Introduction to Financial Economics with R

Lesson 2. Value at Risk I

1. What is Value at Risk (VaR)?

Value at Risk (VaR) is a statistical measure that quantifies and focuses on the potential downside risk of an investment over a specific time horizon. It is widely used by financial institutions to estimate the amount of potential losses in their institutional investments.

 

2. How is Value at Risk (VaR) Calculated?

     (1) Import a CSV Data File in R:

library(quantmod)
library(PerformanceAnalytics)
Apple_CSV <- read.zoo("AAPL.csv",header = TRUE, sep =",",format="%m/%d/%Y")

 

     (2) Clean Imported Data and Calculate Daily Return of AAPL:

AAPL_Prices <- as.xts(x = Apple_CSV$Adj.Close)
AAPL_Returns <- dailyReturn(AAPL_Prices)

• Here, we use Adjusted Closing Price because it reflects accurate stock value after all required accounting actions.
• To calculate daily returns of AAPL, we employ the formula: \[Daily Return = \frac{P_{1} - P_{1}}{{P_{0}}}\]

   

       (3) Summarize AAPL Daily Return Data:
  

head(AAPL_Returns)

##            daily.returns
## 2015-01-02  0.000000e+00
## 2015-01-05 -2.817169e-02
## 2015-01-06  9.450198e-05
## 2015-01-07  1.402209e-02
## 2015-01-08  3.842243e-02
## 2015-01-09  1.072070e-03

tail(AAPL_Returns)

##            daily.returns
## 2019-12-23  0.0163183658
## 2019-12-24  0.0009506422
## 2019-12-26  0.0198403820
## 2019-12-27 -0.0003795103
## 2019-12-30  0.0059351588
## 2019-12-31  0.0073064655

summary(AAPL_Returns)

##      Index            daily.returns       
##  Min.   :2015-01-02   Min.   :-0.0996074  
##  1st Qu.:2016-04-04   1st Qu.:-0.0058529  
##  Median :2017-07-01   Median : 0.0008920  
##  Mean   :2017-07-01   Mean   : 0.0009755  
##  3rd Qu.:2018-09-30   3rd Qu.: 0.0089108  
##  Max.   :2019-12-31   Max.   : 0.0704214

 

     (4) Calculate Value at Risk (VaR) and Conditional Value at Risk (CVaR):

VaR(AAPL_Returns, p=0.95, method = "historical")

##     daily.returns
## VaR   -0.02499576

CVaR(AAPL_Returns, p=0.95, method = "historical")

##    daily.returns
## ES   -0.03617996

• Value at Risk (VaR) does not control cases exceeding VaR, but Conditional Value at Risk (CVaR) allows us to account for losses exceeding VaR. Conditional Value at Risk (CVaR) is also called Expected Shortfall (ES).
• There are three different calculations of Value at Risk (VaR): Parametric, Non-Parametric, and Monte Carlo.

 

Thank You and See You Soon!