Just want the PDF? Download it hereDarwinian Investing: The Science of RejectionThe outperformance of the “Magnificent Seven”1 during 2023 led to many questions from our investors (for instance “why are you underweight the Mag 7?”) but our minds were more focused on thinking about the losers. In this investment letter we want to discuss why avoiding losers is so important. We explore the science of rejection, and how saying ‘no’ more often can lead to better investment performance.One of our colleagues, Ken Stuzin, likens portfolio construction to Darwinian Investing – it is about survival of the fittest. Competition for capital is fierce; some companies thrive for a while, but only the best survive. One of our informal measures of a good book is how many pages are dog-eared (corners folded over) for the return reading. During 2023, one of our most beaten-up books was ‘What I Learned About Investing from Darwin’.2 The science and biology were fascinating, and the statistical application to investing was insightful. The author, a very successful Indian investor, goes into some detail about species evolutionary strategies and their corollaries to investing. In a year of tough competition, having undertaken our first Think Week (a week of uninterrupted reading and learning over the summer to inspire new ideas and ways to improve) this was one of the year’s best investment reads. Investing is about moving the probabilities in our favour. One approach is to steer clear of risks with wide uncertainty of outcomes, including those with a potential windfall payoff if they carry a possible fatal downside. This is encapsulated in Howard Mark’s capital market’s line chart, proudly hanging in our office.3 Another is captured in Bertrand Russell’s Christmas Chicken parable4 – also adorning our walls in graphical form. In a concentrated portfolio, it is the losers that kill you. Another reminder within our office artwork is our often-quoted asymmetry between percentage losers and winners. An investment that declines by -33% must rise by +50% just to get back to flat with where it started. Percentages are very deceptive. We believe that avoiding losers is more important than finding big winners. You have to survive in order to thrive. We are in the rejection business and the statistics are stark as to how we should be very careful whenever investing our clients’ hard-earned dollars.In Charles Darwin's masterpiece “On the Origin of Species by Means of Natural Selection” he investigated the prevalence of species survival due to differing evolutionary strategies. A key pillar was to avoid fatal downsides. If you are deer at the watering hole, it is better to run for the hills if you sense danger than get snatched by a crocodile. Mostly these are false alarms otherwise known as a false negative signal. Out of breath perhaps, but alive and the species will continue to thrive. What you and ultimately the species do not want is complacency and then fatality. This is a false positive signal ("we thought it was OK to drink...") which should have flashed red alert! Investors suffer from both these errors too (see table 1). The first is a false positive, whereby one believes a company is a good potential investment and invests. However, it is either a bad company in disguise or we have overpaid, and it turns out to be a poor investment. Statistically, these are known as Type 1 errors of commission (or inclusion) having fallen for a false positive signal. The other error is when we reject a potential investment as either not meeting our quality hurdles or as too expensive, yet it goes on to outperform. These are errors of omission – statistically a Type 2 false negative – and it is a mistake we often make (Nvidia!). One of the quirks of statistics is that these errors are mirrors of each other and inversely correlated. By trying to minimise a type 1 error of inclusion it is inextricable that, type 2 errors of omission will increase too. Conversely, going for more big winners will likely result in more big losers. The trick is in the balance.Imagine that a team of investors achieves a three in four (75%) success rate within their portfolio of identifying good investments and displays equally good skill in rejecting bad ones.5 As Table 2 below highlights, this team appears to be seriously good! What sort of hit rate should we then expect within their portfolio? If you guess 75%, then it is both natural and wrong. We need to consider one crucial factor: the percentage of successful investments within the universe. Only if the universe is split 50:50 between winning and losing investments does the 75% hit rate for the portfolio hold. However, the universe typically does not follow a normal distribution, not even on a one-year basis. The outperformance of the ‘Magnificent Seven’ was an extreme example during 2023, when only 30% of companies outperformed the MSCI ACWI benchmark. However, it is rare (only once!) during the past decade that more than 50% of companies