Allocating Capital: What the Research Says About Expected Returns, Risk, Position Sizing, Leverage, Valuation, Cycles and Spending

This article summarises published research on allocating capital. It is general information, not financial advice: it doesn't know your situation, your country's tax and pension rules or what is available to you, and it doesn't recommend any product, fund or strategy. Past returns don't predict future ones.

VettedVids rates books and videos by what people report happened after using them. Research is different: we don't score it. We summarise what each study found, the market and period it covers and its limits, and where findings disagree we show both rather than settle it. Several findings come from fund managers or practitioners (AQR Capital Management, Elm Partners and PIMCO, E.O. Thorp and Associates, Cornerstone Wealth Advisors, a practising financial planner and Finance Concepts), and we say where. Much of the research uses US data, and several figures come from working papers rather than the published versions; we say which. Every claim below links to its source, and the same findings are in the Research tab of our Allocate capital page.

Estimating expected returns

• Past equity returns ran well above what dividend and earnings growth implied. Estimating the US equity premium from dividend and earnings growth rather than from realised returns, Fama and French put it at 2.55% a year (dividend growth) and 4.32% (earnings growth) for 1951 to 2000, against 7.43% from the average realised stock return. They attribute the gap to a fall in discount rates that produced a large unexpected capital gain, and conclude that the average return of that half-century 'is a lot higher than expected' (Fama & French 2002, Journal of Finance). This is US data for 1951–2000. The gap between the growth-based and realised figures is the 'change in valuation' part of a return: a re-rating that need not repeat. The estimates depend on which growth measure is used.
• Starting valuation explained about a quarter of 10-year returns, but timing on it barely helped (contested). For US equities from 1900 to 2015, the Shiller earnings yield (the inverse of CAPE) explained about a quarter of the variation in next-10-year returns in sample (R-squared 0.24), 0.05 for next-year returns and 0.00 for next-month returns. A rules-based strategy that held between 50% and 150% in equities depending on valuation had a Sharpe ratio of 0.37, against 0.38 for buy-and-hold, over 1900–2015. Over 1958–2015 it earned 5.4% a year above cash, against 5.5% for buy-and-hold. Neither difference was statistically significant. The authors argue that combining valuation with momentum signals, with only modest tilts, worked better than valuation alone, though this improvement was also not statistically significant (Asness, Ilmanen & Maloney 2017, Journal of Investment Management, Market Timing: Sin a Little). The in-sample link is often read as strong support for shifting a mix on valuation; this strategy test found little benefit. All three authors work at AQR Capital Management, a fund manager that runs timing and factor strategies. The results are hypothetical and before costs and fees, and the in-sample figures use the full history to define 'cheap' and 'expensive', which investors at the time couldn't do. Our Build a portfolio research summary covers the earlier CAPE studies.
• Most published return predictors failed out of sample, in an update to 2021. Goyal, Welch and Zafirov re-tested 29 variables from 26 papers published after Goyal and Welch (2008), plus the original 17, with data to the end of 2021. More than one-third of the new variables were no longer significant even in sample. Of those that were, half performed poorly out of sample. A small number still performed reasonably well both in and out of sample (Goyal, Welch & Zafirov 2024, Review of Financial Studies). This is US equity premium data, and valuation ratios are among the variables tested. Statistical performance alone doesn't show that a timing rule would have paid after costs.
• The world equity premium since 1900, and lower forward estimates. Across 19 countries from 1900 to 2010, the annualised (geometric) equity premium over Treasury bills was 5.3% for the US, 4.3% for the UK, 4.6% averaged across the countries and 4.5% for the World index. Over long government bonds it averaged 3.8%. Removing windfalls from currency moves and rising valuations lowers the World figure from 4.5% to 4.0%, and the average country's US-dollar premium from 4.0% to 3.4%. From a 2.5% dividend yield and an assumed 2% real dividend growth, the authors put the prospective World premium at 3–3.5% geometric, or around 4.5–5% arithmetic, and warn that investors relying on figures as high as 7% geometric or 9% arithmetic 'are likely to be disappointed' (Dimson, Marsh & Staunton 2011, in Rethinking the Equity Risk Premium, CFA Institute Research Foundation). The data end in 2010; the authors' 2026 Yearbook extends the series to 2025, but its full premium tables aren't public. The forward figures are the authors' estimates as of year-end 2010 and depend on the growth assumption. All 19 markets survived the period, which is the subject of the next finding.
• Survivorship: is the US equity record the exception? (contested) Collecting capital-appreciation indexes for 39 markets back to the 1920s, Jorion and Goetzmann found that from 1921 to 1996 US equities had the highest real return, 4.3% a year, against a median of 0.8% for the other countries. They conclude that the high US equity premium 'appears to be the exception rather than the rule' (Jorion & Goetzmann 1999, Journal of Finance). Dimson, Marsh and Staunton reach a different conclusion for the world as a whole: their 19 surviving markets made up an estimated 89% of world equity value in 1900, and even if the missing 11% had all become worthless (investors in Russia in 1917 and China in 1949 lost everything), the world equity premium would be overstated by at most about 0.1 percentage point a year (Dimson, Marsh & Staunton 2011). The two studies measure different things: Jorion and Goetzmann use price indexes without dividends and compare the US with the median country, while Dimson, Marsh and Staunton use total returns weighted by market size. Both treat the US as one of the strongest markets of the period, which makes US-only history a narrow base for forward estimates.

