Archives for the month of: February, 2012

The other week, I posted a simple algorithm to figure out Aumann-Serrano riskiness. The algorithm is slow and not very inventive, so I have been brainstorming all week how to improve it.

Convergence for the calculation of A-S Riskiness for weekly AAPL returns

Since we know exactly the value we are trying to reach and the parameters of the output, I figured we could converge on the solution from both sides and arrive at the solution much more quickly.

Thus, I redesigned the algorithm to bounce back and forth between max and min values, dividing by half for each iteration. Here is the source code for my redesigned version of asRisk(). As always, feed it a vector of possible returns. Read the rest of this entry »

Recently, reading an article by Megan McArdle about income inequality, she speculated about the idea that the share of income of the 1% gets worse during a recession. She posted a graph:

I wasn't a fan of the graph. The ticks distracted from the data being presented, and recessions were not highlighted on the graph, as they are on graphs from places like FRED. Fortunately the data from the graph is available and we can make a run of it using R and ggplot. Read the rest of this entry »

I completed a preliminary function to calculate Aumann-Serrano riskiness in R

 1 2 3 4 5 6 7 8 9 10 11 12 13  asRisk <- function(x){ if (mean(x)<0|min(x)>=0){ return(0) #If expected value is < 0 or there are no negatives, return 0 } else { asNumber <- 0.00001 total <- 2 while (total > 1){ total <- sum((1/length(x))*exp(-x/asNumber)) asNumber <- asNumber + .00001 } return(sprintf("%.5f",asNumber)) } }

To use this function, input a vector of returns. If AS risk cannot be calculated, the function will return "0". If the gambles can be used, it will calculate AS riskiness to 5 decimal points. If more or less are desired, you can change

Generally, to use this, I would recommend using one of the functions in quantmod such as weeklyReturn() or dailyReturn(). An example of this would be

?View Code RSPLUS
 1  asRisk(dailyReturn(AAPL['2010']))

This example will return the AS risk of AAPL stock in 2010. Quantmod uses the TTR package which allows a lot of quick and powerful date selection.

In the future I will add errors/warnings, and maybe make precision adjustable or switch to a solver package. I also need to revise the function to meet a few more of my design parameters. This seems to be a good start and perfect for my research project next semester though!

Currently, I am need of a function that solves for Aumann-Serrano riskiness. AS riskiness is a favorite academic paper of mine, and it establishes a new measure of riskiness developed in response to the financial crisis.

AS Riskiness supposes for each gamble $g$, there exists a unique positive number $R(g)$ that satisfies ${\rm{E}}{e^{ - g/R(g)}} = 1$

There are a few conditions though:

• Gambles must have a positive expected value (you can't use it at Vegas)
• Gambles must include one negative outcome (you must have skin in the game)

When doing research in foreign equities, I always use quantmod and R to get quotes. Google does not usually support CSV downloads of foreign quotes, but in most every case, Yahoo does. The "getSymbols()" function in quantmod is fully equipped for this, except for one crucial problem: foreign exchanges often use numbers rather than alphabetical identifiers for ticker symbols, especially in Asia. Examples of this are HTC in Taiwan(2498.TW), NCSoft in Korea (036570.KS), and Ping An in Hong Kong (2318.HK). Read the rest of this entry »

Recently, in my financial statements analysis class, I had to perform a valuation of Apple Inc. with a number of different valuation methods.  One of the things that made valuation simpler is the lack of long-term debt on Apple's balance sheet.  This simple fact means that Apple's WACC is equal to the cost of equity.

To find the cost of equity, I use CAPM, which states

$E(R_i) = R_f + \beta_{i}(E(R_m) - R_f)\,$

where $E(R_i)$ is the expected return on capital, after accounting for the market risk premium.  To find the component pieces  $R_f$,   $R_m$, and $\beta_{i}$, I will use R with the quantmod package, and I will also use the PerformanceAnalytics Package, although I will show you how to avoid using it if you choose.

The sourcecode for the project:

 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37  #Packages required require(PerformanceAnalytics) require(quantmod) require(car)   #Here we get the symbols for the SP500 (GSPC), AAPL, and 5yr Treasuries (GS5) getSymbols("^GSPC", src = "yahoo", from = as.Date("2008-01-01"), to = as.Date("2011-12-31")) getSymbols("AAPL", src = "yahoo", from = as.Date("2009-01-01"), to = as.Date("2011-12-31")) getSymbols("GS5", src = "FRED", from = as.Date("2008-12-01"), to = as.Date("2011-12-31"))   #Market risk R_m is the arithmetic mean of SP500 from 2009 through 2011 #Riskfree rate is arithmetic mean of 5yr treasuries marketRisk<- mean(yearlyReturn(GSPC['2009::2011'])) riskFree <- mean(GS5['2009::2011'])   #My professor advised us to use weekly returns taken on wednesday #so I take a subset of wednesdays and use the quantmod function #weeklyReturn() AAPL.weekly <- subset(AAPL,weekdays(time(AAPL))=='Wednesday') AAPL.weekly <- weeklyReturn(AAPL['2009::2011']) GSPC.weekly <- subset(GSPC,weekdays(time(GSPC))=='Wednesday') GSPC.weekly <- weeklyReturn(GSPC['2009::2011'])   #Here I use PerformanceAnalytics functions for alpha+beta #Then we calculate Cost of equity using our calculated figures AAPL.beta <- CAPM.beta(AAPL.weekly,GSPC.weekly) AAPL.alpha <- CAPM.alpha(AAPL.weekly,GSPC.weekly) AAPL.expectedReturn <- riskFree + AAPL.beta * (marketRisk-riskFree)   #For my graph, I want to show R^2, so we get it from the #lm object AAPL.reg AAPL.reg<-lm(AAPL.weekly~GSPC.weekly) AAPL.rsquared<-summary(AAPL.reg)$r.squared #Lastly, we graph the returns and fit line, along with info scatterplot(100*as.vector(GSPC.weekly),100*as.vector(AAPL.weekly), smooth=FALSE, main='Apple Inc. vs. S&P 500 2009-2011',xlab='S&P500 Returns', ylab='Apple Returns',boxplots=FALSE) text(5,-10,paste('y = ',signif(AAPL.alpha,digits=4),' + ',signif(AAPL.beta,digits=5),'x \n R^2 = ',signif(AAPL.rsquared,digits=6),'\nn=',length(as.vector(AAPL.weekly)),sep=''),font=2) The code is commented, but I will make some additional comments on specific sections to explain the process for those unsure. I apologize for my unstandardized variable names as well! First of all, I use the getQuotes() function, which has a few sources. In this example, I use Yahoo data for equity data and FRED for information on 5yr Treasuries. For reference, the ticker for retrieving the SP500 on Yahoo is "^GSPC", and the FRED code for 5yr treasuries is "GS5". Other symbols should be self explanatory. Next is the issue of regression parameters. To find alpha and beta, I use the capm functions of PerformanceAnalytics, but to find $R^2$ I read it out of the the regression object using ?View Code RSPLUS  1 2  AAPL.reg <- lm(AAPL.weekly~GSPC.weekly) AAPL.rsquared <- summary(AAPL.reg)$r.squared
It is possible to do this with beta and alpha, however, I did not do this because I did not originally did not start out to find $R^2$, and turned to PerformanceAnalytics out of convenience.