Huai Yeek. The dollar-weighted average will be the internal rate of return between the initial and final value of the account, including additions and withdrawals. Excel can solve this very quickly. Hence, if alpha is not sufficiently large, the portfolio is inferior to the index. Another way to think about this conclusion is to note that, even for a portfolio with a positive alpha, if its diversifiable risk is sufficiently large, thereby reducing the correlation with the market index, this can result in a lower Sharpe ratio.

The IRR i. Under some conditions, the IRR is greater than each of the other two averages, and similarly, under other conditions, the IRR can also be less than each of the other averages. A number of scenarios can be developed to illustrate this conclusion. All rights reserved. No reproduction or distribution without the prior written consent of McGraw-Hill Education. Chapter 24 - Portfolio Performance Evaluation example, consider a scenario where the rate of return each period consistently increases over several time periods.

If the amount invested also increases each period, and then all of the proceeds are withdrawn at the end of several periods, the IRR is greater than either the geometric or the arithmetic average because more money is invested at the higher rates than at the lower rates. On the other hand, if withdrawals gradually reduce the amount invested as the rate of return increases, then the IRR is less than each of the other averages.

Similar scenarios are illustrated with numerical examples in the text, where the IRR is shown to be less than the geometric average, and in Concept Check 1, where the IRR is greater than the geometric average. It is not necessarily wise to shift resources to timing at the expense of security selection. There is also tremendous potential value in security analysis. The decision as to whether to shift resources has to be made on the basis of the macro, compared to the micro, forecasting ability of the portfolio management team.

Note: We used 5 degrees of freedom in calculating standard deviations. The reason for this result is the fact that the greater variance of XYZ drives the geometric average further below the arithmetic average. Therefore, if the data reflect the probabilities of future returns, 10 percent is the expected rate of return for both stocks.

Chapter 24 - Portfolio Performance Evaluation b. The IRR exceeds the other averages because the investment fund was the largest when the highest return occurred. Chapter 24 - Portfolio Performance Evaluation 8.

### Conditions of Use

If you will hold only one of the two portfolios, then the Sharpe measure is the appropriate criterion:. Since the Sharpe measure is higher for Stock A, then A is the best choice. Chapter 24 - Portfolio Performance Evaluation We need to distinguish between market timing and security selection abilities. The intercept of the scatter diagram is a measure of stock selection ability.

Stock selection must be the source of the positive excess returns. Timing ability is indicated by the curvature of the plotted line. Lines that become steeper as you move to the right along the horizontal axis show good timing ability. The steeper slope shows that the manager maintained higher portfolio sensitivity to market swings i.

This ability to choose more market-sensitive securities in anticipation of market upturns is the essence of good timing. In contrast, a declining slope as you move to the right means that the portfolio was more sensitive to the market when the market did poorly and less sensitive when the market did well.

## Performance Evaluation and Attribution of Security Portfolios [Book]

This indicates poor timing. We can therefore classify performance for the four managers as follows: Selection Ability Timing Ability A. Bad Good B. Good Good C.

## Portfolio construction and risk management: theory versus practice

Good Bad D. Bad Bad Bogey: 0. Chapter 24 - Portfolio Performance Evaluation c. Manager: 0. Support: A manager could be a better performer in one type of circumstance than in another.

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For example, a manager who does no timing but simply maintains a high beta, will do better in up markets and worse in down markets. Therefore, we should observe performance over an entire cycle. Also, to the extent that observing a manager over an entire cycle increases the number of observations, it would improve the reliability of the measurement.

Contradict: If we adequately control for exposure to the market i. It is therefore not necessary to wait for an entire market cycle to pass before evaluating a manager. The use of universes of managers to evaluate relative investment performance does, to some extent, overcome statistical problems, as long as those manager groups can be made sufficiently homogeneous with respect to style.

From Black-Jensen-Scholes and others, we know that, on average, portfolios with low beta have historically had positive alphas. The slope of the empirical security market line is shallower than predicted by the CAPM. The most likely reason for a difference in ranking is due to the absence of diversification in Fund A. The Sharpe ratio measures excess return per unit of total risk, while the Treynor ratio measures excess return per unit of systematic risk.

Since Fund A performed well on the Treynor measure and so poorly on the Sharpe Measure, it seems that the fund carries a greater amount of unsystematic risk, meaning it is not well-diversified and systematic risk is not the relevant risk measure. The within sector selection calculates the return according to security selection. This is done by summing the weight of the security in the portfolio multiplied by the return of the security in the portfolio minus the return of the security in the benchmark: Large Cap Sector: 0.

Because the passively managed fund is mimicking the benchmark, the R 2 of the regression should be very high and thus probably higher than the actively managed fund. The euro appreciated while the pound depreciated. Primo had a greater stake in the euro-denominated assets relative to the benchmark, resulting in a positive currency allocation effect. British stocks outperformed Dutch stocks resulting in a negative market allocation effect for Primo.

