AC948 Case Studies in Financial Environments Lecture 4

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AC948 Case Studies in Financial Environments
Lecture 4

• Yuval Millo, AFM, U. of Essex

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Organisational aspects of arbitrage

• In the last lecture we saw how distributed agency
  in hedge funds (investors and traders) affected
  arbitrage positions.
• In this lecture we will focus on how that
  market-based risk management techniques, and
  especially Value at Risk (VaR) effected arbitrage
  operations in hedge funds such as LTCM.

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Discovering the value of a trading portfolio

• Traditional method price at the date of
  buying or selling
• Problem value changed between opening and
  closing positions, and liabilities may lead to
  losses
• Marking to market value is updated using market
  prices
• Assumption markets are liquid and assets can be
  turned to cash at any time

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Marking-to-model

• What if there is no liquid market for the assets
  (such as swaps)?
• Value is found using a mathematical model.
• As a result, the actual liquidity of the assets
  was less significant as a decision-making factor
  than the results that the model produced.
• What are the possible risks that may arise as a
  result?

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Expressing risk in simple terms

• As agency in trading firms become more
  diversified, and more different expertise was
  necessary, decision-making became challenging
• How much capital to allocate to each asset?
• How to spread the capital among the traders?
• Managers were looking for a method that would
  simplify the positions in the market.

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Value at Risk 1

• To allocate capital, it is necessary to assess
  the possible risk.
• For example, what is the maximal amount that a
  certain portfolio can lose during a trading day?
• 95 of the samples in a normal distribution are
  within 1.645 standard deviations from the mean.

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Value at Risk 2

• The maximal daily loss for 95 of the cases is
  calculated by
• 1.645 x x

daily volatility of the portfolio
Size of the portfolio
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RAROC

• Risk adjusted return on capital how much return
  per unit of risk.
• Like in VaR, it is assumed that returns follow a
  normal distribution.
• For example annual return / annual volatility
  can help to decide which stock is a better
  choice.

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VaR and RAROC as managerial tools

• The tools can be used to choose assets (design
  portfolios), but also to decide which trader, and
  which trading strategy gives the best return for
  the risk taken.
• For example, trader who has a low risk-adjusted
  return and high VaR would be demanded to keep
  higher capital reserves to compensate for losses.

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VaR as a managerial tools implication

• Using market-based risk management tools can
  bring about problems
• High market volatility ? breaching of VaR limits?
  Higher reserved capital ? imposed selling ? more
  market volatility
• In addition, as we saw in the 1987 case, such
  selling may be misinterpreted and bring about
  panic selling.