Deciding how much risk to take

• The average return overstates what a typical investor ends up with. Long-horizon cumulative returns are skewed, so the median outcome sits below the mathematical expectation, and the chance of reaching the expected cumulative return falls toward zero as the horizon lengthens. In the authors' simulations of a large-cap stock index, there was only about a 30% probability of meeting or exceeding the expected 30-year cumulative return. To forecast the median outcome, they compound the average log (geometric) return instead. Even with 54 years of data, typical stock volatility of 15% leaves historical averages uncertain by about ±400 basis points (Hughson, Stutzer & Yung 2006, Financial Analysts Journal). This is a statistical argument with simulations, not a study of investors, and the 30% figure depends on the assumed volatility and horizon.
• The Merton share: a constant risky share set by excess return, volatility and risk aversion. Merton solved the combined problem of lifetime consumption and portfolio choice in continuous time. In the two-asset case with constant relative risk aversion, the optimal fraction of wealth in the risky asset is its expected excess return over the riskless asset, divided by relative risk aversion times the asset's return variance. That fraction stays constant over time and doesn't depend on wealth (Merton 1969, Review of Economics and Statistics). This is a theoretical model. It assumes returns follow a random walk with known, constant mean and volatility, no labour income and unchanging risk aversion; changing these changes the answer. The result is very sensitive to the expected excess return, which is itself hard to estimate (see the expected-returns findings above). The formula given here is the paper's two-asset, constant-relative-risk-aversion solution.
• Given a coin weighted 60/40 in their favour, 28% of trained players went bust. Sixty-one young, quantitatively trained participants, mostly economics and finance students and young finance professionals, were each given $25 to bet for 30 minutes on a coin they were told came up heads 60% of the time, with winnings capped at $250. 28% went bust and only 21% reached the cap (finishing with at least $200); the average payout was $91. Eighteen players bet their whole bankroll on a single flip. Betting a constant 20% of the bankroll on heads (the Kelly fraction, 2 × 0.6 − 1) gives a probability of ruin close to zero. The authors also show why a positive average isn't enough: betting 20%, a win followed by a loss leaves 1.2 × 0.8 = 0.96 of the starting amount (Haghani & Dewey 2016, working paper, arXiv 1701.01427). Both authors are practitioners: Haghani is founder and CEO of Elm Partners, a fund manager, and Dewey worked at PIMCO. It is a small, non-random sample playing a one-off game with a payout cap, not a study of investing. The abstract says 'about 30%' went bust; the body gives 28%, defined as finishing with under $2.

We have no dedicated finding on how earnings, age and property change the risky share; the leverage-when-young study below models it, and our Build a portfolio research summary covers future pay as a bond-like asset. Nor do we have a dedicated finding on permanent loss versus short-term volatility; the survivorship finding above and the coin-flip experiment touch on ruin.

