1. Monte Carlo Stock Price Forecasting and Portfolio Optimization
By: Garrett Ashbaugh
Advisor: David Shaffer

2. Overview Background Previous Work My Project Results and Analysis
Questions

3. Background Efficient market Inefficient market Technical Analysis
Impossible to beat market because stocks reflect all available information
Inefficient market
Stock prices not always accurately priced
Technical Analysis
Use historical data to forecast future stock returns

4. Previous Work
Amman Stock Exchange, Dima Alrabadi and Nada Aljarajesh 2012
Compared Monte Carlo Simulation to Simple and Exponential Moving averages ( )
Monte Carlo Simulation correctly predicted their market
Monte Carlo Simulation, Magnu Erik Hvass Pedersen 2015
Compared Monte Carlo results of 3 companies to the S&P 500 index
Optimized portfolio by using mean-variance and geometric mean

5. My Project 3 parts: Quantopian Hypothesis: Monte Carlo Simulation
Portfolio Optimization
Trading
Quantopian
Hypothesis:
Method will yield higher returns than the market

6. Monte Carlo Simulation
Created a list of past 30 returns for a stock
Ran a projection 10 time steps into the future by taking a random sample for each time step
Today_price = Yesterday_price * e^(sample_return)

7. Monte Carlo Simulation cont.
Ran the simulation 1000 times
Took the end price of the simulation and averaged them all together

8. Difference = Projected Price – Yesterday Price Sortino Ratio
1/03/06
Yesterday Price
Projected Price
Difference
Sortino Ratio
ARNC
29.56
30.75
1.19
0.27
BAC
46.11
46.54
0.43
0.06
MRK
31.78
32.90
1.12
0.08
PFE
23.27
24.13
0.86
JPM
39.65
40.26
0.61
0.11
Difference = Projected Price – Yesterday Price
Sortino Ratio
Assets standard deviation of negative asset return
Harmful volatility

9. Portfolio Optimization
Started with universe of Dow Jones Industrial Average
Ran Monte Carlo Simulation
Took top 10 stocks with the highest Sortino Ratio
Out of that 10 took top 5 stocks with highest difference
% of portfolio was based on Sortino of the individual stock/total Sortino ratio of the 5 stocks

10. Total Sortino Ratio = (.27+.06+.08+.08+.11) = .60
1/03/06
Yesterday Price
Projected Price
Difference
Sortino Ratio
ARNC
29.56
30.75
1.19
0.27
BAC
46.11
46.54
0.43
0.06
MRK
31.78
32.90
1.12
0.08
PFE
23.27
24.13
0.86
JPM
39.65
40.26
0.61
0.11
ARNC Sortino Ratio = .27
Total Sortino Ratio = ( ) = .60
ARNC % Of Portfolio = .27/.60 = .45 = 45%

11. Trading Gave the simulation $100,000 to trade with
Buy and rebalance every week (Monday)
If stock dropped out of top 5 then sold all the shares
If stock was still in top 5 we bought/sold shares to reach desired %
Only bought if the Sortino Ratio was positive

12. Results Back tested at 3 different time periods (DOW) 2002-2005
Market fluctuated but ended around the same as it started
Market declined
Market increase

16. 70.46% from low
(18.7)%
(11.3)%

18.
(22.23%)

20. Peak = 16.58%
14.5%
(24.4)%
2.6%
Sortino Ratio

22.
53.98%

24. From low 96%
(6.6%)
Total Return 53.98%
Sortino Ratio 0.466
(16.3%)

25. Conclusions Decent predictor of the market Has Lags Possible changes:
Have short term checks
Short stocks if negative Sortino ratio
Have regression checks against the whole index
Take this algorithm to inefficient markets

26. Questions?

27. Works Cited
Alrabadi, Dima and Aljarayesh, Nada. “Forecasting Stock Market Returns Via Monte Carlo Simulation: The Case of Amman Stock Exchange.” Journal of Business Administration (2015)
Pedersen, Magnus Erik Hvass. "Portfolio Optimization and Monte Carlo Simulation." SSRN Electronic Journal SSRN Journal (2014): n. pag. Web.
Staff, Investopedia. "Efficient Market Hypothesis - EMH." Investopedia. N.p., 28 Sept Web. 18 Apr
Radcliffe, Brent. "Sortino Ratio." Investopedia. N.p., 26 Jan Web. 18 Apr