Eliminating Distortion Caused By Large Cash Flows
An expedient solution to calculating an estimated TWR using the MWR and removing the error associated with large cash flows is to calculate a special valuation when there are large cash flows and to calculate subpe-riod returns for the periods flanking the large cash flow date. To do this, analysts monitor the portfolio for cash flows and identify situations where the MWR is being materially influenced by the cash flows. This is usually done using some threshold net transaction value, such as...
Contribution To Return
Suppose we had a portfolio comprised of four stocks, each held with an equal 25 weight, and each earned 10 during the period. We can see in Exhibit 17.1 that the contribution to return made by each security to the total fund return is 2.50 . The 2.5 contribution for each security was calculated by multiplying the beginning of period weight by the return during the period. Contribution to return Security begin weight x Security return 17.1 EXHIBIT 17.2 Single Period Contribution EXHIBIT 17.2...
Semideviation
Downside risk statistics are based on the concept of partial, or semideviation. Semideviation is the standard deviation of the returns that fall below the mean return. Semideviation is the square root of semivari-ance, and below mean semivariance is the variance of the returns below the mean return. We calculate the semideviation in the same way as standard deviation, except that we modify the formula to use only those returns that fell below the mean return for the period. To calculate the...
MoneyWeighted Return versus TimeWeighted Return
Having established the need to refer to the portfolio's actual security transactions to calculate a security level return, the next issue we face is the timing of these transactions. At the highest level, we need to decide whether we want to calculate a Money-Weighted Return MWR or a Time-Weighted Return TWR . We can calculate segment and security level returns using either an MWR or TWR. Let's look at the security level MWR first. Security level returns that are calculated using MWR are very...
Market Indices
Practitioners have come to accept that a peer group universe does not fulfill all of the requirements for a good measure of relative performance. Jeffrey Bailey set out the criteria of a good performance comparison benchmark, which is unambiguous, investable, measurable, appropriate, and specified in advance.1 Peer group universes do not enjoy all of these ideal characteristics. For example, we cannot invest in an asset called the median manager return. But we still need to understand whether...
Information Ratio
Tracking error is useful in measuring the degree of historical return deviation from the benchmark. But what if we have an active strategy designed to divert from the benchmark in order to exceed the benchmark return We would be interested in measuring the gains over and above the benchmark return relative to the benchmark risk taken, as measured by the tracking error. We do this because in many situations we can earn the benchmark return itself with little tracking error and at low cost by...
Msquared Return
Most investors are intuitively comfortable interpreting the economic meaning conveyed by a rate of return. Some are comfortable interpreting the various measures of risk based on the idea of return deviations. Professional investors understand the information conveyed by the Sharpe ratio. But many consumers of performance measurement statistics, not working day to day with these tools, find Sharpe ratios confusing because they do not know its inputs and meaning. If an investor does not know...
Market Index Less a Component
Benchmarks can also be customized to reflect the investor's restrictions with respect to particular asset classes, instruments, industries, and the like. Instead of building up a new index from the stock level, we can adjust the return of an index by the contribution to return from certain stocks in the index. For example, a large corporate pension plan might use as its benchmark the return of the S amp P 500 index excluding the company's own stock. Or a fund that applies social screens, like...
Geometric Mean Return
When we multiply the average yearly return by the total number of years the result will not equal the compounded return because it does not take into account the interest earned on interest. In the previous example, the 20 return in the second year earned on the first year's 10 return is not accounted for by the arithmetic average. To account for the interest on interest in the calculation, instead of taking the arithmetic mean return we can calculate the geometric mean return. The 1 For more...
Annualizing Returns
Returns are typically presented on a yearly or annual basis. This is done because it is easier to compare investment returns if the time period is the same for each investment, i.e. we cannot compare a cumulative return of 10 to another of 12 if the first was earned over 15 months and the second over 12 months. To analyze the difference in returns between any two investments, it is helpful to hold the time period constant. Yearly or annual presentations are standard. Cumulative returns that...
acknowledgments
This book begins on a note of humility. I did not develop any of the methods that comprise the performance measurement body of knowledge. Many contributors have shaped the evolution of what now represents current practice in the field. I have tried to recognize and reference within the text their works, and recommend them as resources for further information. Those who want to keep current with developments in the field will be especially interested in The Journal of Performance Measurement...