Financial Education

The Sharpe ratio compares excess returns to total portfolio risk, measuring risk as the standard deviation of portfolio returns.

The numerator of the Sharpe ratio is the difference between the portfolio return and the risk-free rate. The denominator is the standard deviation of portfolio returns.

The Sharpe ratio may identify a manager as not being skillful even when the Treynor measure or Jensen’s alpha suggest skill. This could result when the manager accepts large amounts of non-systematic risks (which would be reflected in standard deviation of returns but not portfolio beta.)

Investors measure performance against a number of metrics, some of which can be considered valid benchmarks and others of which cannot.

Absolute return can be an objective (I want to earn 10% annually.) However, a 10% return is not investable and therefore does not make a valid benchmark.

Manager universes are useful comparisons after the fact. But they investments made by the manager universe are not specified in advance so managers cannot use skill to perform better.

Broad market indices meet most of the criteria for benchmarks, and are suitable provided they reflect the manager’s style.

Style indices (such as the S&P 500 Growth Index) are well known, easily understood and widely available. They are generally appropriate as benchmarks, with a couple of caveats:

• Style definition can be ambiguous and may be inconsistent with the manager’s investment process
• Some style indices have larger weights in particular securities or sectors than a manager would consider prudent

Benchmarks based on factor models relate one or more systematic sources of return to the returns on the account. The capital asset pricing model is a single-factor model in which the factor is the market risk premium. Factor models can be useful for performance evaluation because they identify the sources of return and can provide insight as to a manager’s style. However, they are ill suited as benchmarks because the securities are not specified in advance, they are ambiguous, and managers probably do not think in terms of factors when making their decisions.

Returns based benchmarks compare a manager’s return to the returns of several style indices to solve for the combination of styles that best explains the manager’s return. They meet many criteria for being valid benchmarks, but the mix of underlying styles may not reflect the manager’s investment process.  If the manager rotates among styles rather than keeping a relatively constant mix it would be inappropriate.

Custom benchmarks weight the manager’s universe in a fashion that reflects the manager’s weighting style. Custom benchmarks meet all criteria of valid benchmarks and are useful for performance evaluation. However, they can be expensive to construct and maintain, and lack of transparency could be a concern.

The momentum anomaly refers to the fact that a strategy of buying past winners and selling past losers produces returns that are not explained by the Capital Asset Pricing Model framework. Proponents of the efficient market hypothesis (EMH) attribute the momentum anomaly to risk factors that are not captured in Beta, while opponents point to the anomaly as evidence against the EMH.

In the October 2007 Journal of Finance, Avromov et. al. find that the influence of momentum is limited to a small sample (4% of market capitalization) of companies with high credit risk. This study offers support to the efficient market hypothesis and the argument that the excess returns are attributable to a risk factor (in this case, credit quality.)

An unweighted securities index assigns equal value to each index component regardless of its relative price or market capitalization. It is equivalent to investing the same dollar amount in each index component.

Smaller cap stocks will receive a higher weighting in an unweighted index than they would in a value-weighted index. This can lead to a bias toward small cap stocks over time.

Firms complying to Global Investment Performance Standards (GIPS(R)) must disclose whether the returns are being presented gross of fees (return on assets less direct trading expenses) or net of fees (gross return less management fees). Any other fees deducted should also be disclosed, along with the fee schedule appropriate to a given presentation.

Firms must also disclose:

• Their use of leverage or derivatives in sufficient detail to allow investors to identify the related risk
• Conformity with local laws that conflict with GIPS
• Any non-compliant performance records

Firms must show 10 years of GIPS compliant returns (or as many as are available if fewer than 10). This includes the annual return in each year, the number of portfolios and dispersion of returns in the composite (if 6 or more portfolios), the amount of assets in the composite, the total firm assets (or percentage represented by the composite), and the benchmark return.

The Treynor measure relates excess returns to the systematic risks assumed by a manager. In this regard, it provides the same assessment of manager’s skill as does Jensen’s alpha.

The numerator for the Treynor ratio is the difference between the return on the portfolio and the risk free rate. The denominator is the manager’s beta.

The Treynor ratio can be conceived as the slope of a line connecting the risk free rate to the point representing the portfolio’s average return and beta.

In order to determine the success of an investment strategy it must be compared to a benchmark. A valid benchmark should possess the following qualities:

• Unambiguous - the identities and weights of securities or factor exposures should be clearly defined
• Investable - could the investment be placed in the benchmark itself rather than being managed actively
• Measurable - the return should be readily available or calculable
• Appropriate - the benchmark should reflect the manager’s style or expertise
• Reflective of current investment opinions - an equity manager has opinions (positive or negative) on equities but may have no opinions on fixed income securities. The latter should not be included in a valid benchmark.
• Specified in advance - all interested parties should know the benchmark and its constituents before an evaluation period begins
• Owned - the manager is willing to accept responsibility for performance relative to the benchmark

A value weighted security index is calculated by summing the market capitalization of each stock in the index. A derivation of a value weighted index is the float weighted index, which uses only the freely trading shares to calculate market capitalization. Today, most capitalization weighted indexes are actually float-weighted.

A major advantage of value weighted indexes is that they automatically adjust for corporate actions such as stock splits. The decline in value per share following a split is exactly offset by the increase in the total shares outstanding. Stocks with higher market capitalization receive relatively more weight in the index.

The Sharpe ratio is often used for evaluating hedge fund performance. However, it has often been criticized for relying on the assumption that returns are normally distributed.

In the September 2007 Journal of Banking and Finance, Eling and Schuhmacher examine the Sharpe ratio and other performance measurement tools for evaluating hedge funds. By ranking hedge fund returns against 12 different performance measures, they find a high correlation between the different measures, suggesting that the choice of measure may not be a significant concern. The lowest correlations are between the Sharpe ratio, the Treynor ratio and Jensen’s alpha.

Given its practical advantages over other return measures, the Sharpe ratio’s popularity is now supported by empirical evidence. The authors find it to be an adequate measure of hedge fund performance.

In the May 2007 Review of Financial Studies, Duarte, Longstaff and Yu examine the risk/return characteristics of commonly used fixed-income arbitrage strategies. They find that the strategies that require high levels of modeling produce significant positive excess returns even after adjusting for risk, transaction costs and management fees.

Fixed income arbitrage strategies tend to exploit small differences between intrinsic value and market prices for securities. There has been some debate as to whether they are truly low risk arbitrage or whether the small positive returns most frequently earned are offset by infrequent but dramatic losses.

Of five strategies tested, the ones requiring the greatest intellectual capital - yield curve, mortgage and capital structure arbitrage - produced the highest excess returns after controlling for risk and costs. Swap spread arbitrage also produced positive risk adjusted returns.

Volatility arbitrage, or selling options on fixed income instruments and hedging the underlying asset exposure, produced positive excess returns but also had periods of significant losses.