in the MSCI ACWI benchmark at the start of each year outperformed the global benchmark during that year.6 This is in spite of the small cap vs large cap bias documented by Fama and French.7 Over all rolling 5-year periods in the last decade an average of 31% of companies in the MSCI ACWI at the start of each period outperformed that benchmark. There is a significantly longer 90-year study by Professor Hendrik Bessembinder from Arizona State University showing that the best performing 4% of US listed companies created all the value in US stocks from 1926 to 2016.8 He has reproduced similar analysis globally. You might quibble with some of his accounting, but directionally, it is clearly correct in our view. The longer the time period, the fewer the winners. So why is the hit rate not 75%? For illustration let’s assume there are 100 companies in the universe. If we say just under one third (30%) of companies outperform over a 5-year period , we can calculate expected hit rates. If our hypothetical team in Table 2 are 75% correct, then they select 23 of the 30 winning companies (i.e., 75% of 30). Of the 70 losers they correctly reject 53 companies (75% x 70). However, they suffer from the error of including some losers too and they misjudge 25% of the losers and buy 18 (i.e., 25% of 70 losers). Chart 1 visualises the outcome. Altogether 23 companies go on to win out of 40 investments. The hit rate is just 56% (23/40) despite 75% success in identifying both winners and losers! Table 3 summarises these outcomes. Even with 75% accuracy we only move from an investable universe where 30% of constituents outperform to now selecting the portfolio from a pool with a 56% win rate.TThis is why industry hit rates are so low. We all know that a 55% hit rate is the top decile across the industry, and the maths above demonstrates why. Most investors spend most of their time looking for their next great idea. Avoiding type 2 errors of omission drives industry investment behaviour. For as much as investors chase the next big idea and fear of missing out (FOMO) runs rampant (who doesn’t hate missing out?), type 1 errors of including losers are the bigger risk and drag on performance. We only need a few long-term winners to generate performance for our investors and a key part of this is avoiding the far larger majority of losers. This is probably best summed up by Warren Buffett’s first two rules of investing:9Rule #1: Never lose money Rule #2: Never forget Rule #1 Now what happens if our team gets even better at identifying winners? This is where most teams spend their research time – on the hunt for a new opportunity. If they reduce the frequency of missed opportunities by increasing their success rate to 90% when looking for winners, the overall hit rates go up to 61% as demonstrated in the graphs below. Not bad. However, what if they instead look to improve their rejection rate to 90% and make less type 1 errors of inclusion. In this case, the filtered universe win rate jumps to 76%!! Why the huge skew? In the charts below, we can see that by lifting accuracy of identifying losers to 90% means we reduce the type 1 errors of inclusion. This has a significantly larger impact than picking more winners by reducing the type 2 errors of omission. Portfolio outperformance is significantly enhanced by improving the rejection of losers rather than finding more big winners. The trade–off from rejecting more is undoubtedly more missed opportunities too. As noted earlier, type 1 errors are inversely correlated to type 2. Statistics don’t always lie, and this trade-off is unavoidable. If you pick more winners, you will likely also invest in more losers, and vice-versa. When starting at a 56% hit rate within one’s filtered universe, there is not a lot of leeway to include more mistakes! Hence, our null hypothesis should be to reject. There are so many more possible mistakes to make in buying type 1 false positives – investments that appear to be good quality and/or cheap but are not. Interestingly, the Global Leaders portfolio average annual hit rate since inception is 55% although, as we have highlighted in the past, our annual hit rate has ranged between 33%-70%. We have a top team of analysts, but it is not easy, and we must minimise type 1 errors within the portfolio in order to outperform. In other words, we are likely to miss many great opportunities. Both types of error are due to a combination of either mis-assessing the business quality or its valuation (or both). Our 10/10/3 valuation framework using a 10% weighted average cost of capital is undoubtedly conservative and ends up with us missing some big opportunities as type 2 errors of omission. A type 2 error of actively omitting to invest are typically the most psychologically painful errors for a long-term investor. Especially if you assess a company as good quality but reject the investment as being too expensive…then it goes on for years to compound outperformance. Two recent examples of missing