Engineering 25
Prob 7.18
Solution
Stock Market
Simulation:
Buy? Sell? Hold?
Bruce Mayer, PE
Licensed Electrical & Mechanical Engineer
BMayer@ChabotCollege.edu
Engineering/Math/Physics 25: Computational Methods
1
Bruce Mayer, PE
BMayer@ChabotCollege.edu • ENGR-25_HW-01_Solution.ppt
Scenario
 Behavior of Certain Stock
• Price, P, is randomly set by
NORMAL distribution
– µ = $100
– σ = $5
• Simulate Stock behavior over
250 days (1 trading year)
 Trading Algorithm
• If P<100, → BUY 50 Shares
• If P>105 → SELL ALL shares
• If 100< P < 105 → HOLD
• Add to Profit the Value of
Stock HELD at END of Year
Engineering/Math/Physics 25: Computational Methods
2
Bruce Mayer, PE
BMayer@ChabotCollege.edu • ENGR-25_HW-01_Solution.ppt
Key to Problem
 The Critical Issue required to
get close to the BOOK
answer is to realize:
 That at YEAR’S END we
must Assess the Value
of Any Shares NOT
SOLD
• We will Very Likely (84.13%
chance) have shares “Left
Over” if P250 < $105
 Add the Held-Over Value to
the previous selling profit
Engineering/Math/Physics 25: Computational Methods
3
Bruce Mayer, PE
BMayer@ChabotCollege.edu • ENGR-25_HW-01_Solution.ppt
MATLAB Code: Method-1
% Bruce Mayer, PE
% ENGR25 * 24Mar12
% StockMarket Timing Algorithm
% file = P7_18_Stock_Profit_Method1_1203.m
%
P = 5*randn(1,250) + 100; % stock price; a random no.
%
% Initalize changing variable
Profit = 0;
n = 0; % no. shares owned
s = 0; % days to SELL
b = 0; % days to BUY
na = 0; % days of No Activity
SH = 0; % Shares Held Vector
lenP = length(P)
for k = 1:length(P)
if P(k) <100
b = b+1; % buy days
BrokerFee = max(40, 50*.06);
Profit = Profit - 50*P(k) - BrokerFee;
n = n+50;
SH(k) = n;
elseif P(k)>105
s = s+1; % sell days
BrokerFee = max(40, n*.06);
Profit = Profit + n*P(k) - BrokerFee;
n = 0;
SH(k) = n;
else
n = n;
Profit = Profit;
na = na+1; % no activity days
SH(k) = n;
end
end
disp(' ')
disp('===== Stock purchase Profit summary ======')
%
SellDays = s
BuyDays = b
HoldDays = na
NoSharesLeftInPortfolio = n
YearEndPrice = P(250)
% Current Values shares leftover in Portfolio at Year's end
YearEndValue = n*P(250)
DailyProfit = Profit
% Add the year end "lump sum" value to previous day-to-day profit
TotalProfit = DailyProfit + YearEndValue
% Make frequency Plot
Engineering/Math/Physics 25: Computational Methods
4
Bruce Mayer, PE
BMayer@ChabotCollege.edu • ENGR-25_HW-01_Solution.ppt
Method-1 Results (1-Run)
=Stock purchase Profit summary =
SellDays =
38
BuyDays =
133
HoldDays =
79
NoSharesLeftInPortfolio =
50
YearEndPrice =
98.9097
YearEndValue =
4.9455e+003
DailyProfit =
6.4715e+004
TotalProfit =
6.9660e+004
Engineering/Math/Physics 25: Computational Methods
5
Bruce Mayer, PE
BMayer@ChabotCollege.edu • ENGR-25_HW-01_Solution.ppt
Method-1 Day-by-Day
35
30
No. Days
25
20
15
10
5
0
85
90
95
100
stock price
105
110
115
700
Shares Held
600
500
400
300
200
100
0
0
50
100
150
trading day
Engineering/Math/Physics 25: Computational Methods
6
200
Bruce Mayer, PE
BMayer@ChabotCollege.edu • ENGR-25_HW-01_Solution.ppt
250
Method-1 Single Run
35
30
No. Days
25
20
15
10
5
0
80
85
90
95
100
stock price
105
110
115
800
700
Shares Held
600
500
400
300
200
100
0
0
50
100
150
trading day
Engineering/Math/Physics 25: Computational Methods
7
200
250
Bruce Mayer, PE
BMayer@ChabotCollege.edu • ENGR-25_HW-01_Solution.ppt
300
MATLAB Code: Method-2
% Bruce Mayer, PE
% ENGR25 * 25Mar12
% StockMarket Timing Algorithm
% P7_18_Stock_Profit_Method2_1203.m
% METHOD-2
%
clear
%
m = 100; % central Location
s = 5; % Std Dev
n = 499; % number of runs
%
for p = 1:n
price = s*randn(1,250) + m; % generate 250 random prices in a
vector
%
% initialize accumulation vectors
shares_held = 0;