Finally, within the Dutch and British investments, Primo outperformed with the Dutch investments and under- performed with the British investments. Since they had a greater proportion invested in Dutch stocks relative to the benchmark, we assume that they had a positive security allocation effect in total.

However, this cannot be known for certain with this information. It is the best choice, however. To compute M 2 measure, blend the Miranda Fund with a position in T-bills such that the adjusted portfolio has the same volatility as the market index.

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- Introduction.

Using the data, the position in the Miranda Fund should be. The separation of the skilled and lucky from the unskilled but lucky managers and the separation of the skilled but unlucky from the unskilled and unlucky managers is of special interest to all stakeholders in the investment industry. The idea of comparing the performance of different risky investments, for example investment funds, on a quantitative basis dates back to the beginnings of the asset management industry and has been an important field of research in finance since then Jensen, , p.

Based on the idea of the capital asset pricing model CAPM proposed by Treynor , Sharpe , and Lintner , Treynor developed the first quantitative performance measure intended to rate mutual funds, the Treynor Ratio.

Besides academia, the driving force behind the development of more sophisticated performance measures has always been the investors. By combining and applying the results of previous research to a new sample of nearly 10, mutual funds that invest in different countries and asset classes, this thesis clarifies its central research question: Is the Information Ratio a useful and reliable performance measure? In order to answer this central question, it has been split up into the following sub-parts: What are the characteristics of a useful and reliable performance measure?

How does the Information Ratio compare to other performance measures, and what are its strengths and weaknesses? This empirical study aims at answering all of these questions and provides a framework for performance evaluation by use of the Information Ratio. It is a ratio for the excess return of a portfolio relative to a specified benchmark divided by the volatility of the excess returns.

Besides the interesting characteristics of the Information Ratio, it is of special interest because it is founded on two different theoretical frameworks. While the first framework goes back to the founders of the Information Ratio, the second framework closely connects it to the fundamental law of active management, which was developed by Grinold The fundamental law of active management is a central framework for active managers and provides insight on how to use the rationale behind the Information Ratio to construct active portfolios for predefined risk budgets.

Additionally, the Information Ratio has not yet been analyzed in an extensive empirical study across different asset classes and countries, which is therefore a supplementary motivation for this paper. The empirical study is based on return data of nearly 10, funds in the timeframe from January 1, until December 31, and yields some important results, which are summarized very briefly in this paragraph. Using this method, the threshold values of the Information Ratio are found to vary over time and also across different asset classes, so that it becomes necessary to re-calibrate the framework annually.

The quality and reliability of the Information Ratio is dependent on certain factors of the data selection process. Firstly, only one benchmark should be used for all funds in a fund category in order to allow for better comparability and the selection of this benchmark can heavily influence the threshold values. The benchmark should optimally cover a large proportion of the market that is within the investment universe of the respective fund.

Secondly, data frequency should be as high as possible, for example, daily or weekly. Monthly data does not accurately represent the true volatility of returns within a calendar year. Thirdly, non-normally distributed fund returns can affect the usability of the Information Ratio. For example, money market funds show strong non-normal returns, and, therefore, cannot be reliably evaluated with the Information Ratio.

There are, however, other measures available that take higher moments of return distributions into account. In order to separate lucky managers from skilled ones, the track record plays an important role, as luck generally is not persistent over time. Following the introduction and the motivation for the topic, Section 2 lays out the theoretical foundations of this paper. Firstly, Sub-section 2.

Each performance measure is explained briefly and its advantages and disadvantages are outlined in order to get a good overview of the rationale behind these measures. As the Information Ratio is at the center of interest of this study, it is explained in detail in Sub-section 2. In order to better understand the motivation behind active management, Sub-section 2. This leads to a better understanding of the relevant parameters that influence the level of excess returns and clarifies the theoretical framework of the Information Ratio from a different perspective.

Sub-section 2. Section 3 elaborates on the composition and characteristics of the dataset that is used in the empirical study by explaining the selection of mutual funds 3. The empirical study, which is the central part of this thesis, is presented in Section 4. It starts in Sub-section 4.

### What is Portfolio Monitoring?

Sub-sections 4. Other influences that could possibly affect the quality of the Information Ratio, such as non-normality of returns or survivorship bias inherent in the dataset, are described and analyzed in Sub-section 4. In order to separate lucky from skilled managers, the persistency of good Information Ratios over time has been researched in Sub-section 4.

The empirical part concludes with a summary and the development of a specific performance evaluation framework detailed in Sub-section 4. Section 5 sheds light on the experiences and opinions of several practitioners with respect to performance measurement in general and the use of the Information Ratio in particular.

This view will complement the results of the empirical analysis. The thesis concludes with Section 6, where all findings are summarized and starting points for future research are presented. Treynor , p. Firstly, the ratio should provide the same value as long as the performance of the manager does not change, even in unfavorable market conditions. The Information Ratio will be tested on both factors in the empirical part of this paper.

