Minimizing Risk… Maximizing Portfolio Profit

1. Minimizing Risk… Maximizing Portfolio Profit Team 76 – Manalapan High School Jonathan Newman Jesse Beyroutey Dorothea Tsang Andy Liu David Trethewey

2. Goal • Maximize net profit by investing $30,000 in technology stocks • Find the combination of stocks with the minimum risk required to achieve a certain profit

3. Our Approach • Qualitative – Value Investment Theory • Fundamental Analysis • Investor’s discretion • Quantitative – Markowitz Model • Historical stock performance (to determine risk) • Predicted stock price

4. Assumptions • Investors are rational • The market is generally rising • In addition to stocks we can invest in treasury bills (which have no risk) • No transaction cost or commission • The forward price-to-earnings ratio is relatively accurate over one year

5. Value Investment Theory • Used current fundamental indicators to evaluate company performance • Free Cash Flow (FCF) • Return on Investment Capital (ROIC) • Price to Earnings Ratio (P/E ratio) • Price to Sales Ratio (P/S ratio) • Beta (β)

6. Free Cash Flow (FCF)

7. Return on Invested Capital (ROIC)

8. Price to Earnings Ratio (Forward P/E ratio)

9. Price to Sales Ratio(P/S ratio)

10. Beta

11. Value Investment Allocations

12. Modern Portfolio Theory (MPT) • Reduces the risk of investing by diversifying stock allocations • Models stock price variance as “risk” • Includes treasury bills as a risk-free alternative

13. MPT Ramifications • To make greater returns, more risk must be assumed • Investment in any stock must be justified against the no-risk T-bill • A model can be designed to allocate stocks for minimum risk

15. The Magic of Covariance • Find covariance of each pair of stocks with historical price data • Two relationships: • Negative covariance • Positive covariance • Adding a risky stock to our portfolio can decrease the portfolio risk

16. Method Behind the Model • Goal: find the efficient frontier to find a portfolio with a desired return • Quadratic programming optimization model • Constraints • An expected rate of return • A limit on invested capital ($30,000)

17. Inputs to Model • Projected stock price after one year • Assumed the forward P/E ratio was relatively accurate • Used one-year earnings predictions to find stock price • Covariance matrix • Based on historical stock prices • Stocks with negative covariance reduce overall risk

19. Testing the Model • For small returns, most of the money is invested in no risk treasury bills • If bigger returns are expected, the portfolio should take on riskier investments instead of T-bills • For impossibly high returns, no solution is found by the program

20. Testing the Model • We first tried a small return of 3.33% ($1000) • All the money was invested in treasury bills as expected • Moderate return of 10% ($3000) • Diverse portfolio with low volatility • Mostly T-bills • Higher returns of 33% and 100% • T-bills nearly eliminated

21. Distribution of Stocks Moderate Return (33%)

22. Value Investment Performance

23. MPT 10% Performance

24. MPT 33% Performance

25. MPT 100% Performance

26. Profits Between Methods

27. Limitations • Uses normal distribution to model risk • Positive deviation from expected return is viewed the same as negative deviation • Negative deviations should be considered more risky for purposes of the model • Use of only downside semi-variance could correct this

28. Conclusion • In order to mitigate risks, counter-intuitive actions must be taken • For every increase in profit required, a proportional increase in risk is assumed • Value investing strategy is best for picking stocks; the Markowitz model optimizes the distribution among good stocks