out on big winners are Nvidia and Novo Nordisk. We have both of these potential investments on our Ready-to-Buy list, and both had gotten to within 10% of prices where we thought they represented very good value in the past few years (Nvidia in Oct 2022, Novo Nordisk in Dec 2020). However, we did not invest due to our minimum double-digit 5-year IRR hurdle rate. Good process, bad outcome. Classic type 2 errors! This ‘penny pinching’ can be frustrating, and the mind begins to play second-guessing games (Shouldn’t we just pay up? What if we lower our discount rate?). This thinking forgets that less ‘missing out’ comes with more mistakes within the portfolio, as we will inevitably get more Type 1 errors due to inverse correlation. Be careful what you wish for!One caveat is the potential sampling error within the portfolio. This analysis is all based on the frequency of winners within the initial universe and subsequent smaller refined pool to select from, but due to sampling error, this may not be reflected within our actual selection of 30-40 investments in Global Leaders. A second arguably more important issue is that these hit rates have no differentiation for the magnitude of the subsequent outperformance. Ideally, we want both good frequency and large magnitude. Rejecting more losers aims to shift the chances of our success by increasing the percentage of winners in the refined pool we choose from. However, as Nvidia and Novo Nordisk clearly demonstrate magnitude matters too! This is why we no longer use equal weight position sizing in Global Leaders.10 Our IRR-based capital allocation framework aims to get large weights into our biggest percentage winners. Coming back to the Bessembinder study, we invest only in what we believe to be exceptional businesses because most businesses ultimately fail, and we want to reduce uncertainty. It is a truism that 50% of small and medium-sized enterprises (SME) businesses fail within the first five years.11 At Intuit’s Investor Day in September last year, management highlighted the maths within their QuickBooks SME accounting software franchise, whereby any improvement in the success rates (i.e. a reduction in the failure rate of SMEs) they can help their SME customers achieve – typically through better cash management – comes right back as revenue growth due to less churn. All else equal, if SMEs on their platform have an approximately 70% success rate after the first 5 years, that is equivalent to nearly 4% per annum extra growth from that cohort.12 It’s a win-win. We specifically invest against these business survival rate odds in Indonesia too. Bank Rakyat’s micro lending business has approximately 98% annual payback on its loans.13 This is extraordinary within unsecured small business lending globally when half the companies fail within five years. The businesses we like to invest in demonstrably help their customers succeed. It’s a winning formula for everyone, and only then is Charles Darwin’s survival of the fittest on our side.Minimising the number of decisions to be correct (or, other hit-rates to be wary of!)Our coach once jokingly quipped that we ought to consider selling new investments after 24 months and buying them back 18 months later. Our analysis showed the alpha timeline of a typical investment plateaued after 2 years and on average started compounding again at about 3.5 years from our initial investment. Aside from the danger of working with averages, the more pertinent problem is the number of decisions required to get right: 1) timing when to sell; 2) what to do with the money for 18 months (don’t lose it!) in a portfolio with an average holding period approaching ten years; and 3) remembering to buy back in at an opportune moment. Compound probabilities imply that even if we run at an average of 80% correct on each individual decision then our actual chance of getting all three correct sequentially is barely better than a coin flip at 51% (80% x 80% x 80% = 51%). It seems better to stay invested the whole way and reduce decision risk after having already identified a good company. We do adjust our portfolio weights based on competition for capital and changing potential IRRs due to share price movements. Work with our coach shows that this trimming/adding does add value. That said, we are careful not to be hyperactive and typically only trade just over once a month. Even with a high probability of individual decision success, when compounding these together, win rates fall dramatically.In Remembrance of a MasterWe don’t have a portrait of Charles Darwin amongst our office artwork, but perhaps we should. As a scientist celebrated alongside Sir Isaac Newton, his insights into investing deserve more merit than we had realised before reading Pulak Prasad’s astute book.14 Nonetheless, our current artwork does a good job of reminding us we are in the rejection business, and our default setting must be to say ‘no’. We even reordered part of our investment process to reflect this