income_selling = zeros(1,250);
cost_new_shares = zeros(1,250);
commission = zeros(1,250);
for k = 1:250
if price(k) < 100 % BUY Shares in this case
shares_held = shares_held + 50;
commission(k) = max([40, .06*50]);
cost_new_shares(k) = 50*price(k) + commission(k);
shares(k)=shares_held;
end
if (price(k) > 105)&(shares_held > 0) % SELL Shares
commission(k) = max([40, .06*shares_held]);
income_selling(k) = shares_held*price(k) - commission(k);
shares_held = 0;
shares(k)=shares_held;
end
end
cost(p) = sum(cost_new_shares);
income(p) = sum(income_selling);
profit(p) = income(p) - cost(p) + price(250)*shares_held;
total_commission(p) = sum(commission);
shares_held_at_year_end(p) = shares_held;
YrEndPrice(p) = price(250);
end
disp('############################')% to break up runs
mean_yearly_profit = mean(profit)
min_yearly_profit = min(profit)
max_yearly_profit = max(profit)
std_profit = std(profit)
MEAN_YrEnd_Price = mean(YrEndPrice)
AVG_YrEnd_Shares = mean(shares_held_at_year_end)
Engineering/Math/Physics 25: Computational Methods
8
Bruce Mayer, PE
BMayer@ChabotCollege.edu • ENGR-25_HW-01_Solution.ppt
Method-2 Results
mean_yearly_profit =
6.5054e+004
min_yearly_profit =
4.9024e+004
max_yearly_profit =
9.0948e+004
std_profit =
5.7442e+003
MEAN_YrEnd_Price =
99.8867
AVG_YrEnd_Shares =
154.4088
MIN_YrEnd_Shares =
0
MAX_YrEnd_Shares =
1250
Engineering/Math/Physics 25: Computational Methods
9
Bruce Mayer, PE
BMayer@ChabotCollege.edu • ENGR-25_HW-01_Solution.ppt
Method-2 Plots
4
10
x 10
8
profit
6
4
2
0
0
50
100
150
200
250
300
Run No.
350
400
450
500
0
50
100
150
200
250
300
Run No.
350
400
450
500
1400
YearEnd Shares
1200
1000
800
600
400
200
0
Engineering/Math/Physics 25: Computational Methods
10
Bruce Mayer, PE
BMayer@ChabotCollege.edu • ENGR-25_HW-01_Solution.ppt
MATLAB Code: Method-1 →MultiRun
% Bruce Mayer, PE
% ENGR25 * 03Nov11 * Rev 26Mar12
% StockMarket Timing Algorithm
% file = P7_18_Stock_Pr1ce_Simulation_1111.m
% METHOD-1
clear
% run almost 500 Simulations
for m = 1:499
P = 5*randn(1,250) + 100; % stock price; a random no.
% Initalize changing variable
Profit = 0;
n = 0; % no. shares owned
s = 0; % days to SELL
b = 0; % days to BUY
na = 0; % days of No Activity (HOLD shares)
SH = 0; % Shares Held Vector
% lenP = length(P) => used for DeBugging Only
for k = 1:length(P)
if P(k) <100
b = b+1; % buy days
BrokerFee = max(40, 50*.06);
Profit = Profit - 50*P(k) - BrokerFee;
n = n+50;
SH(k) = n;
elseif P(k)>105
s = s+1; % sell days
BrokerFee = max(40, n*.06);
Profit = Profit + n*P(k) - BrokerFee;
n = 0;
SH(k) = 0;
else
na = na+1; % no activity days; HOLD shares
SH(k) = n;
end
end
disp(' ')
% have some Shares Left in portfolio. Sell ALL these at year's
end
EndIncome = P(250)*n;
%
% Build Vectors using m-counter
TotalProfit = Profit + EndIncome;
ProfitByRun(m) = TotalProfit;
SharesLeftInPortfolio(m) = SH(length(P));
SellDays(m) = s;
BuyDays(m) = b;
NoActivityDays(m) = na;
EndSharesByRun(m) = n
%
Bruce Mayer, PE
Engineering/Math/Physics
25: Computational Methods
11
BMayer@ChabotCollege.edu • ENGR-25_HW-01_Solution.ppt
Method-1: 499 Runs
= Stock purchase Profit summary =
MAXProfit =
8.5555e+004
MINProfit =
4.6147e+004
AvgProfit =
6.4593e+004
StdPprofit =
5.7947e+003
AvgEndShares =
168.0361
Engineering/Math/Physics 25: Computational Methods
12
Bruce Mayer, PE
BMayer@ChabotCollege.edu • ENGR-25_HW-01_Solution.ppt
Method-1: 499 Runs
4
10
x 10
8
profit
6
4
2
0
0
50
100
150
200
250
300
Run No.
350
400
450
500
0
50
100
150
200
250
300
Run No.
350
400
450
500
1200
YearEnd Shares
1000
800
600
400
200
0
Engineering/Math/Physics 25: Computational Methods
13
Bruce Mayer, PE
BMayer@ChabotCollege.edu • ENGR-25_HW-01_Solution.ppt