R Commander Plug-in for Risk Demonstration

Description

R Commander plug-in to demonstrate various actuarial and financial risks. It includes valuation of bonds and stocks, portfolio optimization, classical ruin theory, demography and epidemic.

Details

Author(s)

Arto Luoma

Maintainer: Arto Luoma <arto.luoma@wippies.com>

Internal RiskDemo objects

Description

Internal RiskDemo objects.

Details

These are not to be called by the user.

Drawing forward and yield curves

Description

This function draws forward and yields curves, for AAA-rated central governement bonds and/or all central governement bonds.

Usage

bondCurve(date1, date2 = NULL, yield = TRUE, forward = TRUE, 
  AAA = TRUE, all = TRUE, params)

Arguments

Value

No value. Only a figure is produced.

Author(s)

Arto Luoma

References

https://bit.ly/2zfs0G8

Examples

data(params)
bondCurve(as.Date("2004-09-06"),params=params)

Bond price as a function of interest rate.

Description

This function plots the bond price as a function of interest rate. It also shows, using dotted lines, the yield to maturity rate corresponding to the face value, and the flat price corresponding to the yield to maturity.

Usage

bondFigure(buyDate, matDate, rateCoupon, yieldToMat = NULL, 
           bondPr = NULL, nPay)

Arguments

Details

either yieldToMat or bondPr should be given as input.

Value

This function only plots a figure.

Author(s)

Arto Luoma <arto.luoma@wippies.com>

References

Bodie, Kane, and Marcus (2014) Investments, 10th Global Edition, McGraw-Hill Education, (see Section 14.2 Bond Pricing).

See Also

bondPrice, solveYield

Examples

bondFigure("2012-7-31","2018-7-31",rateCoupon=0.0225,yieldToMat=0.0079,
           nPay=2)
bondFigure("2012-7-31","2018-7-31",rateCoupon=0.0225,bondPr=90,nPay=2)

Computing bond prices

Description

This function computes the bond price, given the yield to maturity.

Usage

bondPrice(buyDate, matDate, rateCoupon, yieldToMat, nPay)

Arguments

Details

All the rates are given in decimals.

Value

A list with the following components:

Note

With Excel functions PRICE, DATE, COUPDAYBS and COUPDAYS you can do the same.

Author(s)

Arto Luoma <arto.luoma@wippies.com>

References

Bodie, Kane, and Marcus (2014) Investments, 10th Global Edition, McGraw-Hill Education, (see Bond Pricing between Coupon Dates in Section 14.2).

See Also

solveYield

Examples

bondPrice("2012-7-31","2018-7-31",0.0225,0.0079,2)
bondPrice("2012-7-31","2018-7-31",0.0225,0.0079,4)
bondPrice("2012-7-31","2030-5-15",0.0625,0.02117,2)

Ruin probability computation with infinite time horizon

Description

This function uses classical ruin theory to compute either ruin probability, safety loading or initial capital, given two of them. The time horizon is infinite. Gamma distribution is used to model claim sizes.

Usage

computeRuin(U0 = NULL, theta = NULL, eps = NULL, alpha, beta)

Arguments

Value

The value is a list with the following components:

Author(s)

Arto Luoma <arto.luoma@wippies.com>

References

Gray and Pitts (2012) Risk Modelling in General Insurance: From Principles to Practice, Cambridge University Press.

See Also

computeRuinFinite, solveLund

Examples

computeRuin(U0=1000,theta=0.01,alpha=1,beta=0.1)
computeRuin(eps=0.005,theta=0.01,alpha=1,beta=0.1)
computeRuin(U0=5399.24,eps=0.005,alpha=1,beta=0.1)

Ruin probability computation with finite time horizon

Description

This function uses classical ruin theory to compute either ruin probability, safety loading or initial capital, given two of them. The time horizon is finite. Gamma distribution is used to model claim sizes.

Usage

computeRuinFinite(T0, U0 = NULL, theta = NULL, eps = NULL, lambda, 
                  alpha, beta)

Arguments

Value

The value is a list with the following components:

Author(s)

Arto Luoma <arto.luoma@wippies.com>

See Also

computeRuin, solveLund

Examples

computeRuinFinite(T0=100,U0=1000,theta=0.01,lambda=100,alpha=1,beta=0.1)
computeRuinFinite(T0=1,eps=0.005,theta=0.001,lambda=100,alpha=1,beta=0.1)
computeRuinFinite(T0=500,U0=5347,eps=0.005,lambda=100,alpha=1,beta=0.1)

Mortality data

Description

Mortality data for 10 countries (period death rates and exposures) retrieved from Human Mortality Database. The data are rounded to three significant digits and include the Nordic countries, China, U.S., Russia, Japan and Germany.