Sizing and concentrating positions

• Kelly betting maximises long-run growth, but practitioners bet a fraction of it. Kelly showed that a gambler with an edge can make wealth grow exponentially, at a maximum rate equal to the information rate of the channel (Kelly 1956, Bell System Technical Journal). Betting to maximise the expected logarithm of wealth (the Kelly criterion) gives the highest long-run growth rate; for a simple two-outcome bet, the Kelly wager is the edge divided by the odds. MacLean, Thorp and Ziemba list the drawbacks: the wagers can be very large, so Kelly 'can be very risky in the short term', and in continuous time, betting twice the Kelly amount cuts the growth rate to the risk-free rate. In one example of 700 bets each with a 14% edge, full Kelly turned $1,000 into at least $100,000 16.6% of the time but could also leave $18. Half Kelly could still leave $145, and reached $100,000 or more only 0.1% of the time. Citing Chopra and Ziemba, they note that errors in estimated means mattered roughly 10 times as much as errors in variances and 20 times as much as errors in covariances, and they advise smaller bets when the inputs are uncertain (MacLean, Thorp & Ziemba 2010, Quantitative Finance). These are mathematical results and worked examples, not a study of investors. Kelly worked at Bell Labs; Thorp is listed with E.O. Thorp and Associates. In investing the true edge and odds are unknown, which is the main argument given for betting less than full Kelly.
• Shortfall risk kept falling beyond 100 stocks. Simulating portfolios drawn from 1,000 large US stocks over a 20-year holding period, Domian, Louton and Racine measured shortfall risk: the chance of ending below a wealth target. It kept falling as portfolio size grew, even above 100 stocks. Spreading holdings across industries lowered risk slightly in small portfolios, but adding more stocks lowered it more (Domian, Louton & Racine 2007, Financial Review). This covers US large-cap stocks only, and the abstract doesn't give the sample years. It uses ending wealth rather than volatility: Statman found 30–40 stocks enough under a volatility-based definition (see our Build a portfolio summary), so the answer depends on the measure.
• Concentrated portfolios: signs of skill, more risk, and costly on average (contested). Using US discount-broker accounts from 1991 to 1996, Ivković, Sialm and Weisbenner found that stock trades by households with concentrated portfolios did better than those of diversified households, especially in larger accounts and in local or non-S&P 500 stocks. But the concentrated portfolios carried more total risk and had lower Sharpe ratios (Ivković, Sialm & Weisbenner 2008, Journal of Financial and Quantitative Analysis). Goetzmann and Kumar found most US individual investors under-diversified, in patterns linked to overconfidence, trend-following and local bias, and that under-diversification was costly for most of them; only a small subset appeared to concentrate because of superior information (Goetzmann & Kumar 2008, Review of Finance). Among mutual funds, focused funds (few holdings) did no better than diversified funds before expenses, significantly worse after them, and closed more often (Sapp & Yan 2008, Financial Review). The concentrated-household result shows better stock selection on average, not better risk-adjusted portfolios. All three are US observational studies in which investors and funds chose their own level of concentration.
• Professional managers bought well but sold worse than random. In data on 783 institutional portfolios averaging $573 million, positions the managers added earned over 100 basis points a year more, per dollar bought, than both the benchmark and a strategy of randomly adding to existing holdings. Their sales did worse than a random-selling strategy: in the preferred specification they gave up 80 basis points a year relative to selling at random. The authors link this to a costly, low-attention heuristic used when selling but not when buying (Akepanidtaworn, Di Mascio, Imas & Schmidt 2023, Journal of Finance; figures from NBER Working Paper 29076, 2021). These are institutional managers, not individuals. The shortfall was largest among fundamentals-oriented managers with concentrated, high-tracking-error portfolios, and the study doesn't test alternative selling rules.

