### Project Description

First it may be prudent to establish that conceptually, “performance” is not always positive. That is, even when an investment decreases in value it can still be performing well. Outside of investment you may have a common cognitive bias towards associating “performance” with success and skill, perhaps even going as far as to associate a good performance with a high probability of winning. This bias may prove problematic in investing as an investment may still be “winning” whilst losing money; particularly in the context of “outperforming” another investment or index which is also losing value, i.e simply losing **less **value. As long as this investment is decreasing at a time that **another** investment is **making** money (*and ideally more than that which is lost)* then overall portfolio risk will be decreased, volatility reduced and risk-adjusted returns will result. This is the nature of correlation.

Without statistical measures of “success”, or similar instruments to compare to or **benchmark** against, we are left to a very base understanding of an investment’s performance: did it go up, or did it go down in value? This binary understanding of risk and return will only go as far as to categorize up as good, and down as bad. It is imperative to acknowledge that “performance” in the context of investment is multi-dimensional and **up** or **down** is the result of performance, not the cause. This bias toward price over correlation and volatility is a common one. It is however a myopic view, and proves to be an immovable barrier to creating risk-adjusted portfolios with predictable returns- the presiding goal of the intelligent investor.

The following can be used to guide your own approach to performance analysis. Your investment objectives; choice of assets, tenure, risk profile and experience will ultimately determine the most appropriate measures of “success” and allow you to continue to invest with conviction, irrespective of “the market” and its movements.

**Benchmarks**

Universally, a Benchmark is a standard or point of reference against which things may be compared. Commonly for equity investments people will look to equity indices to provide a point of comparison. For an equity investor investing in a diversified basket of global companies many will look to the **MSCI World Index**, which is a stock market index of 1,643 stocks from across the globe, mainted by MSCI Inc. (formerly Morgan Stanley Capital International). The number of indices has increased exponentially with the introduction of new markets, asset classes and groupings of instruments. If the index produces +7% over the year and the investor produces +8% in the same year then he has *outperformed* the index. Similarly, and somewhat paradoxically, if the index had produced -7% over the year, and the investor had produced -5%, he has **still** outperformed the index. In this instance he has out-performed his benchmark. This is positive **relative performance. **The **for both the investor, and the index have been negative.** The investor’s skill has been rewarded with suffering less losses than his benchmark- the market at large.

**Information Ratio**

To objectively compare performance to a benchmark you may look to the Information Ratio which is a ratio of portfolio returns above the returns of a benchmark (usually an index) to the volatility of those returns. The information ratio (IR) measures a portfolio manager’s ability to generate excess returns relative to a benchmark, but also attempts to identify the consistency of the investor. This ratio will identify if a manager has beaten the benchmark by a lot in a few months or a little every month. The higher the IR the more consistent a manager is and consistency is an ideal trait.

**Sharpe Ratio**

The Sharpe Ratio is a measure for calculating risk-adjusted return, and this ratio has become the industry standard for such calculations. It was developed by Nobel laureate William F. Sharpe and we look at it in detail here. The Sharpe ratio is the average return earned in excess of the risk-free rate per unit of volatility or total risk. Subtracting the risk-free rate from the mean return, the performance associated with risk-taking activities can be isolated. One intuition of this calculation is that a portfolio engaging in “zero risk” investment, such as the purchase of U.S. Treasury bills (for which the expected return is the risk-free rate), has a Sharpe ratio of exactly zero. Generally, the greater the value of the Sharpe ratio, the more attractive the risk-adjusted return.

**Sortino Ratio**

This is a modification of the Sharpe ratio that differentiates harmful volatility from general volatility by taking into account the standard deviation of negative asset returns, called downside deviation. The Sortino ratio subtracts the risk-free rate of return from the portfolio’s return, and then divides that by the downside deviation. A large Sortino ratio indicates there is a low probability of a large loss. This is an improvement on the Sharpe ratio that provides a more holistic picture of risk/return, also factoring in downside volatility.

**R-Squared**

This is a statistical measure that in investment represents the percentage of a fund or security’s movements that can be explained by movements in a benchmark index. For fixed-income securities, the benchmark is the T-bill. For equities, the benchmark is the S&P 500. R squared is reported as a number between 0 and 100. A high R squared value will indicate that performance is attributable to the index. A low R squared does not necessarily mean poor performance; simply less correlative relation to the index. This is not to be confused with *beta,* which is a measure of sensitivity to changes in its index, i.e. more or less sensitive than the index. A low R-squared means you should ignore the beta.

**Jenson Measure**

This is a risk-adjusted performance measure that represents the average return on a portfolio over and above that predicted by the capital asset pricing model (CAPM), given the portfolio’s beta and the average market return. This is the portfolio’s alpha. In fact, the concept is sometimes referred to as “Jensen’s alpha”. The basic idea is that to analyze the performance of an investment manager you must look not only at the overall return of a portfolio, but also at the risk of that portfolio. For example, if there are two mutual funds that both have a 12% return, a rational investor will want the fund that is less risky. Jensen’s measure is one of the ways to help determine if a portfolio is earning the proper return for its level of risk. If the value is positive, then the portfolio is earning excess returns. In other words, a positive value for Jensen’s alpha means a fund manager has “beat the market” with his or her stock picking skills.

**Treynor Ratio**

This ratio, developed by Jack Treynor, measures returns earned in excess of that which could have been earned on a riskless investment per each unit of market risk. The Treynor ratio is calculated as:

**(Average Return of the Portfolio – Average Return of the Risk-Free Rate) / Beta of the Portfolio **

In other words, the Treynor ratio is a risk-adjusted measure of return based on systematic risk. It is similar to the Sharpe ratio, with the difference being that the Treynor ratio uses beta as the measurement of volatility. Treynor was in fact one of the earliest architects of the Capital Asset Pricing Model (CAPM) that is commonly attributed to Sharpe, Litner and Mossin. The evolution of risk management theory will no doubt continue, alongside developments in our financial markets and the instruments that populate them.

Any one of the above performance measurement ratios will be of little use in isolation and no one of them precludes use of the other. In answering the question **“how do I measure investment performance?”** it is important that you establish your own parameters for risk, and then for return, to establish which resulting values of the above ratios will be favorable, and which will put your portfolio outside of its intended remit for risk, return or both. Fundamentally, benchmarking a portfolio can also be impeded by the unique nature of some portfolios which are composed of different instruments from different asset classes which in some cases have no sufficient, representative benchmark. This is particularly true for more esoteric instruments like structured products and hedge funds. A portfolio composed of managed futures hedge funds, frontier market equity, direct real estate investment and peer-to-peer lending funds would be near impossible to model with any degree of useful accuracy. Such is the nature of portfolio management. Isolated scenarios aside, numerous measures can be taken to mitigate and reduce risk and as such **assessing** **performance** in binary *up/down* terms is not only hugely reductive, but can also be damaging.

[sources]

– JOURNAL OF INVESTMENT MANAGEMENT , Vol. 1, No. 2, (2003), pp. 60–72, 2003

– Journal of Economic Perspectives—Volume 18, Number 3—Summer 2004 —Pages 25– 46, The Capital Asset Pricing Model: Theory and Evidence

– Investment Performance Measurement By Bruce J. Feibel

– Calculating Return on Investment of Training Using Process Variation: Santiago Matalonga, Tomás San Feliu.

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