Usage

data("countries.mort")

Format

List of objects of class demogdata.

Source

HMD. Human Mortality Database. Max Planck Institute for Demographic Research (Germany), University of California, Berkeley (USA), and French Institute for Demographic Studies (France). Available at www.mortality.org. (Data downloaded Nov 13, 2023.)

Examples

data(countries.mort)
plot(countries.mort[[1]])

Kalman smoothing of the covid model

Description

This function does Kalman smoothing for the simple model that is used to predict new COVID-19 cases.

Usage

covidSmooth(par, y)

Arguments

Details

See loglikCovid.

Value

Author(s)

Arto Luoma

See Also

loglikCovid

Examples

#Preparing a time series
library(zoo)
data(dataCovidFin)
timeindex <- dataCovidFin[dataCovidFin$Alue=="Kaikki Alueet","Aika"]
series <- dataCovidFin[dataCovidFin$Alue=="Kaikki Alueet","val"]
series <- window(zoo(series,order.by=timeindex),start="2020-03-01",
                 end="2021-03-01") 
#Fitting a state space model and smoothing the components
p0 <- c(-9,-7,-3.3)
fit <- nlm(loglikCovid,p=p0,y=series)
out <- covidSmooth(fit$estimate,y=series)

#Plotting the filtered and smoothed components
smoothed <- zoo(out$Xis[,1:3],order.by=time(series))
filtered <- zoo(out$Xif[,1:3],order.by=time(series))
colnames(smoothed) <- colnames(filtered) <- c("Level","Drift","Seasonal")
plot(filtered,xlab="Time",main="Filtered components of the time series")
plot(smoothed,xlab="Time",main="Smoothed components of the time series")

#Plotting the original time series, and the filtered and smoothed local level 
#series after transforming them to original scale
plot(series,xlab="Time",ylab="Time series")
lines(exp(filtered[,1])-2,col=3)
lines(exp(smoothed[,1])-2,col=2)
legend("topleft",c("original","filtered","smoothed"),col=c(1,3,2),lty=1)

COVID-19 statistics

Description

This data set consists of several statistics about the COVID-19 pandemic in 45 countries.

Usage

data("dataCovid")

Format

A data frame with 18400 observations on the following 27 variables.

location

a character vector

date

a Date

new_cases

a numeric vector

new_cases_per_million

a numeric vector

new_cases_smoothed_per_million

a numeric vector

new_cases_smoothed

a numeric vector

new_deaths_per_million

a numeric vector

new_deaths

a numeric vector

new_deaths_smoothed_per_million

a numeric vector

new_deaths_smoothed

a numeric vector

total_deaths_per_million

a numeric vector

total_deaths

a numeric vector

total_cases

a numeric vector

total_cases_per_million

a numeric vector

hosp_patients

a numeric vector

hosp_patients_per_million

a numeric vector

icu_patients_per_million

a numeric vector

icu_patients

a numeric vector

reproduction_rate

a numeric vector

new_tests

a numeric vector

new_tests_per_thousand

a numeric vector

tests_per_case

a numeric vector

positive_rate

a numeric vector

new_tests_smoothed

a numeric vector

new_tests_smoothed_per_thousand

a numeric vector

total_tests

a numeric vector

total_tests_per_thousand

a numeric vector

Details

This is a subset of the complete data set available online, downloaded on March 31, 2021.

Source

https://covid.ourworldindata.org/data/owid-covid-data.csv

Examples

library(zoo)
data(dataCovid)
casesFin <- subset(dataCovid,subset=location=="Finland", select=c(date,new_cases))
plot(zoo(casesFin$new_cases,order.by=casesFin$date),ylab="New COVID-19 cases in Finland",
xlab="")

Confirmed COVID-19 cases in Finland

Description

This data set provides the confirmed COVID-19 cases in 21 Finnish hospital districts, in addition to the total number.

Usage

data("dataCovidFin")

Format

A data frame with 16082 observations on the following 3 variables.

