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Minimizing Risk… Maximizing Portfolio ProfitPowerPoint Presentation

Minimizing Risk… Maximizing Portfolio Profit

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### Minimizing Risk… Maximizing Portfolio Profit

Team 76 – Manalapan High School

Jonathan Newman

Jesse Beyroutey

Dorothea Tsang

Andy Liu

David Trethewey

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

Our Approach

- Qualitative – Value Investment Theory
- Fundamental Analysis
- Investor’s discretion

- Quantitative – Markowitz Model
- Historical stock performance (to determine risk)
- Predicted stock price

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

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)

Price to Sales Ratio(P/S ratio)

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

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

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

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)

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

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

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

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

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

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