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

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Minimizing risk maximizing portfolio profit

Minimizing Risk… Maximizing Portfolio Profit

Team 76 – Manalapan High School

Jonathan Newman

Jesse Beyroutey

Dorothea Tsang

Andy Liu

David Trethewey

Minimizing risk maximizing portfolio profit

  • 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
Our Approach

  • Qualitative – Value Investment Theory

    • Fundamental Analysis

    • Investor’s discretion

  • Quantitative – Markowitz Model

    • Historical stock performance (to determine risk)

    • Predicted stock price


  • 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
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)

Modern portfolio theory mpt
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
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
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
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
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
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 model1
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


  • 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


  • 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