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Investing as a zero-sum game Adviser brief March 2013 The total of all investors’ returns can be represented as a bell curve, with the market return as the average. In Figure 1, the market is represented by the green curve, with the market return as the black vertical line. Understanding the zero-sum game The concept of a zero-sum game starts with the understanding that at any one time, the holdings of all investors in a particular market make up that market.1 As a result, for every invested pound that outperforms the total market over a given period, there must by definition be another pound that underperforms. Another way of stating this is that the asset-weighted performance of all investors, both positive and negative, will equal the overall performance of the market. Figure 1. Over any given period, the asset-weighted excess performance to the right of the market return in Figure 1 (the outperforming investments) equals the inverse of the assetweighted excess performance to the left of the market return (the underperformers). The sum of the two equals the market return. The zero-sum game Cost of funds Figure 1. Probability Median post-cost return of funds Benchmark return Funds underperforming benchmark -5 -4 Funds outperforming benchmark -3 -2 -1 0 1 2 3 4 Expected return relative to benchmark (pp) Source: The Vanguard Group, Inc. 1 Sharpe, 1991 This document is directed at professional investors only and should not be distributed to, or relied upon by, retail investors. Past performance is not a reliable indicator of future results. The value of investments, and the income from them, may fall or rise and investors may get back less than they invested. 5 The role of costs Putting theory into practice In reality, however, investors pay costs, such as commissions, management fees, taxes, bid-offer spreads and administrative costs, all of which combine to reduce realised returns over time. The aggregate result of these costs shifts the curve to the left. Figure 3 shows the actual distributions of a range of actively managed equity fund categories over five years to 31 December 2012. Although funds account for only a portion of the markets, the chart shows a result that the zero-sum game theory would predict: Although a portion of the after-cost, assetweighted performance continues to lie to the right of the market return, represented by the green region in Figure 1, a much larger portion of the red curve is now to the left of the solid black line. So, after costs, most of the assetweighted performance of investors now falls short of the aggregate market return. 1.The returns of the aggregate actively managed fund universe form a bell curve. 2.Returns are widely distributed around the average, illustrating the wide range of potential outcomes inherent in active management and the variance in costs. 3.The distributions are centred to the left of the benchmark return, clearly showing the impact of costs. Cost is one of the very few things that investors can control. By keeping costs low investors can help ensure that their return is closer to the market return, on average, giving them a greater chance of outperforming similarly positioned investors who incur higher costs. Figure 3. Active equity funds’ return distributions 5 years 350 300 250 200 150 100 50 UK equity Eurozone equity Global equity European equity US equity Emerging equity Greater than 8% 7 to 8% 6 to 7% 5 to 6% 4 to 5% 3 to 4% 2 to 3% 1 to 2% 0 to 1% -1 to 0% -2 to -1% -3 to -2% -4 to -3% -5 to -4% -6 to -5% -7 to -6% -8 to -7% Less than -8% 0 Sources: Vanguard calculations, using data from Morningstar, Inc., FTSE , MSCI and Barclays. Included funds are from the following Morningstar categories: UK equity – flex cap, large-cap blend, large-cap growth, large-cap value, small-cap; Europe equity – large-cap blend, large-cap growth, large-cap value, flexcap, small-cap; Euro zone equity – flex-cap, large-cap, small-cap; Global – large-cap blend, large-cap growth, large-cap value, flex-cap, small-cap; US equity – large-cap blend, large-cap growth, large-cap value, flex-cap, small-cap; Emerging markets equity – emerging markets. Performance is for periods ending on 31 December 2012. Basis of performance calculation is net of fees, income reinvested, closing NAV prices. Benchmarks are specified in the fund prospectuses. Figure 4. Active bond funds’ return distributions 5 years 140 120 100 80 60 40 20 GBP Diversified Bond GBP Government Bond EUR Diversified Bond USD Diversified Bond More than 8% 7 to 8% 6 to 7% 5 to 6% 4 to 5% 3 to 4% 2 to 3% 1 to 2% 0 to 1% - 1 to - 0% - 2 to - 1% - 3 to - 2% - 4 to - 3% - 5 to - 4% - 6 to - 5% -7 to - 6% - 8 to -7% Less than - 8% 0 Global Bond Sources: Vanguard calculations, using data from Morningstar, Inc., FTSE, MSCI and Barclays. Included funds are from the following Morningstar categories: Europe bond – EUR diversified; US bond – USD diversified; Global bond – global; UK bonds – UK diversified, UK government. Performance is for periods ending on 31 December 2012. Basis of performance calculation is net of fees, income reinvested, closing NAV prices. Benchmarks are specified in the fund prospectuses. The zero-sum game and bond markets The same zero-sum dynamic also appears to affect actively managed bond funds. Figure 4 provides the evidence for this, comparing actively managed bond funds against their respective benchmark indices over five years. Conclusion Index funds typically carry lower charges than their active counterparts. At the same time, the distribution of returns from index funds tends to be narrower, with fewer instances of significant out- or underperformance. Considering all of these factors, we believe that setting a long-term asset allocation based on pre-agreed investment goals, and achieving this allocation through low-cost funds, is likely to be the most successful approach for the vast majority of investors. Investment markets are effectively a zero-sum game, with every outperforming pound being balanced by a pound that lags the benchmark. The unpredictable nature of markets and the lack of performance persistency among funds1 mean that selecting an investment that outperforms consistently is extremely difficult. Moreover, the chances of success are further reduced by the impact of costs. This impact is likely to be magnified by frequent trading in pursuit of the latest top-performing fund or asset class. 1 See our adviser brief ‘Can active funds deliver persistent performance?’, March 2013 Connect with Vanguard™ > vanguard.co.uk > Adviser support > 0800 917 5508 Important information This document is designed only for use by, and is directed only at persons resident in the UK. The information on this document does not constitute legal, tax, or investment advice. You must not, therefore, rely on the content of this document when making investment decisions. The material contained in this document is not to be regarded as an offer to buy or sell or the solicitation of any offer to buy or sell securities in any jurisdiction where such an offer or solicitation is against the law, or to anyone to whom it is unlawful to make such an offer or solicitation, or if the person making the offer or solicitation is not qualified to do so. The value of investments, and the income from them, may fall or rise and investors may get back less than they invested. Past performance is not a reliable indicator of future results. Issued by Vanguard Asset Management, Limited which is authorised and regulated in the UK by the Financial Services Authority. © 2013 Vanguard Asset Management, Limited. All rights reserved. VAM-2013-03-26-0659