refreshed mentality after our 2023 offsite in October. To us, the statistics above also strongly advocate for portfolio concentration into fewer winners and fewer potential losers as type 1 errors are minimised. In other words, don’t bend on quality/customer outcome/moats/RoIC/etc. nor on valuation and IRR in order to avoid type 1 errors of inclusion. In nature it turns out that survival of the fittest statistically means error minimisation, particularly when those errors can be fatal. Whilst that means missing out on a few more winners, the numbers suggest it will increase our portfolio’s chances of survival in the long run!We are very grateful for the support & trust from our clients as we approach our ninth anniversary and we wish you a healthy and happy 2024. Mick, Bertie and the Global Leaders Team Download the full letter >The Global Leaders Strategy invests in a concentrated portfolio of market-leading companies from across the globe. We believe that companies that combine exceptional outcomes for their customers with strong leadership can generate high and sustainable returns on invested capital (ROIC) which can lead to outstanding shareholder returns.DisclosuresPast performance may not be a reliable guide to future performance and investors may not get back the amount invested. All investments involve risk. The value of the investment and the income from it will vary. There is no guarantee that the initial investment will be returned.The views expressed are those of the author and Brown Advisory as of the date referenced and are subject to change at any time based on market or other conditions. These views are not intended to be and should not be relied upon as investment advice and are not intended to be a forecast of future events or a guarantee of future results. The information provided in this material is not intended to be and should not be considered to be a recommendation or suggestion to engage in or refrain from a particular course of action or to make or hold a particular investment or pursue a particular investment strategy, including whether or not to buy, sell, or hold any of the securities mentioned. It should not be assumed that investments in such securities have been or will be profitable. To the extent specific securities are mentioned, they have been selected by the author on an objective basis to illustrate views expressed in the commentary and do not represent all of the securities purchased, sold or recommended for advisory clients. The information contained herein has been prepared from sources believed reliable but is not guaranteed by us as to its timeliness or accuracy, and is not a complete summary or statement of all available data. This piece is intended solely for our clients and prospective clients, is for informational purposes only, and is not individually tailored for or directed to any particular client or prospective client.Sustainable investment considerations are one of multiple informational inputs into the investment process, alongside data on traditional financial factors, and so are not the sole driver of decision-making. Sustainable investment analysis may not be performed for every holding in the strategy. Sustainable investment considerations that are material will vary by investment style, sector/industry, market trends and client objectives. The Strategy seeks to identify companies that it believes may be desirable based on our analysis of sustainable investment related risks and opportunities, but investors may differ in their views. As a result, the Strategy may invest in companies that do not reflect the beliefs and values of any particular investor. The Strategy may also invest in companies that would otherwise be excluded from other funds that focus on sustainable investment risks. Security selection will be impacted by the combined focus on sustainable investment research assessments and fundamental research assessments including the return forecasts. The Strategy incorporates data from third parties in its research process but does not make investment decisions based on third-party data alone.Bloomberg is a trademark and service mark of Bloomberg Finance L.P., a Delaware limited partnership, or its subsidiaries. Any other trademarks or service marks are property of their respective owners. The MSCI ACWI® Index (All Country World Index), MSCI’s flagship global equity index, is designed to represent performance of the full opportunity set of large- and mid-cap stocks across developed and emerging markets. As of May 2022, it covers more than 2,933 constituents across 11 sectors and approximately 85% of the free float-adjusted market capitalization in each market. All MSCI indexes and products are trademarks and service marks of MSCI or its subsidiaries.The MSCI ACWI® Index MSCI’s flagship global equity index, is designed to represent performance of the full opportunity set of large- and mid-cap stocks across developed and emerging markets. As of May 2022, it covers more