Exercise Set 2, Question 6

T=5;
a=0.15;
b=0.1;
r=0.05;

M=5000;
N=1000;
h=T/N;

A=(a-b^2/2)*h;
B=b*sqrt(h);
Z=randn(M,N);

valueatend=zeros(M,2);   % results of the investment by the 2 strategies

for j=1:M

S=1;
F=0;     % F=0 implies that 75% profit has not yet been acheived 

for i=1:N
   S=S*exp(A+B*Z(j,i));
   if S>=1.75 & F==0
     F=S*exp(r*T*(1-i/N));
   end
end

if F==0
   F=S;
end

valueatend(j,1)=F;
valueatend(j,2)=S;

end

mean(valueatend(:,1))
mean(valueatend(:,2))
std(valueatend(:,1))
std(valueatend(:,2))

Answers (reproduced in several runs) gave the expected value of the "sell high" strategy to be about 1.83 and the expected value of the "hold 5 years" strategy to be about 2.12 (the exact value for this, from question 3, is exp(0.75)=2.1170). BUT the standard deviation of the first strategy is only about 0.18 while for the second strategy it is 0.48. Thus, as usual in these things, the "cost" of a strategy with a high average return is high risk. It is interesting to look at the distributions of the returns from the 2 strategies, beyond just their means and variances, to decide what is relevant for an investment decision.

Back to main course page
Back to my main teaching page
Back to my home page