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Functions

Functions. Downloads. Today’s work is in: matlab_lec02.m Functions we need today: myfunction.m, windsorise.m, npv.m. Overview. Logic Control Structures (if, for) Functions Financial Example: NPV and Gordon Growth Model. Logic. 1 means True, 0 means False

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Functions

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  1. Functions

  2. Downloads • Today’s work is in: matlab_lec02.m • Functions we need today: myfunction.m, windsorise.m, npv.m

  3. Overview • Logic • Control Structures (if, for) • Functions • Financial Example: NPV and Gordon Growth Model

  4. Logic • 1 means True, 0 means False • == is used for logic, = to assign values >>1==1 ans = 1 >>1==2 ans = 0 >>x=5; %assigns value 5 to x >>x==5; %checks if x is equal to 5, returns either 1 %or 0 >>x=(x==5); %checks if x is equal to 5, then %assigns True (1) or False (0) to x

  5. Logical Operators == % equal to ~= % not equal to > % greater than >= % greater than or equal to < % less than <= % less than or equal to & % and | % or (top left of keyboard)

  6. Examples >>A=[zeros(3,1); ones(3,1); 2*ones(3,1); 3*ones(3,1)]; >>in1=(A>0); >>A(A>0); % is same as A(in1) >>in2=(A<1 | A>2); >>in3=(A>1 & A<3); >>in4=(A~=2);

  7. Examples • In the matlab prompt

  8. if statements >>if A(1)==0; x=5; y=x; end; • All function names are lower case >>if (logical statement); (command to be executed); end;

  9. if-else statements >>if A(3)==A(4); x=A(5); y=A(4); elseif A(3)==0; x=5; y=0; elseif A(3)==1; x=4; y=5; else; x=3; y=8; end; • Just like if statement but adds a elseif and else

  10. for statements and loops >>T=100; s=0; x=0; >>for i=1:T; s=s+i; x=x+i*i; end; • This loop calculates a sum and a sum of squares s=1+2+3+… 100 x=12+22+32+… 1002 • Be careful with variables having same name as index, or making changes to index while inside loop • Make sure variables are initialized

  11. Nested Loops >>for i=1:5; for j=1:5; B(i,j)=min(i,j); end; end;

  12. Loop withoutusing for >>i=0; >>while i<10; i=i+1; disp(i); end; • Beware of infinite loops!

  13. Alternatives to Loops • Loops are slow, matrix operations are fast • Avoid using loops if you can! >>x=0; >>for i=1:5; x=x+i*i; end; • Alternative: >>A=[1:5]; x=sum(A.*A);

  14. Example: Mean and StDev >>[T L]=size(bp); >>s=0; s2=0; >>for i=1:T; s=s+bp(i,4); s2=s2+(bp(i,4)^2); end; >>M=s/T; StD=sqrt((s2/T)-M*M); >>disp([mean(bp(:,4)) M]); >>disp([std(bp(:,4)) StD]);

  15. Functions • Functions created in .m files • Unlike scripts, you can call on functions, and functions can return values • For example f(x,y)=5*x+3*y is a function that takes in arguments x and y, returns f(x,y) • Matlab has many intrinsic functions (i.e. log(.), corrcoef(. , .), mean(.) • Functions can take in zero, one or many arguments • Functions can return zero or one argument, but that argument can be a matrix

  16. A simple function function z=myfunction(x,y); z=(x.^2)+2*x.*y+(y.^2); %-This function can take in scalars or vectors %-Functions do not change the values of the % arguments that are passed to them, that % is, they are independent of the external % environment

  17. Windsorization function W=windsorise(x,lowcut,highcut); [T L]=size(x); z=x; y=sort(x); for i=1:T; if z(i)<y(round(lowcut*T)); z(i)=y(round(lowcut*T)); end; if z(i)>y(round(highcut*T)); z(i)=y(round(highcut*T)); end; end; W=[z y];

  18. Using windsorise • In matlab prompt plot regular series and windsorised series >>data_bp; >>X=windsorise(bp(:,4),.05,.95); >>plot(bp(:,4)); >>hold on; >>plot(X(:,1), 'r');

  19. NPV:The Model • Model: • When D(t+1)=D(t)*(1+g) and the sum is infinite, this reduces to Gordon Growth Model: • When g=0, this reduces to: • What if growth stops after Ts? • How else can you modify this model? Value firms vs. Growth firms?

  20. NPV: The function function y=npv(d,r,g,T,Ts); y=0; cf=zeros(T,1); cf(1)=d; for t=1:T; if t<=Ts; cf(t+1)=cf(t)*(1+g); else; cf(t+1)=cf(t); end; y=y+cf(t)/((1+r)^t); end;

  21. Using the NPV function >>d=1; r=.05; g=.02; T=20; Ts=10; >>p=npv(d,r,g,T,Ts); >>T=200; p=zeros(T,1); >>for t=1:T; p(t)=npv(d,r,g,t,t); end; >>hold off; plot([1:T],p, 'b'); >>hold on; >>plot([1:T],ones(1,T)*(d/(r-g)), 'r--');

  22. NPV function: extensions • Growth firms: little cash flow now, lots of cash flow later • Value firms: lots of cash flow now • Cash flows that vary arbitrarily? ie input an arbitrary cash flow stream • Cash flows that vary randomly? Use rand() and randn() functions • Time varying returns?

  23. Next week • Randomization • Simulation • Real finance!

  24. Functions we learned • Logic: ==, ~=, <, <=, >, >=, &, | • Control Structures: if, else, for • Math: sort • Ours: windsorize, npv

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