than 2,933 constituents across 11 sectors and approximately 85% of the free float-adjusted market capitalization in each market. All MSCI indexes and products are trademarks and service marks of MSCI or its subsidiaries.Return on invested capital (RoIC) is a measure of determining a company’s financial performance. It is calculated as NOPAT/IC; where NOPAT (net operating profit after tax) is (EBIT + Operating Leases Due 1-Yr)*(1-Cash Tax Rate) and IC (invested capital) is Total Debt + Total Equity + Total Unfunded Pension + (Operating Leases Due 1-Yr * 8) – Excess Cash. ROIC calculations presented use LFY (last fiscal year) and exclude financial services.The internal rate of return (IRR) is a measure of an investment’s rate of return. The internal rate of return is a discount rate that makes the net present value (NPV) of all cash flows from a particular project equal to zero. It is also called the discounted cash flow rate of return.Tracking Error is the standard deviation of the difference in the portfolio and benchmark returns.Alpha is a measure of performance on a risk-adjusted basis. Alpha takes the volatility (price risk) of a portfolio and compares its risk-adjusted performance to a benchmark index.Annualized Return is the geometric average amount of money earned by an investment each year over a given time period. It is calculated as a geometric average to show what an investor would earn over a period of time if the annual return was compounded.Volatility is a statistical measure of the dispersion of returns for a given security or market index. Volatility can either be measured by using the standard deviation or variance between returns from that same security or market index.Weighted Average Cost of Capital (WACC) presents a firm's average after-tax cost of capital from all sources, including common stock, preferred stock, bonds, and other forms of debt. WACC is the average rate a company expects to pay to finance its assets. **Return is for period May 1, 2015 through December 31, 2015Brown Advisory Institutional claims compliance with the Global Investment Performance Standards (GIPS®) and has prepared and presented this report in compliance with the GIPS standards. Brown Advisory Institutional has been independently verified for the periods from January 1, 1993 through December 31, 2022. The Verification reports are available upon request. A firm that claims compliance with the GIPS standards must establish policies and procedures for complying with all the applicable requirements of the GIPS standards. Verification provides assurance on whether the firm's policies and procedures related to composite and pooled fund maintenance, as well as the calculation, presentation, and distribution of performance, have been designed in compliance with the GIPS standards and have been implemented on a firm-wide basis. Verification does not provide assurance on the accuracy of any specific performance report. GIPS® is a registered trademark of CFA Institute. CFA Institute does not endorse or promote this organization, nor does it warrant the accuracy or quality of the content contained herein.1. *For the purpose of complying with the GIPS standards, the firm is defined as Brown Advisory Institutional, the Institutional and Balanced Institutional asset management divisions of Brown Advisory. As of July 1, 2016, the firm was redefined to exclude the Brown Advisory Private Client division, due to an evolution of the three distinct business lines.2. The Global Leaders Composite (the Composite) aims to achieve capital appreciation by investing primarily in global equities. The strategy will invest in equity securities of companies that the portfolio manager believes are leaders within their industry or country, as demonstrated by an ability to deliver high relative return on invested capital over time. The minimum account market value required for Composite inclusion is $1.5 million.3. Sustainable investment considerations are one of multiple informational inputs into the investment process, alongside data on traditional financial factors, and so are not the sole driver of decision-making. Sustainable investment analysis may not be performed for every holding in the strategy. Sustainable investment considerations that are material will vary by investment style, sector/industry, market trends and client objectives. The Global Leaders Strategy (“Strategy”) seeks to identify companies that it believes may be desirable based on our analysis of sustainable investment related risks and opportunities, but investors may differ in their views. As a result, the Strategy may invest in companies that do not reflect the beliefs and values of any particular investor. The Strategy may also invest in companies that would otherwise be excluded from other strategies that focus on sustainable investment risks. Security selection will be impacted by the combined focus on sustainable investment research assessments and fundamental research assessments including