Risk Management for Mutual Fund Portfolios

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Risk Management for Mutual Fund Portfolios

• An Analysis of Linear Rebalancing Strategies

Mehmet ÖNAL David WIMBERLY
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Introduction

• We seek to apply formal risk management
  methodology to the optimization of mutual fund
  portfolios
• Our solution methodology is based on the CVaR
  approach outlined in Krokhmal et. al (2002)

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Introduction

• The problem is to find a strategy to allocate
  available fund to some number of accounts
• These accounts have daily returns

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Introduction

• The solution approach outlined in Krokhmal et al
  (2002) is to maximize expected daily rate of
  return subject to constraints on risk measure

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Introduction

• Krokhmal et al (2002) use several risk measures
• Mean Absolute Deviation (MAD)
• Conditional Drawdown at Risk (CDaR)
• Maximum Loss
• Conditional Value at Risk (CVaR)
• In our work we choose CVaR to be our risk measure

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Problem Formulation

• Maximize
• Subject to

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Problem Formulation

• where

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Problem Formulation

• We can reduce this program to a linear program
  with scenarios of equal probability of occurrence
• Each scenario is a vector of daily returns of
  accounts i1,2,,n

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Problem Formulation

• Maximize
• Subject to

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Problem Formulation

• where

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Problem Formulation

• As the days pass we obtain more information on
  the performances of the accounts
• We suggest resolving this optimization as the
  daily data become available, i.e., as the
  scenarios to consider increase

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Solution Approach

• Starting with a sufficient number of scenarios
  (in this work it is one year), we suggest
  re-optimizing (rebalancing the portfolio) in
  every 20 business days with the updated scenarios

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Solution Approach
time
Scenarios start on this day
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Solution Approach

• Begin with a sufficiently large number of
  scenarios
• While you are controlling the funds
• Run optimization on the in sample set
• Observe the performance of the portfolio for the
  following 20 days
• Update the in-sample set by adding 20 business
  days data

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Solution Approach

• We have approximately 5 years data to test the
  performance of this algorithm
• The data was obtained from Theta Research, Inc.,
  a mutual fund research firm which monitors mutual
  fund managers and their portfolio results

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Solution Approach

• We first optimize with the scenarios obtained in
  the first year (in-sample set data of 260 days)
• We then regularly rebalance the portfolio every
  20 business days, increasing the size of the
  in-sample set in each iteration

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Results

• We did all our calculations in MATLAB
• Optimal accounts found in the last in-sample
  optimization and their historical performances in
  the last 5 years are presented in the next slides
• The results were obtained with CVaRalt-0.995,
  a0.90 (recall that we worked on the loss
  function)

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Results

• Historical performance of our portfolio is shown
  below

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Results

• We were able to increase the performance of our
  methodology if we make the CVaR constraint
  tighter and constrain that no more than 15 of
  the funds can be allocated to any account

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• Historical performance of our portfolio with the
  additional constraints

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Conclusion

• Despite some issues with the data set, we were
  able to construct an efficient frontier and an
  optimal portfolio with the in-sample data
• We were able to run out-of-sample calculations
  and reached an overall result of a 5 loss on the
  first run
• On the second run, we were able to improve this
  to a breakeven position

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• We observed that we were dealing with funds which
  were all fund of funds
• It appeared the managers were all benchmarking
  the SP 500
• But our results were better than the SP 500 by a
  considerable margin

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