Firstly, the ratio has to assign a performance of zero to the passive benchmark portfolio. Secondly, the ratio has to be a linear function in order to allow for good comparability and to ensure that outperformance can be attributed to superior information. Next, the performance measure has to be continuous so that funds with an equal performance receive the same performance value.

Lastly, the function of the ratio has to be nontrivial. As outlined in detail within the introduction, the development of the first performance measures dates back to the proposal of the CAPM by Treynor , Sharpe and Lintner While Treynor was the first to introduce a meaningful performance measure, immediately after, this field of research was extended by Sharpe and Jensen All of these measures are still widely used in the fund management industry, although some of them have been developed more than 40 years ago.

As the Information Ratio is in the center of interest of this thesis, it will be explained and analyzed in detail in a separate section cf. Chapter 2. Treynor , pp. The Treynor Ratio is defined according to Equation While Treynor , p. However, it has certain drawbacks which limit its practical use. Secondly, it is unstable and imprecise for market-neutral funds, such as certain hedge fund strategies. Introduced by Sharpe , the Sharpe Ratio SR , which was initially called reward-to-variability ratio, is meant as an extension of the Treynor Ratio.

While Treynor strived to only evaluate fund performance ex post, Sharpe explicitly aimed at predicting future performance with his measure and also by using the Treynor Ratio p. The Sharpe Ratio has been discussed heavily in literature, and its theoretical foundation was also extended twice by the founder in Sharpe and Sharpe Using Equation 2, the Sharpe Ratio can be easily calculated:. The formula clearly highlights the differences between the Sharpe Ratio and the Treynor Ratio.

The Treynor Ratio only considers the systematic part of the risk of a mutual fund but does not take into account the diversifiable risks. In contrast to this, the Sharpe Ratio uses the total risk in its denominator. Therefore, the Sharpe Ratio is also able to highlight the risks inherent in an inappropriately diversified fund Sharpe, , p. These characteristics advise the use of the Sharpe Ratio if one investment portfolio is to be chosen as the single investment of a particular investor. In this case, only total risk counts. Therefore, style portfolios will generally not be evaluated by the use of Sharpe Ratios.

A style portfolio consists of a defined group of asset that shares similar characteristics, such as value stocks or small cap stocks. In terms of practical applications, the Sharpe Ratio has several drawbacks. Another problem arises if returns that are used to calculate the Sharpe Ratio are not normally distributed.

In this case, it is not possible to easily compare Sharpe Ratios that are based on returns with different distribution characteristics without further adjustments Mahdavi, , p. A different, yet important, problem can arise from the estimation of returns and volatilities, which are the two input factors of the Sharpe Ratio. Additionally, the Sharpe Ratio can provide false rankings if the numerator becomes negative, that is the fund performance is below the risk-free rate Scholz, , p.

The alpha itself is then a measure of outperformance or underperformance relative to the return that would be expected based on the CAPM. The rankings of both measures will therefore differ depending on the level of unsystematic risk inherent in the respective funds. When combining both measures, it is actually possible to find funds with a high level of unsystematic risk as these funds will show low Sharpe Ratios but high alpha measures Moy, , pp.

These funds lack diversification. In contrast to the assumptions of standard portfolio theory, investors do not judge upside-risk and downside-risk equally. Logically, all investors prefer positive over negative returns but the widely used standard deviation measure does not differentiate between positive volatility leading to additional positive returns and negative volatility leading to additional negative returns. While the idea of adverse volatility had already been proposed by Levy , p. Together with the Sortino Ratio, the idea of downside deviation is introduced and explained.

Downside deviation is a measure for negative volatility, and it is calculated based only on returns that are below the minimum acceptable return MAR. The Sortino Ratio can be calculated based on Equation Compared to the Information Ratio, the Sortino Ratio is the same except that the tracking error volatility is calculated based only on returns that are below the minimum acceptable return. In terms of practical applications, the Sortino Ratio can be unreliable or impossible to calculate if there are no or only very few returns below the MAP within the observation period.

This could lead to the denominator being equal to zero in an extreme case or to a false estimate of the downside risk if there are only few returns below the MAP present. Their measure adjusts the risk standard deviation of an investment portfolio by mixing it with the risk-free rate so that it exactly matches the standard deviation of the respective benchmark, which in most cases is a market index.

This adjustment allows the investor to actually compare the outperformance or underperformance of a particular fund versus its benchmark on a risk-adjusted basis. According to Muralidhar , p. Only funds that can be classified into the first category are really superior to an investment into the benchmark. Omega is directly based on the cumulative distribution function of the returns and is therefore able to incorporate all higher moments of this distribution.

The ratio introduces a loss threshold and weights possible gains or losses relative to this threshold by their probability.

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Equation 6 formalizes this relationship:.