Using (or avoiding) leverage

• Daily-reset leveraged funds drift from their stated multiple over longer periods. In a US regulator example, over four months an index gained 2% while a fund seeking twice its daily return fell 6%, and a fund seeking twice the inverse fell 25%. Over the same period a fund seeking three times another index's daily return fell 53% while that index gained about 8%. In the regulator's two-day illustration, an index falls 10% then rises 10%, ending down 1%, while a 2x fund falls 20% then rises 20%, ending down 4% (SEC Office of Investor Education and Advocacy 2023, Updated Investor Bulletin: Leveraged and Inverse ETFs). Avellaneda and Zhang derive an exact formula linking a leveraged fund's return to the multiple of the index's return and the index's realised variance. It closely matched the quarterly returns of 56 leveraged funds (44 double, 12 triple) from January 2008, and they conclude such funds 'may be unsuitable for buy-and-hold investors' (Avellaneda & Zhang 2010, SIAM Journal on Financial Mathematics). The regulator examples are selected real cases plus a hypothetical. In periods of large returns and low volatility, leveraged funds can beat the static multiple, and Avellaneda and Zhang note a few such periods. Their study tested the formula over quarterly horizons from 2008. The authors are listed with NYU's Courant Institute and Finance Concepts, a firm.
• Leverage when young: a case for it, and the margin-call risk (contested). Using US stock data back to 1871, Ayres and Nalebuff find that holding stocks at up to 2:1 leverage early in working life, then reducing equity exposure later, produced the same average retirement wealth as a constant 75% stock allocation with a 21% smaller standard deviation. For an investor with relative risk aversion of 4, they estimate a 37% gain in certainty-equivalent wealth. The worst month was October 1929, when a fully leveraged young investor's portfolio fell 53% in that month. About one cohort in eight (11 of 96) lost more than 40% in at least one month. At 2:1 leverage with a 25% maintenance margin, forced selling starts after a market fall of about one-third (Ayres & Nalebuff 2013, Journal of Portfolio Management; figures from Ayres & Nalebuff 2010, Diversification Across Time, Yale Law School working paper). The result depends on its assumptions: cheap borrowing, monthly rebalancing and continuing to invest through crashes. The figures are from the 2010 working paper, and the 2013 published version may differ. Regulators (the SEC, FINRA and ASIC's Moneysmart) warn that margin calls can force sales at low prices; their pages are linked on the Allocate capital page.

Our research set has no study comparing the cost and forced-selling risk of margin loans, investment-property loans, leveraged funds and home equity, and we found no regulator data on how often margin calls lead to forced sales.

Valuing a business

• Long-run earnings growth barely persisted beyond chance. Across US firms from 1951 to 1997, the median growth rate of operating performance roughly matched GDP growth, and only about 10% of firms grew faster than 18% a year over ten years. For income before extraordinary items, about 3% of surviving firms beat the median growth rate five years in a row, close to the 3.1% expected by chance. Analysts' long-term (IBES) growth forecasts were too optimistic and added little predictive power. The authors conclude that valuations assuming persistently high growth 'rest on shaky foundations' (Chan, Karceski & Lakonishok 2003, Journal of Finance; figures from NBER Working Paper 8282, 2001). This covers US firms. Sales growth showed some persistence; earnings growth showed essentially none. It bears on reading what a price implies: high long-run growth has been rare.
• Profitability reverts toward the mean, at about 38% a year. In a simple partial-adjustment model, Fama and French estimate that firms' profitability moves back toward the mean at about 38% a year. Reversion is faster when profitability is below its mean and when it is further from the mean in either direction, and this mean reversion makes changes in earnings partly predictable (Fama & French 2000, Journal of Business). This covers US firms, and the abstract gives no sample period. It is an average across firms: some keep high returns on capital for long periods, which is what judging competitive advantage tries to identify.
• Companies use hurdle rates about twice their cost of capital. Matching a survey of chief financial officers to company data, the authors find that firms use discount rates averaging twice their cost of financial capital. Firms with plenty of capital but limited management or staff capacity appear to pass up profitable projects to keep room for better ones later. Firms using high discount rates had strong balance sheets, low leverage and large cash holdings, and firms also raised discount rates to allow for company-specific risk (Jagannathan, Matsa, Meier & Tarhan 2016, Journal of Financial Economics). These are US firms responding to a survey, and hurdle rates are self-reported. The study describes how companies set hurdle rates, not what rate an investor needs to require.
• Returns after buyback announcements: strong in the 1980s, gone by 2003–2012 (contested over time). For open-market buyback announcements from 1980 to 1990, the average abnormal four-year buy-and-hold return was 12.1%, and 45.3% for 'value' stocks, with no positive drift for 'glamour' stocks (Ikenberry, Lakonishok & Vermaelen 1995, Journal of Financial Economics). Fu and Huang find that the long-run abnormal returns after buybacks (and after share issues) disappeared for events in 2003–2012, and link the change to more institutional investment, lower trading costs, better liquidity and tighter governance and disclosure rules (Fu & Huang 2016, Management Science). Both are US studies, and long-run abnormal returns depend heavily on the benchmark used. Neither judges whether a particular company's buyback was a good use of its cash.
• Acquirers' shareholders lost $240 billion in 1998–2001. Acquiring-firm shareholders lost 12 cents per dollar spent around acquisition announcements from 1998 through 2001, $240 billion in total, against $7 billion (1.6 cents per dollar) in all of the 1980s. Most of the 1998–2001 loss came from a small number of deals by firms with very high valuations; without those deals, acquirers' shareholders would have gained. Firms that made large-loss acquisitions performed poorly afterwards (Moeller, Schlingemann & Stulz 2005, Journal of Finance). These are US public acquirers. Announcement returns are the market's immediate verdict, not the deal's eventual value, and averages hide wide variation between deals.