Aika

Date

Alue

character vector: hospital district

val

numeric vector: number of new confirmed cases

Details

The data were downloaded on March 31, 2021, via THL's open data API.

Source

https://bit.ly/2PO1DnS

References

https://bit.ly/3ryfwE4

Examples

library(zoo)
data(dataCovidFin)
casesFin <- subset(dataCovidFin, subset = Alue=="Kaikki Alueet")
plot(zoo(casesFin$val,order.by=casesFin$Aika),ylab="New COVID-19 cases in Finland",xlab="")

Plotting epidemic statistics

Description

This function plots several epidemic statistics for selected countries.

Usage

drawBars(data, countries, start = "2020-06-01", end = "last", measure = "new_cases", 
    atop = TRUE, perMillion = FALSE, drawMean = TRUE, bars = TRUE)

Arguments

Value

No value.

Author(s)

Arto Luoma <arto.luoma@wippies.com>

See Also

drawBarsFin, dataCovid

Examples

data(dataCovid)
drawBars(data=dataCovid, countries=c('Finland','France'),start='2020-6-1',
         measure='new_cases',perMillion=TRUE)

Plotting epidemic statistics with Finnish data

Description

This function plots the new cases or total cases of an epidemic for selected regions in Finland.

Usage

drawBarsFin(data, pop, regions, start = "2020-06-01", end = "last", 
    measure = "new_cases", atop = TRUE, perMillion = FALSE, drawMean = TRUE, 
    bars = TRUE)

Arguments

Value

No value.

Author(s)

Arto Luoma <arto.luoma@wippies.com>

See Also

drawBars, dataCovidFin

Examples

data(dataCovidFin)
data(popRegionsFin)
drawBarsFin(dataCovidFin,popRegionsFin,regions=popRegionsFin$Alue[1:7])

Efficient frontier and return distribution figures

Description

Plots the efficient frontiers of risky investments and all investments. The optimum points corresponding to the risk aversion coefficient are indicated by dots. Further, the function plots a predictive return distribution figure.

Usage

drawFigure(symbol, yield, vol, beta, r = 1, 
  total = 1, indexVol = 20, nStocks = 7, balanceInt = 12, A = 10, 
  riskfree = FALSE, bor = FALSE)

Arguments

Details

The function uses the single-index model and Markovitz portfolio optimization model to find the optimum risky portfolio. The returns are assumed to be log-normally distributed. The maximized function is mu - 0.5*A*var where mu is expected return, A is risk aversion coefficient, and var is return variance.

Value

Author(s)

Arto Luoma <arto.luoma@wippies.com>

References

Bodie, Kane, and Marcus (2014) Investments, 10th Global Edition, McGraw-Hill Education, (see Section 7.4 The Markowitz Portfolio Optimization Model and Section 8.2 The Single-Index Model).

See Also

portfOptim

Examples

data(stockData, package="RcmdrPlugin.RiskDemo")
with(stockData,drawFigure(symbol=rownames(stockData),yield=divYield,
  vol=vol,beta=beta,r=1,total=100,indexVol=10, 
  nStocks=5,balanceInt=12,A=10,riskfree=TRUE,bor=FALSE))

Plotting incidence curves of an epidemic

Description

This function plots incidence curves of an epidemic for selected countries. The incidences are new cases per 100 000 inhabitants within one or two weeks.

Usage

drawIncidence(data, countries, start = "2020-06-01", end = "last", weeks = 2, 
    log = TRUE)

Arguments

Value

No value

Author(s)

Arto Luoma <arto.luoma@wippies.com>

See Also

drawIncidenceFin, dataCovid

Examples

data(dataCovid)
Europe <- c("Germany","France","United Kingdom","Italy","Spain","Poland","Romania",
    "Netherlands","Belgium","Greece")
drawIncidence(dataCovid,countries=Europe)

Plotting incidence curves of an epidemic with Finnish data

Description

This function plots incidence curves of an epidemic for selected regions of Finland. The incidences are new cases per 100 000 inhabitants within one or two weeks.

