CORPFIN 2503 – Business Data Analytics
2021 S2, Workshop 8: Monte-Carlo simulation
£ius
1 Daily stock price data
Let’s download daily stock price data from finance.yahoo.com for the 14/09/2020
� 10/09/2021 for :
� Amazon.com, Inc. (AMZN)
� . (AAPL).
Then compute the daily log returns and the following properties:
� mean log return for each stock
� covariance matrix of both log returns.
2 Generation of correlated random variables
Let’s generate 5,000 random values for 2 variables with properties similar to those
for AMZN and AAPL stocks:
data work.stocks(type=COV) ;
input _TYPE_ $ 1-4 _NAME_ $ 5-9 AMZN AAPL;
datalines ;
COV AMZN 0.000305534 0.000213946
COV AAPL 0.000213946 0.000332822
MEAN Mean 0.000446199 0.001048394
;
1
finance.yahoo.com
PROC SIMNORM DATA=work.stocks OUTSIM=work.stocks_sim
NUMREAL = 5000;
VAR AMZN AAPL;
RUN;
For �xed formatted data (i.e., data that has no delimiters such as spaces, com-
mas, or tabs) to separate �xed formatted data, column de�nitions are required for
every variable in the dataset. That is, one needs to provide the beginning and end-
ing column numbers for each variable. This also requires the data to be in the same
columns for each case. For example, _TYPE_ $ 1− 4 means that
� the name of the �rst variable is _TYPE_
� this variable is character (because of $ following the variable name)
� variable name consists of 4 symbols (1− 4): starting with the �rst column and
ending with the fourth column.
Then using SAS procudere SIMNORM we generate 5,000 random values for 2
variables (AMZN AAPL). These two variables will have the same (or at least, very
similar) statistical properties to those in �work.stocks� �le.
3 Monte Carlo simulation
Using random variables generated in Task 2, compute the changes in the value of
the portfolio consisting of:
� US$100 million investment into Amazon.com, Inc. (AMZN)
� US$75 million investment into . (AAPL).
data work.stocks_sim;
set work.stocks_sim;
portf=100*AMZN+75*AAPL;
run;
Then compute:
1. the expected change in the portfolio value
2
2. minimum and maximum values
3. the lowest 1st and 5th percentiles of the change in the portfolio value (value at
risk (VaR)):
� e.g., if 1-day VaR on the portfolio is $100m at 95% con�dence level, it
means that there is a only a 5% chance that the value of the portfolio
will drop more than $100m over any 1 day
4. histogram of the change in the portfolio value
5. the probability that the the change in the portfolio value is non-negative.
4 Monte Carlo simulation II (at home)
Expand Task #2 to include the third stock (e.g., Microsoft Corporation (MSFT)).
Assume that US$50 million has been invested into Microsoft stock and use 100,000
(rather than 5,000) random values. Hint : covariance matrix will become 3× 3.
3
Daily stock price data
Generation of correlated random variables
Monte Carlo simulation
Monte Carlo simulation II (at home)