Our research set has no study on estimating owner earnings or free cash flow from a company's accounts; the page points to company filings and free valuation spreadsheets for that.

Reading capital and market cycles

• Shipping booms: high earnings and heavy investment came before low returns. In dry bulk shipping from 1976 to 2011, high current ship earnings went with high secondhand ship prices and heavy investment in new ships, but forecast low future returns. Annual returns to owning a ship ranged from −76% (December 2007 to December 2008) to +86% (June 1978 to June 1979). The baseline regressions put expected one-year excess returns between −43% and +16%. Orders for new ships rose from under 10% of the active fleet in December 2001 to over 75% in August 2008. The authors' model explains this as firms over-extrapolating demand and partly neglecting their competitors' investment (Greenwood & Hanson 2015, Quarterly Journal of Economics; figures from NBER Working Paper 19246, 2013). This is one industry, where new ships take 18–36 months to deliver, and the published version may differ from the working paper. It illustrates the capital cycle; it isn't evidence that every industry behaves this way.
• Fast-growing balance sheets predicted lower stock returns. Across US stocks, a firm's annual growth in total assets strongly predicted lower future abnormal returns, including among large companies. Compared with book-to-market, size, past returns, accruals and other growth measures, asset growth stood out as an economically and statistically significant predictor (Cooper, Gulen & Schill 2008, Journal of Finance). This is observational, and the abstract gives no magnitudes or sample period. A related 'investment' factor appears in the Fama-French five-factor model, and published return patterns often weaken after publication; our factor investing research summary covers both.
• Frothy credit markets came before wider spreads and weaker growth. Using US data from 1929 to 2015, López-Salido, Stein and Zakrajšek find that elevated credit-market sentiment in one year was followed two to three years later by a decline in economic activity. When credit risk was priced aggressively, spreads later widened, and the timing of the widening was closely tied to the start of contractions (López-Salido, Stein & Zakrajšek 2017, Quarterly Journal of Economics). Greenwood and Hanson find that the credit quality of corporate bond issuers falls during credit booms, that this fall forecasts low excess returns to corporate bondholders, and that it was a more reliable sign of overheating than rapid overall credit growth (Greenwood & Hanson 2013, Review of Financial Studies). Both use US data. These are average forecasting relationships, not precise timing signals, and neither study says when spreads will widen; see the out-of-sample update under expected returns above.
• Credit growth has been a strong predictor of financial crises. Across 14 countries from 1870 to 2008, total credit rose strongly relative to output and money in the second half of the 20th century. Credit growth was a powerful predictor of financial crises. Monetary policy responses to crises became more aggressive over time, but the output costs of crises stayed large (Schularick & Taylor 2012, American Economic Review). This is country-level data for developed economies. It predicts crises, not market returns, and crises are rare, so the estimates rest on relatively few events.