Usage

drawIncidenceFin(data, pop, regions, start = "2020-06-01", end = "last", weeks = 2, 
    includeAllRegions = TRUE, log = TRUE)

Arguments

Value

No value

Author(s)

Arto Luoma <arto.luoma@wippies.com>

See Also

drawIncidence, dataCovidFin

Examples

data(dataCovidFin)
data(popRegionsFin)
drawIncidenceFin(data = dataCovidFin, pop = popRegionsFin, 
    regions = popRegionsFin$Alue[1:5], start = "2020-06-01", end="last", weeks=2, 
    includeAllRegions = TRUE)

Plotting the positive rate of COVID-19 tests or the tests per case

Description

This function plots a time series of either the positive rate of COVID-19 tests or the number of tests per case.

Usage

drawPositiveRate(data, countries, start = "2020-06-01", end = "last", 
    measure = "positive_rate", curve = TRUE, bars = FALSE, log = FALSE)

Arguments

Value

No value.

Author(s)

Arto Luoma <arto.luoma@wippies.com>

See Also

dataCovid, drawTests

Examples

data(dataCovid)
drawPositiveRate(dataCovid,countries=c("Finland","France"))

Plotting simulations of a surplus process

Description

This function plots simulation paths of a surpluss process. The claims are assumed to arrive according to a Poisson process and the claim sizes are assumed to be gamma distributed.

Usage

drawRuin(nsim = 10, Tup = 10, U0 = 1000, theta = 0.01, 
         lambda = 100, alpha = 1, beta = 0.1)

Arguments

Value

No value; only a figure is plotted.

Author(s)

Arto Luoma <arto.luoma@wippies.com>

References

Kaas, Goovaerts, Dhaene, Denuit (2008) Modern actuarial risk theory using R, 2nd ed., Springer.

See Also

computeRuinFinite,

Examples

computeRuinFinite(T0=10,U0=1000,eps=0.05,lambda=100,alpha=1,beta=0.1)
drawRuin(nsim=10,Tup=10,U0=1000,theta=0.0125,lambda=100,alpha=1,beta=0.1)

Plotting time series related to COVID-19 testing

Description

This function plots time series of new and total COVID-19 tests, possibly in proportion to population.

Usage

drawTests(data, countries, start = "2020-06-01", end = "last", measure = "new_tests", 
    atop = TRUE, perThousand = FALSE, drawMean = TRUE, bars = TRUE, log = FALSE)

Arguments

Value

No value.

Author(s)

Arto Luoma <arto.luoma@wippies.com>

See Also

dataCovid, drawPositiveRate

Examples

data(dataCovid)
drawTests(dataCovid,countries=c("Finland","France"),perThousand=TRUE)

Mortality data for Finland

Description

Mortality data for Finland Series: female male total Years: 1878 - 2015 Ages: 0 - 110

Usage

data("fin")

Format

object of class demogdata

Details

This is part of the countries.mort data (countries.mort[[11]]).

Source

HMD. Human Mortality Database. Max Planck Institute for Demographic Research (Germany), University of California, Berkeley (USA), and French Institute for Demographic Studies (France). Available at www.mortality.org. (Data downloaded Nov 13, 2023.)

Examples

data(fin)
print(fin)
plot(fin)

Finnish mortality forecast

Description

Finnish mortality forecast 50 years ahead (2023-2072) for 0 - 100 years old. The forecast is based on an estimated Lee-Carter model. The kt coefficients were forecast using a random walk with drift. Fitted rates were used as the starting value.

Usage

data("fin.fcast")

Format

An object of class "fmforecast"; for details, see documentation of package "demography".

Details

The forecast was produced using function "forecast.lca" of package "demography".

Examples

data(fin.fcast)
print(fin.fcast)
plot(fin.fcast)

Lee-Carter model fit for Finnish data

Description

Lee-Carter model fit obtained by function "lca" of package "demography". The fit is based on Finnish mortality data for ages from 0 to 100 and years from 1950 to 2022.

Usage

data("fin.lca")

Format

object of class "lca"

Details

Both sexes were included in the input mortality data.

Examples

data(fin.lca)
plot(fin.lca) 

Computing the log-likelihood of the covid model

Description

This function computes -2 times the log-likelihood of the simple model that is used to predict new COVID-19 cases and to estimate the effective reproduction number.

