Workshop 1, Financial Econometrics 1

Downloading online financial data and calculating returns

Here I will download Financial Data from Yahoo

rm(list=ls())
# To avoid scientific notation for numbers: 
options(scipen=999)

Load the quantmod package

Here I download the Quantmod Package

library(quantmod)

Loading required package: xts
Loading required package: zoo

Attaching package: ‘zoo’

The following objects are masked from ‘package:base’:

    as.Date, as.Date.numeric

Loading required package: TTR
Registered S3 method overwritten by 'quantmod':
  method            from
  as.zoo.data.frame zoo 

Downloading real financial prices

getSymbols(Symbols=c("BTC-USD"), from="2017-01-01", src="yahoo", periodicity="daily")

‘getSymbols’ currently uses auto.assign=TRUE by default, but will
use auto.assign=FALSE in 0.5-0. You will still be able to use
‘loadSymbols’ to automatically load data. getOption("getSymbols.env")
and getOption("getSymbols.auto.assign") will still be checked for
alternate defaults.

This message is shown once per session and may be disabled by setting 
options("getSymbols.warning4.0"=FALSE). See ?getSymbols for details.

Warning: BTC-USD contains missing values. Some functions will not work if objects contain missing values in the middle of the series. Consider using na.omit(), na.approx(), na.fill(), etc to remove or replace them.

[1] "BTC-USD"

Show the content of datasets

head(`BTC-USD`,5)

           BTC-USD.Open BTC-USD.High BTC-USD.Low BTC-USD.Close
2017-01-01      963.658      1003.08     958.699       998.325
2017-01-02      998.617      1031.39     996.702      1021.750
2017-01-03     1021.600      1044.08    1021.600      1043.840
2017-01-04     1044.400      1159.42    1044.400      1154.730
2017-01-05     1156.730      1191.10     910.417      1013.380
           BTC-USD.Volume BTC-USD.Adjusted
2017-01-01      147775008          998.325
2017-01-02      222184992         1021.750
2017-01-03      185168000         1043.840
2017-01-04      344945984         1154.730
2017-01-05      510199008         1013.380

tail(`BTC-USD`, 5)

           BTC-USD.Open BTC-USD.High BTC-USD.Low BTC-USD.Close
2021-08-13     44439.69     47831.98    44282.42      47793.32
2021-08-14     47810.69     48098.68    46177.63      47096.95
2021-08-15     47096.67     47357.11    45579.59      47047.00
2021-08-16     47019.96     47998.10    45700.32      46004.48
2021-08-17     45980.96     47110.70    45436.33      45883.68
           BTC-USD.Volume BTC-USD.Adjusted
2021-08-13    31744259539         47793.32
2021-08-14    31211354442         47096.95
2021-08-15    30988958446         47047.00
2021-08-16    32776876610         46004.48
2021-08-17    31748257792         45883.68

Visualization of prices

plot(`BTC-USD`)

chartSeries(`BTC-USD`, theme=("white"))

Data Cleaning

`BTC-USD` <- na.omit(`BTC-USD`)

Calculation of financial returns

prices <- Ad(`BTC-USD`)

colnames(prices) <- "adj_price"

prices$lag1 <- lag(prices$adj_price, n=1)

prices$R_a <- prices$adj_price / prices$lag1 -1

prices$R_b <- prices$adj_price / lag(prices$adj_price, n=1) -1

prices$GrowthR <- 1 + prices$R_a

prices$r_b <- log(prices$adj_price / prices$lag1)

prices$r_from_R <- log(1 + prices$R_a)

head(prices, 5)

           adj_price     lag1         R_a         R_b   GrowthR
2017-01-01   998.325       NA          NA          NA        NA
2017-01-02  1021.750  998.325  0.02346429  0.02346429 1.0234643
2017-01-03  1043.840 1021.750  0.02161974  0.02161974 1.0216197
2017-01-04  1154.730 1043.840  0.10623277  0.10623277 1.1062328
2017-01-05  1013.380 1154.730 -0.12240955 -0.12240955 0.8775905
                   r_b    r_from_R
2017-01-01          NA          NA
2017-01-02  0.02319324  0.02319324
2017-01-03  0.02138934  0.02138934
2017-01-04  0.10096034  0.10096034
2017-01-05 -0.13057525 -0.13057525

plot(prices$R_a)

Calculation of holing-period return

n <- as.numeric(nrow(prices))

price_0 <- as.numeric(prices$adj_price[1])
price_n <- as.numeric(prices$adj_price[n])

HPR1 <- (price_n / price_0) - 1
cat("HPR1 = " ,HPR1)

HPR1 =  44.96066

sumr <- sum(prices$r, na.rm = TRUE)
HPR2 <- exp(sumr) - 1

cat(HPR1, HPR2)

44.96066 0

Q Descriptive Statistics of financial returns

rm(list = ls())

getSymbols(Symbols = "SBUX", from="2008-01-01", periodicity="monthly", src = "yahoo")

