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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

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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!

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)

In exchange for these restrictions, one gets a measure of risk that is strictly monotone with respect to stochastic dominance. Additionally, a paper in 2011 by Homm and Pigorsch (link) established an economic performance measurement similar to the Sharpe Ratio, but one that excels at situations in which returns are not normally distributed (such as the 2008 GFC). In my classes, I did an initial exploration of the relation of returns and AS riskiness and found that the tendency of AS riskiness to rapidly respond to losses does have advantages for risk-conscious investors. See the shape of AS risk vs. Return below:

SP500 Component AS Risk vs Return for 2010

For future investigation, I want to have an R function that calculates AS riskiness, so my prototype is as follows:

-Name: asRisk()
-Input: vector of returns in percent
     -This makes it easy to use the function with quantmod
     -Also more versatile
-Dependencies/Requirements: none
     -One possible way to solve for AS risk is to use an R package with a solver, such as ROI
     -I would rather not have any dependencies, as my need for precision isn't very high
-Precision: 1/1000
-Method: Iterative from 0.0001 to 1000
     -The program will give up at 1000, as the function goes out to infinity as returns approach zero
     -In most cases, our risk scores are much much lower, so any sane situation should have no problem with this
     -If this method is too slow on modern computers (unlikely), I will consider moving to a solver package
-Error Checking: We will check for
     -Negative overall return (return Error)
     -No negative outcomes (return Error)
     -Failed sanity check, AS Score > 1000 (return Warning)
-Output: AS risk score

This will be my first R function other than "Hello, World!", so I am going to try to keep the solution as simple as possible.  Once I have a solid foundation with my current solver, I will attempt to work towards using option chains to counteract the negative overall return error, and potentially to use a solver.  The simple version will be a large improvement over Excel though, with its floating point errors that are a huge source of errors with large numbers of observations.

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).

This nomenclature has obvious implications for computer languages which will generally disallow variable names that begin with numbers. In R, this is also the case, and quantmod will attempt to create a dataframe with the name of the ticker symbol. This problem took a while for me to discover, since quantmod will not give you an error when you try to retrieve the quote. For instance, let me try to retrieve Apple (AAPL):
> getSymbols("AAPL", src = "yahoo")
[1] "AAPL"

I enter the command "getSymbols()" and when R has finished downloading the data, it echos the name of the dataframe created "AAPL".  Let's try HTC (2498.TW) now:
> getSymbols("2498.tw", src = "yahoo")
[1] "2498.TW"

It would appear as though the data has been downloaded correctly, and if you have automated this process, you wouldn't know the problem.  The only way the problem will present is as a frustrating error:
> length(AAPL)
[1] 4536
> length(2498.TW)
Error: unexpected symbol in "length(2498.TW"

The fix for the problem is very simple or very difficult, depending on your situation.  The solution to the problem is to set "auto.assign=FALSE" when calling getSymbols(). This will allow you to assign the data returned to a variable name of your choice. For example:
> HTC.TW <- getSymbols("2498.TW", src = "yahoo", auto.assign=FALSE)

This code will not echo like the previous examples, since you are explicitly naming the variable yourself.  As I mentioned before, the solution is either simple or complex.  If one were running a long script with many equities from different countries, the lack of errors might cause big problems.  Correcting the names on a large scale would likely rely on using regular expressions or a predefined list of alternate ticker symbols combined with the technique listed above.

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:

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#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

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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.

Finally, I graphed the results and regression line for the benefit of my teacher, the results of which can be seen here:

S&P500 vs. Apple, 2009-2011