Tracking portfolios

Tracking Portfolio: A portfolio assembled with securities that will replicate a specific risk profile.

• Tracking portfolios commonly mirror an expected benchmark index, such as an index of global large capitalization stocks.

• The theoretical construction of a tracking portfolio done through multifactor modeling is done by setting each factor sensitivities equal to the factor sensitivities of the benchmark.

• For example, if a mid cap stock index is made of 500 stocks, then the portfolio manager can create a tracking portfolio through a sample of the 500 stocks that has a collective risk factor sensitivity equal to that of the index.

• Tracking portfolios can be used for hedging/risk management.

• For example, a portfolio manager may want to temporarily decrease the portfolio's risk exposure to a certain asset class (stocks, bonds, commodities, etc.) or sub-asset class (small cap stocks, high yield debt, gold, etc.) sector.

Investor Risk Tolerance and Multifactor Models

• Different individual investors will have different individual degrees of ability to bear risk.
• Therefore, not all investors should hold the same portfolio.
• A multifactor model can be used to design the optimal portfolio for the individual investor by overweighting and underweighting exposure different asset classes in the portfolio.
• Investors can increase their relative exposure to certain risk factors whenever their tolerance for the priced risk exceeds that of the average investor.

Fundamental Multifactor Models

Whereas APT is usually associated with economic risk exposures such as GDP growth, inflation, and interest rates, multifactor models can also be applied to a security's fundamental valuation traits following the multiple variable regression technique.

Standardized Beta = (Fundamental stock i - Fundamental avg stock ) / σ fund all stocks

• The standardized beta scales a fundamental value metric across all stocks.
• This formula can be applied to any stock fundamental valuation metric, such as price to earnings ratio.

Factor Models and the Sources of Risk and Return

• Fundamental multifactor models can be used to assess the sources of return and sources of risk for a portfolio manager's performance.

• Portfolio managers are commonly evaluated against some benchmark.

• For example, a U.S. small cap fund manager might be evaluated against the Russell 2000 index.

Active Return = Portfolio Return - Benchmark Return

Active Risk = Standard deviation of active returns = σ active returns

• Active risk is also called tracking risk or tracking error.

• Active returns for multiple periods are required to calculate active risk.

• Active Risk and Investment Strategy

• Indexing Strategy is a tracking error less than or equal to 1%.

• Enhanced Indexing is a tracking error of 2%.

• Moderately Active Strategy is a tracking error of 2% - 6%.

• Aggressive Active Strategy is a tracking error of 6% - 9%.

• The Information Ratio - Evaluating Active Risk

• Variation on the Sharpe Ratio to measure active return per unit of active risk.

IR = (Avg. Return Port - Avg. Return Benchmark)/ σ active returns

• A high information ratio may indicate that increased active management is worthwhile.
• For two active portfolios with the same benchmark, the portfolio with the higher information ratio is considered superior.

Active Risk Squared and Active Risk Factor Modeling

• Active risk can be explained using a fundamental factor model, just the same as active return can be explained with a fundamental factor model.

Active Risk Squared = Variance of Active Risk = The square of the standard deviations of active return = σ2 active returns

• Active Factor Risk: Comes from the portfolio manager assuming factor risk exposures that vary from the benchmark index.

• This is active risk factor mismatching by the portfolio manager.

• Active Specific Risk: Comes from portfolio weights on the asset sub-portfolios that comprise the whole portfolio.

• This is active security selection by the portfolio manager.

Active Risk Squared translates to = Active Factor Risk + Active Specific Risk.