Usage

loglikCovid(y, par, it = TRUE)

Arguments

Details

Some multiplicative and additive constants are omitted when the negative log-likelihood is computed. Before computing the log-likelihood, the transformation y=log(x+a), where a=2, is applied to the time series. The model is a simple local linear model with local level, drift and seasonal component. The variance parameters of the level and seasonal component are estimated while the variance of the level component is computed as max(exp(xi[1]) - a, 0.1)/exp(xi[1])^2, where xi[1] is the current estimate of the level. This is based on the assumption that the number of new cases is approximately Poisson distributed, so that the variance equals the level. The max operation is taken in order to prevent the exression from being negative. In order to facilitate estimation, a penalty term is added which corresponds to a prior of N(-9,1) for the logarithm of the drift variance.

Value

Author(s)

Arto Luoma <arto.luoma@wippies.com>

References

Hamilton (1994) Time Series Analysis, Princeton University Press, (see Chapter 13 The Kalman Filter).

See Also

covidSmooth

Examples

#See examples for covidSmooth.

Yield curve parameter data

Description

Yield curve parameters from the European Central Bank (ECB), downloaded on Nov 4, 2023

Usage

data("params")

Format

A data frame with 4902 observations on the following 13 variables.

date

a Date

b0

a numeric vector

b1

a numeric vector

b2

a numeric vector

b3

a numeric vector

t1

a numeric vector

t2

a numeric vector

c0

a numeric vector

c1

a numeric vector

c2

a numeric vector

c3

a numeric vector

d1

a numeric vector

d2

a numeric vector

Details

The parameters b0 to b3 are the beta-parameters, and t1 and t2 the tau-parameters for AAA-rated government bonds. The parameters c0 to c3 are the beta-parameters, and d1 and d2 the tau-parameters for all government bonds.

Source

https://bit.ly/2zfs0G8

Examples

data(params)
bondCurve(as.Date("2004-09-06"),params=params)

Forecasting new covid cases

Description

This function forecasts the numbers of new covid cases using a simple linear state space model.

Usage

plotForecast(data, region, start = NULL, end = NULL, np = 30, predInt = 0.95, 
    log = TRUE)

Arguments

Value

No value.

Author(s)

Arto Luoma <arto.luoma@wippies.com>

See Also

plotR, dataCovidFin

Examples

data(dataCovidFin)
plotForecast(data=dataCovidFin, region='All regions', start="2020-09-01")

Plotting the effective reproduction number (R)

Description

This function plots a time series of the effective reproduction number R and its confidence interval.

Usage

plotR(data, region, start = NULL, end = NULL, confInt = 0.95)

Arguments

Value

No value

Author(s)

Arto Luoma <arto.luoma@wippies.com>

See Also

plotForecast, dataCovidFin

Examples

data(dataCovidFin)
plotR(data=dataCovidFin, region='All regions')

Population forecasting

Description

Population forecasting using mortality forecast and simple time series forecast for age 0 population

Usage

pop.pred(mort, mort.fcast)

Arguments

Details

ARIMA(0,2,2)-model is used to forecast age 0 populaton.

Value

population forecast of class 'demogdata'

Author(s)

Arto Luoma <arto.luoma@wippies.com>

Examples

data(fin)
data(fin.fcast)
fin.pcast <- pop.pred(fin,fin.fcast)
plot(fin,plot.type="functions",series="total",transform=FALSE,
     datatype="pop",ages=c(0:100), years=c(1990+0:5*10), xlab="Age")
lines(fin.pcast,plot.type="functions",series="total",transform=FALSE, 
      datatype="pop",ages=c(0:100), years=c(1990+0:5*10), lty=2)

Population data on Finnish hospital districts

Description

This data set provides the populations of the 21 hospital districts, in addition to the total Finnish population.

Usage

data("popRegionsFin")

Format

A data frame with 22 observations on the following 2 variables.

Alue

character vector: hospital district

val

numeric vector: population

Details

The data were downloaded on March 31, 2021, via THL's open data API.

Source

https://bit.ly/39uZy7C

References

https://bit.ly/3ryfwE4

Examples

data(popRegionsFin)
print(popRegionsFin)

Portfolio optimization for an index model

Description

Finds an optimal portfolio for long-term investments and plots a return distribution.

Usage

portfOptim(i, symbol, yield, vol, beta, 
  indexVol = 0.2, nStocks = 7, total = 1, balanceInt = 1, 
  C = 0.05, riskProportion = 1, riskfreeRate = 0, sim = FALSE)

Arguments

Details

The arguments vol, beta, indexVol, riskProportion and riskfreeRate are given in decimals. The portfolio is optimized by minimizing the variance of the portfolio yield for a given expected yield. The returns are assumed to be log-normally distributed. The covariance matrix is computed using the single index model and the properties of the log-normal distribution.