Setting a spending rule

Three findings below give different withdrawal rates. They use different data, different rules and different definitions of failure, so we show all three rather than pick one.

• Where the 4% rule came from, and how much inflation adjustment matters. Bengen tested a 50/50 mix of US stocks and intermediate-term Treasuries from 1926. A 4% first-year withdrawal, raised with inflation each year, never exhausted the portfolio in under 33 years; 4.25% could run out in as little as 28 years (Bengen 1994, Journal of Financial Planning, reprinted 2004). In the Trinity study authors' 2011 update (US large-company stocks and high-grade corporate bonds, 1926–2009), a 75/25 portfolio supported a 7% withdrawal for 30 years in 91% of past periods when withdrawals were fixed in dollars, but in only 45% when they rose with inflation. All but one of the 18 failed 30-year periods for 5% inflation-adjusted withdrawals from a 50/50 portfolio spanned the high-inflation late 1970s (Cooley, Hubbard & Walz 2011, Journal of Financial Planning, Portfolio Success Rates: Where to Draw the Line). This is US history only, before fees and taxes, and overlapping periods give far fewer independent observations than the counts suggest. Bengen was a practising financial planner.
• A 38-country sample points to a much lower withdrawal rate (contested). Using asset-class returns from 38 developed countries, Anarkulova, Cederburg, O'Doherty and Sias estimate that a 65-year-old couple willing to accept a 5% chance of financial ruin could withdraw just 2.31% a year, which they call 'materially lower' than conventional advice such as the 4% rule (Anarkulova, Cederburg, O'Doherty & Sias 2025, Journal of Pension Economics and Finance). This is far below US-history results such as Bengen's 4%. The sample includes countries with poor real returns, and the paper's keywords point to survivor bias and 'easy data' bias in narrower samples. As with the 4% rule, withdrawals are a fixed inflation-adjusted amount set as a percentage of the balance at retirement, and 'ruin' means running out of money (confirmed from the working-paper version; the published text is paywalled). The comparison with Bengen still differs in how failure is defined (a 5% lifetime chance of ruin for a couple, versus no failure over 30+ years), the portfolio and the data.
• Guardrails: rules that cut or raise spending let higher starting rates last. Guyton and Klinger ran Monte Carlo tests of 40-year retirements, using return data from 1973–2004 and from 1928–2004, and added two 'guardrail' rules to two rules kept from Guyton's earlier work: no inflation increase after a year of negative portfolio returns (when the withdrawal rate is above its starting level), and a rule on which assets to sell. If the current withdrawal rate rises more than 20% above the initial rate, that year's withdrawal is cut by 10%; this rule stops 15 years before the end of the planning horizon. If the rate falls more than 20% below the initial rate, the withdrawal is raised by 10%. With at least 65% in equities, initial withdrawal rates of 5.2–5.6% were sustainable at a 99% confidence standard, which also required median purchasing power to be kept; with 50% equities, the maximum fell to as low as 4.6%. The two data periods gave virtually identical results (Guyton & Klinger 2006, Journal of Financial Planning, Decision Rules and Maximum Initial Withdrawal Rates). The higher starting rate is paid for with spending cuts after poor markets, so income can fall in real terms. Guyton was principal of a wealth-advisory firm (Cornerstone Wealth Advisors); Klinger's background is in software development. Results depend on the simulation assumptions and on applying the rules every year.
• In theory, retirees gain from annuities, and pricing is close to fair for typical buyers. Yaari (1965) showed that, for a consumer with an uncertain lifespan and no bequest motive, full annuitisation is optimal (Yaari 1965, Review of Economic Studies). Davidoff, Brown and Diamond show that full annuitisation remains optimal under much weaker conditions when markets are complete, and that some annuitisation remains optimal in many cases when they are not, a considerable share in their calculations. They suggest that limited annuity purchases are plausibly due to psychological or behavioural biases (Davidoff, Brown & Diamond 2005, American Economic Review). On pricing, Poterba and Solomon (2021, revised 2025) estimate that US immediate annuities on sale in May 2024, bought at 65, paid out about 87 cents per premium dollar for a buyer with average US population mortality, and about one dollar for a typical annuity buyer. For a deferred annuity bought at 65 with payments from 75, the figures were 73 cents and close to one dollar (Poterba & Solomon 2021, revised 2025, NBER Working Paper 28557; prices from May 2024). This is theory plus US market pricing. We didn't read Yaari's 1965 paper directly: its result is given here as Davidoff, Brown and Diamond summarise it. Money's-worth estimates depend on the mortality and discount-rate assumptions, and buying an annuity gives up access to the lump sum and any bequest from it.
• Few retirees buy annuities, and framing may explain part of why. In a four-arm internet survey of 1,342 people over 50, 72% preferred a life annuity to a savings account when the choice was framed in terms of consumption, but only 21% when it was framed in terms of investment features (Brown, Kling, Mullainathan & Wrobel 2008, American Economic Review, Papers and Proceedings). In the UK, in the year to 31 March 2026, 100,144 annuities were bought and 401,137 plans entered drawdown, out of 1,047,008 pension plans accessed for the first time (Financial Conduct Authority 2026, Retirement income market data 2025/26). The survey asked about hypothetical choices between options designed to be actuarially equivalent, not real purchases. The UK figures are regulator data on what people chose, not on why; 45.8% of pots accessed were cashed in entirely, and many pots are small. The FCA data reflect firm submissions as of 7 August 2026 and may be revised.

