Introduction

1. Introduction

2. Downloads • Today’s work is in: matlab_lec01.m • Datasets we need today: data_bp.m, data_vlcm.m • All course materials can be found here: http://personal.lse.ac.uk/faviluki/fm457.html • Save all of your matlab files to H:\Matlab • Make sure same folder is selected as Current Folder at the top of the Matlab window

3. What is Matlab? • “The Language of Technological Computing” • A very fancy calculator • A simple and user friendly programming language • A tool for data analysis and statistics • A tool to produce pretty plots

4. Accessing Matlab

5. Basics • From any LSE computer: Start/Programs/Specialist and teaching software/Mathematics/Matlab/Matlab R2012a • Student version can be purchased at discount: http://www.mathworks.co.uk/academia/student_version/ • One of several online tutorials: http://www.indiana.edu/~statmath/math/matlab/gettingstarted/index.html • Matlab Website: http://www.mathworks.com/

6. Course Outline • Introduction to Matlab • Simulation • Volatility • GARCH and VAR • Multiple Securities • Factor Models • Option Pricing • Fixed Income Only by practicing what you see in class will you get comfortable with Matlab!!!

7. .m files • .m files are just text files • Do work in .m file • Paste work into Matlab prompt • Use ; to end lines • Save .m files • Use % to add comments

8. The Matlab Prompt • This is where commands are executed >> denotes where you type commands • Type or paste commands, then hit enter • If entering multiple commands, separate them by ; • Multiple commands may be on same line, as long as they are separated by ; • Ending a command with ; also tells Matlab to not display the output • If want output displayed, do not use ; >>2+2 ans = 4 >>

9. Variables • Variables are the basic building blocks • Capitalization matters, x not same as X • Matrix is a variable that contains multiple entries, i.e. V=[.98 1.02 .99 1.07]; • Matlab is great with vectors and matrices, however, their orientation and size matter • You will get errors if try to add vectors of different size or different orientation

11. Basic Operations • Always use brackets [ ] to define matrices • Always use parenthesis ( ) to call values of matrices • The row is always first, the column is always second, i.e. M1(3,2) is not the same as M1(2,3) • To see which variables exist, use >>whos • To delete variables x and y, use >>clear x y • To find out size use >>size(M1)

13. Elementary Algebra • Use +, -, *, / for basic operations • Use ./ and .* for element by element operations on matrices and vectors • Use / and * for matrix multiplication, but this only makes sense if you are familiar with Linear Algebra • Use ‘ to transpose a matrix • You can always multiply a matrix by a scalar • You can always overwrite old variables

16. Ranges of numbers Colon specifies range of numbers >>V3=[1:5] sets V3 to be the numbers 1 through 5 >>V3=[1:3:13]’ sets V3 to be the numbers 1 through 13, skipping every 3rd. Note, it is transposed >>M5=M1(1:2,1:5) sets M5 to be all the numbers in rows 1-2 and columns 1-5 of M1 >>V3=M1(:,2) sets V3 to be the whole second column of M1

18. Finding Data: Yahoo • Go to finance.yahoo.com • Enter a quote and hit get quotes • Click on historical prices (left toolbar) • Enter a date range, scroll to bottom and click Download To Spreadsheet • Open spreadsheet in Excel • Problem: dates come out weird if load into Matlab • Problem: this gives prices, usually need to convert them to returns

19. Finding Data: WRDS • Go to http://wrds-web.wharton.upenn.edu/wrds/connect/ • Follow directions to sign in • Select dataset (i.e. CRSP) • Select series (i.e. daily stocks) • Select company name (i.e. VLCM) and which info you want (i.e. prices and holding period return) • Click submit request and wait a moment • Open the text file • CRSP has historical stock and bond data, COMPUSTAT has accounting data

20. Stock Return • For most of our purposes the correct security return to use is the Holding Period Return • This is the return to you if you buy the security today, sell the security tomorrow, and keep any dividend payments from the security • Rt+1=(Pt+1+Dt)/Pt • Sometimes 1 is subtracted so that when the return is 3%, .03 instead of 1.03 is reported • CRSP does this • Use whatever convention you are most comfortable with, but make sure you are consistent

