|
|
|
|
Multicurrency AttributionPerformance attribution methods can be divided into two fundamental approaches:
Before we go on to multicurrency attribution, we should deal with a couple of misconceptions about single-currency attribution. One misconception is that a single-currency attribution system can only be used on one particular currency. For example, under this idea, one could not use the same system for doing attribution on a US Dollar portfolio and a British pound portfolio. This is completely incorrect. A single-currency attribution system does not do any currency conversions at all. So long as the holdings in each portfolio are consistently specified in any particular currency, a single-currency attribution system will do all of the calculations using those numbers. Another misconception is that single-country attribution cannot be used on a multicurrency portfolio. This is not the case at all. Using an analogy, doing single-currency attribution on a multicurrency portfolio is like taking a black-and-white photograph of a colorful object. As everybody knows, a good black-and-white photo of a colorful object can give a very clear image of the shape, texture, contour, and size of the object. The one thing that it cannot do is provide a clear understanding of the colors used in an object. Similarly, a single-currency attribution analysis of a multicurrency portfolio is by no means a futile effort. It can convey a great deal of information about the portfolio's performance. Arguably, a good single-currency attribution analysis of a multicurrency portfolio will be much more useful than a poor-to-average multicurrency attribution analysis of the same portfolio. This is because a poor-to-average multicurrency attribution analysis may reveal little useful insight (and indeed it may mislead with spurious insights). On the other hand, a good single-currency attribution analysis will at least give a completely reliable picture of the value being added through stock selection, and it may give a fairly reliable picture of the value being added through asset allocation also. Having said all of that, of course it is quite useful -- all other things being equal -- to have the benefit of multicurrency analysis on a multicurrency portfolio. A fundamental concept for understanding multicurrency attribution is the distinction between base currency and local currency. Base Currency and Local CurrencyWhenever one is doing any kind of multicurrency analysis on an investment portfolio, a key distinction is between base currency and local currency. The base currency is the currency in which the portfolio's returns are normally reported and analyzed. This will usually be determined by who the client is. For example, a London-based investment manager would use a base currency of GBP (British Pounds) for portfolios they manage on behalf of British clients. But they would use US dollars for portfolios managed on behalf of US clients, Euro for funds managed on behalf of European clients, etc. Once you have crossed the threshold of multicurrency measurement and attribution, it should not in fact be too difficult to get used to the idea of using different base currencies for different portfolios. At the end of the day, the return that matters to the client is the base currency return. The term "local currency" refers to measuring value or performance in the currency of each individual security. So, the local currency returns for Microsoft would be in US dollars, while the local currency returns for Union Bank of Switzerland would be in Swiss Francs. Simple (Traditional) Approach to Multicurrency AttributionOne can speak of "traditional" approaches to multicurrency attribution, to distinguish them from the broad approach that emerges from the insights offered by Karnosky and Singer (see below). A well-known traditional approach to multicurrency attribution is to use the classic Sector Attribution model on the local currency returns. This certainly makes sense for the stock selection attribute (when one is doing the attribution by country), because it makes sense to try and pick the Swiss stocks that will outperform the Swiss country index in Swiss Francs, the Japanese stocks that will outperform the Japanese country index in Japanese Yen, etc. So far as the asset allocation attribute is concerned, this traditional approach is congruent with the idea that good asset allocation consists of overweighting the markets with the highest local currency returns, and underweighting the markets with the lowest local currency returns. Some people definitely think about global asset allocation this way. Indeed, some portfolio managers state that the aim of their asset allocation is to pick the markets with the highest local currency returns. So from this point of view also, the traditional approach to multicurrency attribution has some intuitive backing. However, the chief insight of Karnosky and Singer was that this view of asset allocation, while perhaps intuitive, was not actually optimal in terms of the entire opportunity set that the portfolio manager has available (for more detail see below). So, how does this traditional approach deal with currency effects? In short, it takes a very simple approach. The "non currency" attributes (asset allocation, stock selection, and interaction) in this model explain the local currency excess return (i.e. the local currency portfolio return less the local currency benchmark return). However, the overall goal is to explain the base currency excess return. So this model simply assigns the difference between the base currency return and the excess currency return to a "currency" attribute. Nobody seems to argue that this calculation gives any particular insight into the currency management process. But it does at least have the virtue of simplicity. In another major blow for simplicity, this model provides a "currency" attribute for each item (e.g. a sector) in the attribution report. This is done using contributions (see the the Attribution Basics page for an explanation about how to calculate contribution). So, for example, any given sector's currency attribute would be:
This traditional approach as described here is a fairly natural way to start thinking about multicurrency attribution. One way of understanding different (and possibly more elaborate) models is by comparing them with this approach. A practical advantage of this approach to multicurrency attribution is that it is reasonably easy to implement. Currency HedgingAs we will discuss when we consider the Karnosky-Singer approach to multicurrency attribution, currency hedging is a fundamental tool for all international investors. Currency hedging enables an investor to separate their decisions about which markets they want to be in from their decisions about which currencies they want to be in. For example, consider an investment manager who is managing (for an Australian client) a portfolio whose base currency is Australian Dollars (AUD). The manager may wish to invest in German equities, but they may also not wish to take an exposure to the Euro (EUR). By using a Forward Rate Agreement (FRA), the manager can easily buy the German equities, but then hedge the EUR exposure into any other currency they wish. The arithmetic of currency hedging depends upon the calculation of forward rates in a Forward Rates Agreement (FRA). If the multicurrency investment manager we have been discussing does indeed make an investment in German Equities, he will want to hedge this out of EUR into a favored currency. Assuming that he hedges back into his portfolio's base currency (AUD), the FRA will specify a purchase of a known amount of AUD in exchange for a known amount of EUR on the maturity date. The forward exchange rate will generally vary somewhat from the current "spot" rate. The difference between the spot rate and the forward rate depends on the cost to a bank of providing the FRA. This, in turn, depends simply on the difference between AUD and EUR interest rates. Consider what a bank has to do in order to risklessly provide a FRA to the fund manager. On the maturity date, the bank will be providing AUD to the fund manager, and taking EUR in payment. To do this without incurring risk, the bank can allocate some of its existing EUR cash, and convert it to AUD cash at the moment the FRA is made. The bank then holds this AUD cash until the maturity date, at which point it provides AUD to the fund manager, and receives EUR in return. The cost to the bank of doing this is that the bank earns interest on its cash deposit at the AUD rate (rather than the EUR rate) for the life of the FRA. So, for example, if the return on AUD cash over the life of the FRA is 6%, while the return on EUR cash during this period is only 5%, the bank will earn an extra 1%. Hence, the forward rate that the bank can provide on the EUR/AUD hedge is in fact more favorable to the fund manager than the spot rate. We will consider more examples of currency hedging in the following section on Karnosky and Singer's approach. The basic principle behind all currency hedging calculations is that they depend on differences in cash rates. The key thing to remember about currency hedging is that currency markets are very deep and competitively priced. One can easily decide the market allocation question quite independently of the currency allocation decision. Currency hedging is the tool that makes this separation of concerns an everyday reality. The Karnosky-Singer ApproachDenis Karnosky and Brian Singer revolutionized thinking about multicurrency attribution with a monograph they published in 1994. This tutorial, published by Damien Laker in 2005, explains one of the examples that Karnosky and Singer provided in their monograph. In the example, one's assessment of the desirable approach to market (i.e. country) allocation would have been entirely wrong if one allocated assets toward the markets that had the highest local-currency returns. Instead, the best approach would have been (as Karnosky and Singer's theories suggest) to allocate assets to markets that had the highest local-currency return premia. The local currency return premium is the extent to which the market's local currency return exceeds the cash return in that currency. To explain that, here are some numbers from the tutorial which will help us to see the differences introduced by the Karnosky-Singer approach, and the reasons for those differences. The example uses a small global equities portfolio whose base currency is the Australian Dollar (AUD). The benchmark information looks like this:
Note that this example uses continuously compounding returns, so that the exchange rate conversions can be done by simple addition. For example, the local currency (EUR) return for German equities is 7.00%, and the base currency (AUD) return for that market is 7.00% + 1.00% = 8.00%. If the returns were not expressed in a continuously compounding form, the calculation would be (1.07) x (1.01) - 1 = 8.07%. For a deeper explanation of continuously compounding interest rates, see the section about continuously compounding returns on the Performance Measurement Page. Given that most people want to maximize their wealth, the most interesting way to analyze this problem is to consider it from the standpoint of return maximization. How one could maximize one's return if one had perfect foreknowledge of the numbers in the above table? We are considering this problem from the standpoint of a fund whose base currency is AUD. Therefore, while the local currency returns are interesting information, they are not decisive. To understand why, consider what would happen if the fund manager tried to capture the 10.50% return of UK equities. If the fund manager simply held the UK equities (without engaging in any currency hedging), they would have made a return of 10.50% in the equities market, but they would have also made a 3% loss in the currency market. This would not have been a winning strategy. In fact, one can see from the rightmost column of the table that the based currency return from an unhedged investment in UK equities would have been 7.50%: lower than any of the other alternatives. So, from this perspective, the best decision would have been investing in Japanese equities. The Japanese market produced a return of 9.50%, and the exchange rate movement reduced this by only 1.00%. The net return to the AUD investor was 8.50%. However, there is something further to consider also. The analysis in the above paragraph is based on the premise that the investor is prepared to make a combined bet on markets and currencies (for example, one could only obtain exposure to Japanese equities by simultaneously taking an exposure to the Yen). An naive investor might be happy to proceed on this basis, but it is not really a satisfactory basis for performance attribution. Ideally, an attribution analysis should be able to analyze the rewards from market-allocation decisions separately from the rewards of currency-allocation decisions. This is possible by taking into account the possibility of currency hedging. By using Forward Rate Agreements (FRAs) to lock-in a future exchange rate, investment managers gain the freedom to make market bets independently of currency bets. Since it is desirable for attribution calculations to be able to quite separately assign value-added to market selection or currency selection, attribution analysis should consider how FRA's and hedging could achieve this result. Since local currency cash returns are central to currency hedging calculations, a Karnosky Singer attribution system would need the following data on cash returns:
Using those data, one is able to create a ranked list of all the possible investment alternatives (market allocations and currency allocations). If you understand the ranked list, you understand the basic principles of KS attribution. For this example, the ranked list looks like this:
This list is not a performance attribution, but it is an extremely useful accompaniment to any performance attribution calculation based on the market and currency returns used in this example. What it makes plain for us, is that the highest return strategy was German Equities hedged into GBP (i.e. 100% market exposure to Germany, 100% currency exposure to GBP). A list like this can be included in a Karnosky Singer Attribution report in order to make the results more intuitive. The full details of an attribution analysis using these numbers can be found in Karnosky and Singer's monograph. The spreadsheet example Karnosky Singer Worked Example.xls shows the data and formulae necessary for calculating the example discussed above. This example is identical with Karnosky and Singer's example from pp. 21-40 of the monograph, excepts that it uses AUD as the base currency.
What Differences Does a Karnosky-Singer Approach Make?How much difference would it make to a typical asset manager if they started using Karnosky-Singer (KS) Attribution? Arguably, it would make a great deal of difference to the reports that they issued. Many people are unfamiliar with the finance theory that justifies KS, and in any event, some sort of regular reminder would be a useful addition in attribution reports. It is worth devoting a great deal of effort to designing the right reports do that KS attribution results will be intelligible to an intelligent (but not necessarily expert) reader. In terms of the actual numbers, KS has different levels of impact for different attributes:
Practical Issues Associated with Adopting Karnosky-Singer AttributionMost firms who are considering adopting a KS approach try to initially provide KS attribution side-by-side with a more traditional approach to multicurrency attribution. Part of the rationale for this is that people will take time to adapt to the KS paradigm. Reporting the attribution two different ways like this could be a rich source of detailed education, given that it permits people to compare a whole range of practical situations when analyzed through the KS prism or through a more traditional prism. On the other hand, two separate sets of attribution reports could lead to confusion and lack of confidence in the numbers. To a large extent, the quality of any particular implementation (including report design, quality assurance, and providing access to a knowledgeable "performance team helpdesk" will be critical for the success of a KS attribution initiative. Reference Karnosky, Denis S. and Brian D. Singer, Global Asset Management and
Performance Attribution The Research |
|
Send mail to
webmaster@compoundinghappens.com with
questions or comments about this web site.
|