The bias ratio is an indicator used in
finance
Finance is the study and discipline of money, currency and capital assets. It is related to, but not synonymous with economics, the study of production, distribution, and consumption of money, assets, goods and services (the discipline of fina ...
to analyze the returns of investment portfolios, and in performing
due diligence
Due diligence is the investigation or exercise of care that a reasonable business or person is normally expected to take before entering into an agreement or contract with another party or an act with a certain standard of care.
It can be a l ...
.
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
A hedge fund is a pooled investment fund that trades in relatively liquid assets and is able to make extensive use of more complex trading, portfolio-construction, and risk management techniques in an attempt to improve performance, such as sho ...
– are from an unbiased distribution. Thus the bias ratio of a pure
equity index
In finance, a stock index, or stock market index, is an index that measures a stock market, or a subset of the stock market, that helps investors compare current stock price levels with past prices to calculate market performance.
Two of the ...
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](_blank)
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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
The ''Financial Times'' (''FT'') is a British daily newspaper printed in broadsheet and published digitally that focuses on business and economic current affairs. Based in London, England, the paper is owned by a Japanese holding company, Nik ...
'' on 22 January 2009 titled "Bias ratio seen to unmask Madoff"![Bias ratio seen to unmask Madoff (Financial Times 22 January 2009)](_blank)
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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
A mortgage-backed security (MBS) is a type of asset-backed security (an 'instrument') which is secured by a mortgage or collection of mortgages. The mortgages are aggregated and sold to a group of individuals (a government agency or investment ba ...
. Your peer group consists of funds with similar mandates, and all have track records with high 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 ...
s, 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
''Sui generis'' ( , ) is a Latin phrase that means "of its/their own kind", "in a class by itself", therefore "unique".
A number of disciplines use the term to refer to unique entities. These include:
* Biology, for species that do not fit in ...
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
Net asset value (NAV) is the value of an entity's assets minus the value of its liabilities, often in relation to open-end, mutual funds, hedge funds, and venture capital funds. Shares of such funds registered with the U.S. Securities and Exch ...
("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
A histogram is an approximate representation of the distribution of numerical data. The term was first introduced by Karl Pearson. To construct a histogram, the first step is to " bin" (or "bucket") the range of values—that is, divide the ent ...
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
The Sumitomo copper affair refers to a metal trading scandal in 1996 involving Yasuo Hamanaka, the chief copper trader of the Japanese trading house Sumitomo Corporation (Sumitomo). The scandal involves unauthorized trading over a 10-year period by ...
as well as the demise of Barings Bank
Barings Bank was a British merchant bank based in London, and one of England's List of oldest banks in continuous operation, oldest merchant banks after Berenberg Bank, Barings' close collaborator and German representative. It was founded in 1762 ...
.
Mathematical formulation
Although the hump at 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: the closed interval from the mean to standard deviation of returns (including )
Let: _measures_risk-adjusted_returns,_and_valuation_biases_are_expected_to_understate_volatility,_one_might_reasonably_expect_a_relationship_between_the_two.__For_example,_an_unexpectedly_high_Sharpe_ratio_may_be_a_flag_for_skeptical_practitioners_to_detect_smoothing_.__The_data_does_not_support_a_strong_statistical_relationship_between_a_high_bias_ratios_and_a_high_Sharpe_ratio.__High_bias_ratios_exist_only_in_strategies_that_have_traditionally_exhibited_high_Sharpe_ratios,_but_plenty_of_examples_exist_of_funds_in_such_strategies_with_high_bias_ratios_and_low_Sharpe_ratios.__The_prevalence_of_low_bias_ratios_funds_within_all_strategies_further_attenuates_any_relationship_between_the_two.
Hedge_fund_investors_use_serial_correlation_to_detect_smoothing_in_hedge_fund_returns.__Market_frictions_such_as_transaction_costs_and_information_processing_costs_that_cannot_be_arbitraged_away_lead_to_serial_correlation,_as_well_as_do_stale_prices_for_illiquid_assets.__Managed_prices_are_a_more_nefarious_cause_for_serial_correlation.__Confronted_with_illiquid,_hard_to_price_assets,_managers_may_use_some_leeway_to_arrive_at_the_fund's_NAV.__When_returns_are_smoothed_by_marking_securities_conservatively_in_the_good_months_and_aggressively_in_the_bad_months_a_manager_adds_serial_correlation_as_a_side_effect.__The_more_liquid_the_fund's_securities_are,_the_less_leeway_the_manager_has_to_make_up_the_numbers.
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