21. CRSP output

22. Loading Data • Open new .m file • Type dataset=[ ]; • Copy all of the data from your Excel or text file and paste it inside [ ] • Save the .m file in Matlab’s work directory (I recommend H:\Matlab) • For example call the file matlabin.m

23. Loading Data • At the Matlab prompt type: matlabin; • This executes any code in the file matlabin.m • Inside matlabin.m you have defined a matrix called dataset, this matrix now exists in Matlab’s memory just like any other matrix

24. Potential Problems • All rows must have same size!!!!!!!! • Matlab only knows numbers, it will give you errors if there are any letters in what you pasted!!!!!!! • Do not include field headings in your copy/paste

25. Potential Problems • Date formats (i.e. 28-Dec-1979) may be problematic. If pasting from Excel, I suggest not pasting dates, or formatting them to numbers • Don’t forget semicolon, otherwise all data will appear on screen • This procedure may crash your computer if dataset is too big (50000 numbers should be no problem)

26. Writing Data • Matlab can write any variable to a text file >>dlmwrite(‘filename.txt’, X, ’ ’); • You can then open this text file manually, or have Excel open it • If open in notepad, sometimes line breaks look weird. Just open it in something else, like Word or Wordpad • Related functions: dlmread, xlswrite, xlsread

27. Data Sets • I have created datasets from two securities British Petroleum (BP) and Volcom (VLCM) which are stored in files data_bp.m and data_vlcm.m • These contain the daily return for the year 2006 for each security • When you type >>data_bp; into the Matlab prompt a variable called bp is loaded into Matlab • Note that the file name (data_bp) is different from the variable name (bp), having same name will lead to problems!

28. Data Sets • bp has length 251 (251 trading days in 2006) • bp has width 4, the rows are: • Perm Number (unimportant info from CRSP) • Date • Price • Holding period return

29. Useful functions

32. More functions >>var(bp(:,4)) %variance >>cov(bp(:,4),bp(:,4)) %similar to corrcoef but gives the variance and covariance >>sum(bp(:,4)) %adds up all numbers in the 4th row of dataset >>abs(x) %absolute value >>x.^3 %takes powers (note, . only needed for element by element) >>exp(x) %exponent >>sqrt(x) %square root >>round(x) %rounds to nearest integer

33. Plots >>[a b]=size(vlcm); t=1:a; >>plot(t,vlcm(:,4),’b’);

34. Plots >>hold on; %keeps what is on current plot >>plot(t,bp(:,4),’r--’);

35. Multiple plots >>hold off; %turns off hold on >>subplot(2,1,1); %splits plot into 2 plots %split is vertical, currently on top plot >>plot(t,vlcm(:,3),’b’); >>subplot(2,1,2); %switches to bottom plot >>plot(vlcm(:,4),bp(:,4),’k.’);

37. Labels >>xlabel(‘Volcom’); >>ylabel(‘British Petroleum’); >>title(‘Scatter Plot of Returns’);

39. Saving your work >>save workspace1 x y % saves the %variables x and y in a file called %workspace1.mat >>save workspace1 % saves all variables in %workspace1.mat >>load workspace1 % loads the variables in %workspace1.mat >>clear all % deletes all variables

40. Getting help >>help %lists topic areas, for example %one of these is graph2d >>help graph2d %lists functions within %graph2d, for example plot >>help plot %gives help on plot >>lookfor keyword %searches for keywords within help, pretty slow

41. Next week • Logic • Loops • Creating your own functions

42. Functions we learned • General: whos, clear, size, dlmwrite, save • Matrix: zeros, ones, whos • Math: +, -, *, /, ^,sum, exp, abs, sqrt, round • Stats: min, max, mean, std, corrcoef, var, cov • Plots: plot, hold, subplot, xlabel, ylabel, title