2012...

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Stat 107 Section #2 February 10, 2012 Logistics • Bambo Sosina,sosina@fas.harvard.edu. Office hours (SC-600): Fri 1-3pm • Course website: my.harvard.edu/k85336 . • All section material will be posted under 'Sections → Bambo's Sections' on the course website: Topics for Section - Expectations and Variances (of discrete RV’s) - Linear Combination of Random Variables - Simple Hypothesis Testing (comparing 2 means (t-test), 2 variances (F-test)) - R - for loops - functions - random sampling from a distribution - yearly returns monte carlo sampling (most likely for Section #3) Practice Problems: 1) What critical value along a standard normal distribution do we use for a 95% confidence interval? What is the 2-sided p-value for a statistic of z = 2.58? What is the 2-sided p-value for a statistic of t = 2.58 with df = 60? Let’s get R to calculate these for us: > #Normal Distribution > z.95=qnorm(0.975) > qnorm(0.975) [1] 1.959964 > 2*(1-pnorm(2.58)) [1] 0.009880032 > 2*(1-pt(2.58, df=60)) [1] 0.01234615 2) An investor is looking to build a portfolio based on 4 different technology stocks: IBM (IBM), Microsoft (MSFT), Cisco (CSCO), and Adobe (ADBE). a) Do you believe a portfolio based on these 4 stocks has potential to be a well-diversified portfolio? Why or why not?

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b) Which of these stocks do you think will have the highest correlation? The lowest? Do you believe any will be negative? Below are some summary stats for these 4 stocks' daily percentage changes since February 1, 2011: > library(quantmod) > tickers = c("IBM", "MSFT", "CSCO", "ADBE") > getSymbols(tickers, from = "2011-02-01", to = "2012-02-01") [1] "IBM" "MSFT" "CSCO" "ADBE" > stocks=list(IBM,MSFT,CSCO,ADBE) > > means=100*apply(cbind(dailyReturn(IBM),dailyReturn(MSFT),dailyReturn(CSCO),dailyReturn( ADBE)),2,mean) > sds=100*apply(cbind(dailyReturn(IBM),dailyReturn(MSFT),dailyReturn(CSCO),dailyReturn(AD BE)),2,sd) > ns=apply(! is.na(cbind(dailyReturn(IBM),dailyReturn(MSFT),dailyReturn(CSCO),dailyReturn(ADBE))),2,
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## This note was uploaded on 02/21/2012 for the course STATS 107 taught by Professor Parzen during the Spring '12 term at Harvard.

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Section 2 TFs - Stat 107 Section #2 February 10, 2012...

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