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Equity Portfolio Tracking Error. Raman Vardharaj Quantitative Portfolio Manager Guardian Life Insurance. This presentation is based on the following unpublished paper: “Determinants of tracking error for equity portfolios” by Raman Vardharaj, Frank Jones and Frank Fabozzi.

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equity portfolio tracking error

Equity Portfolio Tracking Error

Raman Vardharaj

Quantitative Portfolio Manager

Guardian Life Insurance

This presentation is based on the following unpublished paper: “Determinants of tracking error for equity portfolios” by Raman Vardharaj, Frank Jones and Frank Fabozzi.

slide2

How do you measure the risk of a stock portfolio?

  • Absolute risk: Volatility of returns
  • Relative risk: Volatility relative to a benchmark
      • Example: Tracking error or Active risk
slide3

Definition of Tracking Error

  • Active return = Portfolio return - Benchmark return
  • Tracking error = standard deviation of active returns
    • Application:Information ratio = alpha / tracking error
    • (Alpha = average active return)
  • Estimation of tracking error:
    • - Trailing active returns (backward looking estimate)
    • - Risk model e.g., Barra (forward looking estimate)
slide4

A Measure of Risk

  • An important risk metric for portfolios that are managed versus a benchmark
  • Typical values:
    • - 0% for index funds
    • - less than 2% for enhanced index funds
    • - 5% for active large cap stock funds
slide5

Tracking Error: An Example

Tracking Error = 4%

Cumulative

Return

Rtn(BM) +4%

Benchmark

Cumulative

Return

1 Std Dev

or

66% confident

Rtn(Benchmark)

Rtn(BM) -4%

Today

Time

One year

from now

slide6

Tracking Error: An Example

Tracking Error = 1%

Cumulative

Return

Benchmark

Cumulative

Return

Rtn(BM) +1%

1 Std Dev

or

66% confident

Rtn(Benchmark)

Rtn(BM) -1%

Today

Time

One year

from now

slide7

Determinants of tracking error

  • Number of stocks held - those in the benchmark and those not in the benchmark
  • Size or Style or Sector bets
  • Beta
  • Benchmark volatility
slide8

Effect of number of stocks

  • Tracking error falls as the portfolio includes more and more of the stocks in the benchmark
  • An optimally constructed portfolio of just 50 stocks can track the S&P 500 within 2%
  • Tracking error rises as the portfolio starts to include stocks that are not in the benchmark
slide13

Effect of size and style

  • Tracking error rises as the portfolio deviates from its benchmark in terms of average market cap (size) or investment valuation (style)
  • Different portfolios can have the same tracking error
slide15

Effect of sector bets and beta

  • Tracking error rises as the portfolio’s sector allocations begin to differ from those of the benchmark
  • Tracking error rises as the portfolio’s beta with respect to the benchmark begins to differ from 1
  • Holding cash decreases a portfolio’s overall volatility but increases its tracking error
slide18

Why is it important to monitor the portfolio tracking error?

  • Probability of dramatic shortfall (active return < -10%) rises with tracking error
  • Probability of dramatic outperformance also rises with tracking error
  • Management consequences of the two are asymmetric