What this means for each step

This is how the findings above line up with the steps on the Allocate capital page. It describes the evidence, not what any one person ought to do.

• Estimate expected returns. The research breaks a return into income, growth and a change in valuation, and the valuation part is the one that need not repeat. Starting valuation has said something about the next 10 years in US data, but timing strategies built on it did no better than holding steady, and most predictors weakened out of sample. A written estimate that is a range, with its sources, fits this evidence better than a single number from US history.
• Decide how much risk to take. The Merton share gives a framework, but its answer moves a lot with the expected excess return, which the step before shows is uncertain. The median outcome sits below the average, and the coin-flip game shows how quickly over-betting leads to ruin even with an edge.
• Size and concentrate positions. Kelly sizing gives the bet that maximises long-run growth when the edge is known, betting more lowers growth, and the drawdowns at full Kelly are large; with an uncertain edge the research points to smaller bets. Evidence on concentration cuts both ways, and in one study professional managers lost ground on what they sold rather than on what they bought (the study didn't test alternative selling rules).
• Use (or avoid) leverage. The case for leverage when young rests on cheap borrowing and continuing to invest through crashes, and its own worst month fell 53%. Daily-reset leveraged funds drift from their multiple over time. The regulator pages linked on the page describe margin calls and forced sales; zero leverage is one of the answers this step allows.
• Value a business. High long-run earnings growth has been rare, profitability has tended to revert, and acquisition and buyback results vary with the period studied. These give outside-view checks on what a valuation or a price assumes.
• Read capital and market cycles. Heavy investment, fast asset growth and frothy credit have come before weaker returns on average, but none of these findings gives a precise timing signal. Doing nothing is a rule this step accepts.
• Set a spending rule. The withdrawal rate depends on the data set and the rule: about 4% in US history, 2.31% across 38 countries at a 5% chance of ruin, and 5.2–5.6% with guardrails that cut spending after poor markets (plus two further rules and at least 65% in equities). Annuity theory favours more annuitisation than people choose, and the pricing and take-up data show both sides.

How we put this together

We collected research that answers questions an experienced investor faces when allocating capital: what returns to expect and how far valuation helps, how much risk to take, how large and how concentrated positions get, what leverage does, how to value a business and judge how its managers use cash, what capital and credit cycles imply, and how much a portfolio can support in spending. The sources are peer-reviewed journals, working papers, a CFA Institute Research Foundation book, and regulator bulletins and data, and we note which is which. Each finding is listed with the market and period it covers, the type of evidence and its limits in the Research tab of the Allocate capital page, alongside rated books, official guides on margin loans, leveraged products and retirement income, free data, tools and channels. Last checked 18 October 2026.