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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

  • 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