Value

Note

This function is usually called by drawFigure.

Author(s)

Arto Luoma <arto.luoma@wippies.com>

References

Bodie, Kane, and Marcus (2014) Investments, 10th Global Edition, McGraw-Hill Education, (see Section 7.4 The Markowitz Portfolio Optimization Model and Section 8.2 The Single-Index Model).

See Also

drawFigure

Examples

data(stockData, package="RcmdrPlugin.RiskDemo")
with(stockData,portfOptim(i=1:5,symbol=rownames(stockData),
  yield=divYield/100,vol=vol/100,beta=beta/100,total=100, sim=TRUE))

Computing expected returns and their covariance matrix

Description

Computing expected returns and their covariance matrix when the returns are lognormal.

Usage

returns(volvec, indexvol, beta)

Arguments

Details

The arguments are given in decimals. The single index model is used to compute the covariance matrix of a multivariate normal distribution. The mean vector is assumed to be zero. The properties of the log-normal distribution are then used to compute the mean vector and covariance matrix of the corresponding multivariate log-normal distribution.

Value

Author(s)

Arto Luoma <arto.luoma@wippies.com>

References

Bodie, Kane, and Marcus (2014) Investments, 10th Global Edition, McGraw-Hill Education, (see Section 8.2 The Single-Index Model).

Examples

returns(volvec=c(0.1,0.2,0.3),indexvol=0.2, beta=c(0.5,-0.1,1.1)) 

Solving Lund's exponent

Description

This function solves Lund's exponent or adjustment coefficient. The claim sizes are assumed to be gamma distributed.

Usage

solveLund(alpha, beta, theta)

Arguments

Value

Lundberg's exponent (or adjustment coefficient)

Author(s)

Arto Luoma <arto.luoma@wippies.com>

References

Gray and Pitts (2012) Risk Modelling in General Insurance: From Principles to Practice, Cambridge University Press.

See Also

computeRuin, computeRuinFinite

Examples

solveLund(1,1,0.1)

Computing bond yields

Description

This function computes the yield to maturity, given the (flat) bond price.

Usage

solveYield(buyDate, matDate, rateCoupon, bondPr, nPay)

Arguments

Details

all the rates are given in decimals

Value

A list with the following components:

Note

With Excel function YIELD you can do the same.

Author(s)

Arto Luoma <arto.luoma@wippies.com>

References

Bodie, Kane, and Marcus (2014) Investments, 10th Global Edition, McGraw-Hill Education, (see Bond Pricing between Coupon Dates in Section 14.2).

See Also

bondPrice

Examples

solveYield("2012-7-31","2018-7-31",0.0225,100,2)

Computing stock prices

Description

This function computes the intrinsic stock price using the constant growth dividend discount model.

Usage

stock.price(dividend, k = NULL, g = NULL, ROE = NULL, b = NULL, 
  riskFree = NULL, marketPremium = NULL, beta = NULL)

Arguments

Details

All the above rates are given in percentages (except the dividends). One should provide either k or the following three: riskFree, marketPremium, beta. Further, one should provide either g or the following two: ROE and b. In the output, k and g are given in decimals.

Value

Author(s)

Arto Luoma <arto.luoma@wippies.com>

References

Bodie, Kane, and Marcus (2014) Investments, 10th Global Edition, McGraw-Hill Education, (see Dividend Discount Models in Section 18.3).

Examples

  stock.price(dividend=c(1),k=12,g=10)
  stock.price(dividend=c(1),ROE=50,b=20,riskFree=5,marketPremium=8,
              beta=90)

Stock data

Description

Stock data on large companies in Helsinki Stock Exchange, downloaded from Kauppalehti web page (www.kauppalehti.fi), on May 13, 2017

Usage

data("stockData")

Format

A data frame with 35 observations on the following 7 variables.

names

name of the firm

abbrs

abbreviation of the firm

quote

closing quote

vol

volatility (%)

beta

beta (%)

div

dividend (eur/stock)

divYield

dividend yield (%)

Source

www.kauppalehti.fi

Examples

data(stockData)
plot(stockData[,-(1:2)])