Bias ratio (finance)

The bias ratio is an indicator used in finance to analyze the returns of investment portfolios, and in performing due diligence.

The bias ratio is a concrete metric that detects valuation bias or deliberate price manipulation of portfolio assets by a manager of a hedge fund, mutual fund or similar investment vehicle, without requiring disclosure (transparency) of the actual holdings. This metric measures abnormalities in the distribution of returns that indicate the presence of bias in subjective pricing. The formulation of the Bias Ratio stems from an insight into the behavior of asset managers as they address the expectations of investors with the valuation of assets that determine their performance.

The bias ratio measures how far the returns from an investment portfolio – e.g. one managed by a hedge fund – are from an unbiased distribution. Thus the bias ratio of a pure equity index will usually be close to 1. However, if a fund smooths its returns using subjective pricing of illiquid assets the bias ratio will be higher. As such, it can help identify the presence of illiquid securities where they are not expected.

The bias ratio was first defined by Adil Abdulali, a risk manager at the investment firm Protégé Partners. The concepts behind the bias ratio were formulated between 2001 and 2003 and privately used to screen money managers. The first public discussions on the subject took place in 2004 at New York University's Courant Institute and in 2006 at Columbia University.Courant Institute Study
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The bias ratio has since been used by a number of Risk Management professionals to spot suspicious funds that subsequently turned out to be frauds. The most spectacular example of this was reported in the ''Financial Times'' on 22 January 2009 titled "Bias ratio seen to unmask Madoff"!Bias ratio seen to unmask Madoff (Financial Times 22 January 2009)
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Explanation

Imagine that you are a hedge fund manager who invests in securities that are hard to value, such as mortgage-backed securities. Your peer group consists of funds with similar mandates, and all have track records with high Sharpe ratios, very few down months, and investor demand from the " ne per cent per month crowd. You are keenly aware that your potential investors look carefully at the characteristics of returns, including such calculations as the percentage of months with negative and positive returns.

Furthermore, assume that no pricing service can reliably price your portfolio, and the assets are often sui generis with no quoted market. In order to price the portfolio for return calculations, you poll dealers for prices on each security monthly and get results that vary widely on each asset. The following real-world example illustrates this theoretical construct.

When pricing this portfolio, standard market practice allows a manager to discard outliers and average the remaining prices. But what constitutes an outlier? Market participants contend that outliers are difficult to characterize methodically and thus use the heuristic rule "you know it when you see it." Visible outliers consider the particular security's characteristics and liquidity as well as the market environment in which quotes are solicited. After discarding outliers, a manager sums up the relevant figures and determines the net asset value ("NAV"). Now let's consider what happens when this NAV calculation results in a small monthly loss, such as -0.01%. Lo and behold, just before the CFO publishes the return, an aspiring junior analyst notices that the pricing process included a dealer quote 50% below all the other prices for that security. Throwing out that one quote would raise the monthly return to +0.01%.

A manager with high integrity faces two pricing alternatives. Either the manager can close the books, report the -0.01% return, and ignore new information, ensuring the consistency of the pricing policy (Option 1) or the manager can accept the improved data, report the +0.01% return, and document the reasons for discarding the quote (Option 2).

The smooth blue histogram represents a manager who employed Option 1, and the kinked red histogram represents a manager who chose Option 2 in those critical months. Given the proclivity of Hedge Fund investors for consistent, positive monthly returns, many a smart businessman might choose Option 2, resulting in more frequent small positive results and far fewer small negative ones than in Option 1. The "reserve" that allows "false positives" with regularity is evident in the unusual hump at the -1.5 Standard Deviation point. This psychology is summed up in a phrase often heard on trading desks on Wall Street, "let us take the pain now!" The geometry of this behavior in figure 1 is the area in between the blue line and the red line from -1σ to 0.0, which has been displaced, like toothpaste squeezed from a tube, farther out into negative territory.

By itself, such a small cover up might not concern some beyond the irritation of misstated return volatility. However, the empirical evidence that justifies using a "slippery slope" argument here includes almost every mortgage backed fund that has blown up because of valuation problems, such as the Safe Harbor fund, and equity funds such as the Bayou fund. Both funds ended up perpetrating outright fraud born from minor cover ups. More generally, financial history has several well-known examples where hiding small losses eventually led to fraud such as the Sumitomo copper affair as well as the demise of Barings Bank.

Mathematical formulation

Although the hump at $-\hat\sigma$ is difficult to model, behavior induced modifications manifest themselves in the shape of the return histogram around a small neighborhood of zero. It is approximated by a straightforward formula.

Let: , +\hat\sigma= the closed interval from the mean to $+1$ standard deviation of returns (including $0$)

Let: normally_distributed_returns_around_a_zero_mean.__Such_markets_have_distributions_with_a_bias_ratio_of_less_than_1.0.__Major_market_indices_support_this_intuition_and_have_bias_ratios_generally_greater_than_1.0_over_long_time_periods.__The_returns_of_equity_and_fixed_income_markets_as_well_as_Alpha_(investment).html" ;"title="normal distribution">normally distributed returns around a zero mean. Such markets have distributions with a bias ratio of less than 1.0. Major market indices support this intuition and have bias ratios generally greater than 1.0 over long time periods. The returns of equity and fixed income markets as well as alpha_generating_strategies_have_a_natural_positive_skew_that_manifests_in_a_smoothed_return_histogram_as_a_positive_slope_near_zero.__alpha_generating_strategies_have_a_natural_positive_skew_that_manifests_in_a_smoothed_return_histogram_as_a_positive_slope_near_zero.__Fixed_income">Fixed_income_strategies_with_a_relatively_constant_positive_return_("carry")_also_exhibit_total_return_series_with_a_naturally_positive_slope_near_zero.__Cash_investments_such_as_90-day_ alpha_generating_strategies_have_a_natural_positive_skew_that_manifests_in_a_smoothed_return_histogram_as_a_positive_slope_near_zero.__Fixed_income">Fixed_income_strategies_with_a_relatively_constant_positive_return_("carry")_also_exhibit_total_return_series_with_a_naturally_positive_slope_near_zero.__Cash_investments_such_as_90-day_T-bills#Treasury_bill">T-Bills_

United_States_Treasury_securities,_also_called_Treasuries_or_Treasurys,_are_government_debt_instruments_issued_by_the_United_States_Department_of_the_Treasury_to_finance_government_spending_as_an_alternative_to_taxation._Since_2012,_U.S._gov_...
_have_large_bias_ratios,_because_they_generally_do_not_experience_periodic_negative_returns.__Consequently,_the_bias_ratio_is_less_reliable_for_the_theoretic_hedge_fund_that_has_an_un-levered_portfolio_with_a_high_cash_balance.
Due_diligence,_due_to_the_inverted_x_and_y_axes,_involves_manipulation_and_instigation_and_extortion_etc.

_Contrast_to_other_metrics

_Vs._Sharpe_ratios

Since_the_Sharpe_ratio_
In_finance,_the_Sharpe_ratio_(also_known_as_the_Sharpe_index,_the_Sharpe_measure,_and_the_reward-to-variability_ratio)_measures_the_performance_of_an_investment_such_as_a_security_or_portfolio_compared_to_a__risk-free_asset,_after_adjusting_for_its_...