the return forecasts. The Strategy incorporates data from third parties in its research process but does not make investment decisions based on third-party data alone.4. The Composite creation date is August 26, 2015. The Composite inception date is May 1, 2015.5. The benchmark is the MSCI ACWI Net Index. The MSCI ACWI Net Index captures large and mid-cap representation across Developed Markets (DM) and Emerging Markets (EM) countries. The Index covers approximately 85% of the global investable equity opportunity set. All MSCI indexes and products are trademarks and service marks of MSCI or its subsidiaries. An investor cannot invest directly into an index. Benchmark returns are not covered by the report of the independent verifiers.6. As of September 1, 2022, the Composite benchmark was changed from the FTSE All-World Net Index to the MSCI ACWI Net Index. The change was applied retroactively from the Composite inception date. The Advisor determined that MSCI indices are more widely used for global products, and thereby provide more relevant data to shareholders and prospects as well as comparisons to competitors.7. Composite dispersion is an equal-weighted standard deviation of portfolio gross returns calculated for the accounts in the Composite for the entire calendar year period. The composite dispersion is not applicable (N/A) for periods where there were five or fewer accounts in the Composite for the entire period.8. Gross-of-fees performance returns are presented before management fees but after all trading commissions, and gross of foreign withholding taxes (if applicable). Net-of-fees performance returns are calculated by adjusting the gross-of-fees performance return by the highest fee for the institutional strategy as outlined in Part 2A of the firm’s Form ADV, applied on a monthly basis. Certain accounts in the Composite may pay asset-based custody fees that include commissions. For these accounts, gross returns are also net of custody fees. Other expenses can reduce returns to investors. The standard management fee schedule is as follows: 0.80% on the first $50 million; 0.55% on the next $50 million; 0.45% on the next $50 million; and 0.40% on the balance over $150 million. Further information regarding investment advisory fees is described in Part 2A of the firm’s Form ADV. Actual fees paid by accounts in the Composite may differ from the current fee schedule.9. Effective July 1, 2023, the firm transitioned from using actual account fees in the calculation of net performance returns to applying the highest fee for the institutional strategy as outlined in Part 2A of the firm’s Form ADV. The net performance track record was revised back to Composite inception.10. The investment management fee for the Investor Shares of the Brown Advisory Global Leaders Fund (the Fund), which is included in the Composite, is 0.65%, and represents the highest fee charged excluding Advisor Shares. The total expense ratio for the Investor Shares of the Fund as of the most recent fiscal year end (June 30, 2022) was 0.90%. Further information regarding investment management fees and expenses is described in the fund prospectus and annual report.11. The investment management fee for the Dollar Class B Acc Shares of the Brown Advisory Global Leaders Fund (the UCITS), which is included in the composite, is 0.75%. The total expense ratio for the Dollar Class B Acc Shares of the UCITS as of the most recent fiscal year end (October 31, 2022) was 0.87%. Further information regarding investment management fees and expenses is described in the fund prospectus and annual report.12. The three-year annualized ex-post standard deviation measures the variability of the Composite (using gross returns) and the benchmark for the 36-month period ended on December 31. The 3-year annualized standard deviation is not presented as of December 31, 2015, December 31, 2016 and December 31, 2017 because the 36 month returns were not available for the Composite (N/A).13. Valuations and performance returns are computed and stated in U.S. Dollars. All returns reflect the reinvestment of income and other earnings.14. A complete list of composite descriptions and broad distribution and limited distribution pooled funds is available upon request.15. Policies for valuing investments, calculating performance, and preparing GIPS Reports are available upon request.16. Past performance is not indicative of future results.17. This is not an offer to sell securities. That may only be accomplished by the issuance of a private offering memorandum/subscription documents. 18. This piece is provided for informational purposes only and should not be construed as a research report, a recommendation or suggestion to engage in or refrain from a particular course of action or to make or hold a particular investment or pursue a particular investment strategy, including whether or not to buy, sell or hold any of the securities mentioned, including any mutual fund managed by Brown Advisory.