[1] "SBUX"

returns.df <- as.data.frame(diff(log(Ad(SBUX))))

colnames(returns.df) <- "r_SBUX"

summary(returns.df)

     r_SBUX        
 Min.   :-0.38548  
 1st Qu.:-0.02651  
 Median : 0.01956  
 Mean   : 0.01661  
 3rd Qu.: 0.05766  
 Max.   : 0.26354  
 NA's   :1         

library(PerformanceAnalytics)

Attaching package: ‘PerformanceAnalytics’

The following object is masked from ‘package:graphics’:

    legend

table.Stats(returns.df$r_SBUX)

mean_r_SBUX <- mean(returns.df$r_SBUX, na.rm=TRUE)

sd_r_SBUX <- sd(returns.df$r_SBUX, na.rm=TRUE)

var_r_SBUX <- var(returns.df$r_SBUX, na.rm=TRUE)

cat("Mean =", mean_r_SBUX)

Mean = 0.01661223

cat("Standard deviation = ", sd_r_SBUX)

Standard deviation =  0.07607764

cat("Variance = ", var_r_SBUX)

Variance =  0.005787807

Q Mean, standard deviation and variance of simple returns

returns.df$R_SBUX <- SBUX$SBUX.Adjusted / lag(SBUX$SBUX.Adjusted, n=1) - 1

table.Stats(returns.df$R_SBUX)

mean(returns.df$R_SBUX, na.rm=TRUE)

[1] 0.01963446

sd(returns.df$R_SBUX, na.rm=TRUE)

[1] 0.07617523

var(returns.df$R_SBUX, na.rm=TRUE)

            [,1]
[1,] 0.005802666

Q The Histrogram

#You have to remember what is a histogram :)

hist(returns.df$r_SBUX, main="Histogram of SBUX monthly returns", 
     xlab="Continuously Compounded returns", col="dark green")

##QUESTIONS:

QUESTION: INTERPRET THIS HISTOGRAM WITH YOUR OWN WORDS

If we increase the compound frequency to its limit, we are compounding continuously. Returns are being compounded constantly resulting in money acquiring strength through interest rates. Continiously compounded returns exhibit an increment in frequency in the 0.0-0.1 range.

QUESTION: HOW MEAN AND STANDARD DEVIATION IS RELATED WITH THE HISTOBRAM?

To calculate the mean we add up the observed values and divide by the number of them. Thus the histogram demonstrates the frequency a continious compound through time using mean. “A standard deviation is a statistic that measures the dispersion of a dataset relative to its mean” (Bland, J.M.; Altman, D.G.) and in this histogram the standard deviation does just that, it demonstrates how far away the mean spreads through the frequency of continious compounding.

Q Histogram using simulated data for returns

rSBUX_sim <- rnorm(n=nrow(returns.df), mean = mean_r_SBUX, sd=sd_r_SBUX)

rSBUX <- na.omit(returns.df$r_SBUX)

hist_sim_SBUX<- hist(rSBUX_sim,plot = FALSE)

hist_SBUX <- hist(rSBUX_sim,plot = FALSE)

xlim <- range(hist_SBUX$breaks,hist_sim_SBUX$breaks)
ylim <- range(0,hist_SBUX$density,
              hist_sim_SBUX$density)

plot(hist_sim_SBUX,xlim = xlim, ylim = ylim,
     col = rgb(1,0,0,0.4),xlab = 'Lengths', freq = FALSE, main = 'Distribution of simulated and real Starbucks Returns')

“No pude hacer el último histograma con colores, me aparece error al meter el codigo del Rpubs así que lo modifiqué para que mínimo apareciera una tabla. Me gustaría saber si podemos revisar esto en clase.” Stefan S.

opar <- par(new = FALSE)
plot(hist_SBUX,xlim = xlim, ylim = ylim)
col = rgb(0,0,1,0.4)
fill=rgb(0.1,0.4,0.5,0.7)
freq = FALSE
main = 'Distribution of simulated and real Starbucks Returns'
legend('topleft',c('Simulated Returns','Real Returns'),
       fill = rgb(1:0,0,0:1,0.4), bty = 'n')

QUESTION: WHAT DIFFERENCE DO YOU SEE IN THE HISTOGRAMS? HOW REAL RETURNS ARE DIFFERENT FROM THE THEORETICAL NORMAL DISTRIBUTION OF RETURNS? BRIEFLY EXPLAIN.

Creating a budget vs. actual comparison is extremely important for all businesses because it allows them to alter their future financial forecasts based upon the numbers collected in the monthly reports. Real returns hang on the positive side of the balance, indicating future adjustments must be made.

QUESTION: WHAT WOULD BE THE 95% CONFIDENCE INTERVAL? WHAT IS THE INTERPRETATION OF THIS INTERVAL? EXPLAIN.

Remembering my previous statistics classes, there was always a degree of uncertainty, which would vary according to numerous factors. Widely accepted is the 5% uncertainty degree, thus one can be sure of the other 95% of the available data.