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Benchmark Construction and Benchmark CalculationsA benchmark specifies the neutral asset allocation for an investment portfolio. For example, a simple domestic portfolio's benchmark specification might be 100% Nasdaq. Or it might be 90% Nasdaq, 10% cash. For diversified portfolios, it is usual to specify a benchmark that includes cash, domestic and global equities, domestic and global fixed income, and perhaps a bit of real estate or hedge funds. The benchmark return is one of the first things that we look for when we seek to evaluate the performance of a portfolio. An investor's first question might be "what was the portfolio return?" Their second question might be "what was the benchmark return?" We explore that question on this web page. The third question is likely to be "what decisions made the portfolio return differ from the benchmark return?" We explore that question in the Performance Attribution section of this web site.
Benchmark Rebalancing Calculations If an investment portfolio had 50% of its assets in US domestic equities, and 50% of its assets in US domestic bonds at the start of the year 1950, by 1999 this would have drifted to 98% equities and 2% bonds. This effect is caused by long-term outperformance by equities relative to bonds. It demonstrates why portfolios need to be rebalanced from time to time toward what is considered their neutral position (say 50% equities, 50% bonds). Just as portfolios need to be rebalanced, one also needs to use a rebalancing assumption when calculating benchmark returns. By default, monthly benchmark rebalancing has applied over the last few decades. This is because most people did monthly performance measurement. So, consider a portfolio whose benchmark is 50% equities, 50% bonds. If one takes a 50/50 weighted sum of the monthly returns, and then compounds them out over longer periods, this calculation assumes that the weight of each asset class has been rebalanced back to exactly 50% at the start of each month. This calculation will not reconcile with the returns that one obtains by doing a 50/50 weighted sum of daily returns, and then compounding them out (because the daily calculation assumes daily returns). Most firms realize the need to adopt daily performance measurement and attribution some time soon. Not everybody realizes that a naive implementation of daily calculations can inadvertently bring with it a daily portfolio rebalancing assumption, which is not necessarily desirable. However, with a bit of care, one can implement monthly benchmark rebalancing (or any other rebalancing assumption that one chooses) using daily calculations. The following documents show how. The paper Benchmark Rebalancing Calculations, by Damien Laker, was published in the Journal of Performance Measurement, Spring 2003, PP. 8-18. It explains the need for benchmark rebalancing calculations, and then it works through a detailed example in order to make the calculations clear. Finally, it shows the relevance of this topic to tasks such as specifying investment mandates, or calculating performance attribution. The sample spreadsheet Simple Example of Rebalancing.xls demonstrates in full detail how the benchmark rebalancing calculations work over two full rebalancing periods. It uses numbers from the above journal article. The following excerpt from these documents illustrates how to do the daily calculations for a benchmark that is not rebalanced daily. In this case, the benchmark is 60% equities, 40% bonds. To make the differences more obvious, the equities return on each day is 3%, while the bonds return is 1%. At the start of the period, the weights for equities and bonds are indeed 60/40. However, because of the growing differences in cumulative return of these asset classes over time, the equities weight drifts higher, and hence the bonds weight drifts lower. On each day, the total benchmark return is a weighted sum using the weights shown in the table. At any point where a rebalance happens, all one needs to do is reset the weights to 60/40, then restart the calculation from that point.
Using this kind of approach, it is possible to do daily performance measurement and attribution on a portfolio that has monthly benchmark rebalancing, or indeed any other kind of benchmark rebalancing. This approach also works on leveraged funds. For example, if a fund has a benchmark of 150% equities, and minus 50% cash, the arithmetic works in exactly the same way.
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