## Risk, Return and Analyst Ratings

Today I want to discuss a connection between Risk, Return and Analyst Ratings. Let’s start with defining our universe of stocks : 30 stocks from Dow Jones Industrial Average (^DJI) index. For each stock I will compute the number of Upgrades and Downgrades, Risk, and Return in 2010:2011. I will run a linear regression and compute correlation between the number of Upgrades and Downgrades and Risk and Return.

Let’s implement this plan using R and Systematic Investor Toolbox.

First, let’s load Systematic Investor Toolbox and quantmod package

# load Systematic Investor Toolbox setInternet2(TRUE) source(gzcon(url('https://github.com/systematicinvestor/SIT/raw/master/sit.gz', 'rb'))) load.packages('quantmod,car')

I will get the list of stocks in Dow Jones Industrial Average (^DJI) index from Yahoo Finance:

# download Dow Jones Components url = 'http://finance.yahoo.com/q/cp?s=^DJI+Components' txt = join(readLines(url)) # extract table from this page temp = extract.table.from.webpage(txt, 'Symbol', hasHeader = T) # Symbols Symbols = temp[, 'Symbol']

I will get the Upgrades & Downgrades History for each stock from Yahoo Finance:

# Matrix with number of Upgrades/Downgrades in 2010:2011 up.down.stats = matrix( NA, nrow = len(Symbols), ncol = 3 ) rownames(up.down.stats) = Symbols colnames(up.down.stats) = spl('N,Return,Risk') # Get Upgrade/Downgrade statistics and compute Risk and Return for each symbol for( Symbol in Symbols ) { cat('Downloading', Symbol, '\n') # download Upgrade/Downgrade table url = paste('http://finance.yahoo.com/q/ud?s=', Symbol, sep = '') txt = join(readLines(url)) # extract table from this page temp = extract.table.from.webpage(txt, 'Research Firm', hasHeader = T) # find number of Upgrades/Downgrades in 2010:2011 event.year = format(as.Date(temp[, 'Date'], '%d-%b-%y'), '%Y') up.down.stats[Symbol, 'N'] = sum(event.year == '2010' | event.year == '2011') # download price history from Yahoo data = getSymbols(Symbol, from = '1980-01-01', auto.assign = FALSE) returns = ROC(Cl(data['2010::2011']), type = 'discrete') returns = na.omit(returns) # compute basic measures of Return and Risk up.down.stats[Symbol, 'Return'] = 252 * mean(returns) up.down.stats[Symbol, 'Risk'] = sqrt(252) * sd(returns) }

Let’s have a look at the data:

# sort up.down.stats by number of events up.down.stats = up.down.stats[ order(up.down.stats[,'N']), , drop = FALSE] up.down.stats[, spl('Return,Risk')] = round(100 * up.down.stats[, spl('Return,Risk')], 1) # plot table plot.table(up.down.stats) # barplot of Number of Upgrades & Downgrades in 2010:2011 par(mar = c(5,4,2,1), cex = 0.8) barplot( up.down.stats[, 'N'], xlab = 'Symbols', ylab = 'Number of Upgrades & Downgrades in 2010:2011', main = 'Upgrades & Downgrades in 2010:2011 from Yahoo Finance', names.arg = rownames(up.down.stats), las = 2 )

Let’s run a linear regression and compute correlation between the number of Upgrades and Downgrades and Risk and Return:

# run linear regression and compute correlation between number of events and Returns / Risk for( measure in spl('Risk,Return') ) { x = up.down.stats[, 'N'] y = up.down.stats[, measure] # linear regression fit = lm(y ~ x) print(summary(fit)) par(mar = c(5,4,2,1)) plot(x, y, xlab = 'Number of of Upgrades & Downgrades', ylab = measure, main = paste(plota.format(100 * cor(x,y), 0, '', '%') , 'correlation between', measure, 'and Number of Events')) grid() text(x, y, rownames(up.down.stats), col = 'blue', adj = c(1,1), cex = 0.8) abline(coef = coef(fit), lty=2) # compute ellipsoid at 50% confidence level d = dataEllipse(x, y, levels = c(0.5), draw = FALSE) lines(d, col='red', lty=3) }

Coefficients: Estimate Std. Error t value Pr(>|t|) (Intercept) 20.1766 2.3879 8.449 3.45e-09 *** x 0.6589 0.3022 2.180 0.0378 * --- Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1 Multiple R-squared: 0.1451, Adjusted R-squared: 0.1146 F-statistic: 4.753 on 1 and 28 DF, p-value: 0.0378

There is a positive correlation between the number of Upgrades & Downgrades and Risk. The beta coefficient in linear regression is positive and significant at 5% confidence.

Coefficients: Estimate Std. Error t value Pr(>|t|) (Intercept) 14.5098 4.5533 3.187 0.00352 ** x -1.6238 0.5763 -2.818 0.00877 ** --- Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1 Multiple R-squared: 0.2209, Adjusted R-squared: 0.1931 F-statistic: 7.94 on 1 and 28 DF, p-value: 0.008769

There is a negative correlation between the number of Upgrades & Downgrades and Returns. The beta coefficient in linear regression is negative and significant at 1% confidence.

One could conclude from these observations that as the number of Upgrades & Downgrades increases the Risk goes up and Return goes down in 2010:2011 period. However, I see a few problems with this analysis:

- we examined all stocks in the same way; yet companies from different sectors might have naturally occurring different risk/return characteristics
- we treated all events in the same way; yet Upgrade/Downgrade/Initiated actions may have different influences on company’s stock price

Please tell me what else do you think is wrong with my analysis.