Sell in May, go away and lose money

Overview

At some point, and particularly at this time of year, you’ve probably encountered the phrase “sell in May and go away” (see, for example, Kerry Sun, “Should you ‘Sell in May and go away’?” Market Index, 1 May 2025). Australia’s financial media regularly parrot it, yet on its face – and as a couple of prominent commentators have tacitly acknowledged – it’s questionable. Moreover, Australian investors as a whole have ignored academic research which rejects it. This article 

1. clarifies the phrase, its origins and implications;
2. reviews the Australian and overseas research which assesses it;
3. demonstrates that, over short-term (six-month and 12-month) and medium-term (five-year) periods, the seasonality of Australian equities’ CPI-adjusted short-term total returns since 1975 has been much more apparent than real.

Over the past half-century, Australian equities’ returns have superficially been seasonal. What’s more, this ostensible seasonality has affirmed the adage “sell in May and go away.” Examining data in detail, however – which previous research often hasn’t – I show that the seasonality of Australian equities’ returns is a mirage.

Statistically, this “seasonality” is merely random fluctuation (which careful examination of academic analyses of Australian data, by researchers in Australia as well as overseas, confirms).

Finally, I also show why “sell stocks in May and go away,” which I dub “sell and switch” (hereafter “S&S”), when repeated over medium-term (five-year) periods, once did but no longer beats a “buy and hold” (“B&H”) approach.

Crucially, however, stocks’ seasonality never underlay S&S’s past success; and even when excluding the cost of transactions and taxes, it’s now a recipe for medium-term losses.

“Sell in May and Go Away”

Casual observation and market folklore has long contended that the calendar affects stocks’ returns. Mark Twain’s caution was one of the first and undoubtedly among the most astute. In The Tragedy of Pudd’nhead Wilson (1894) he warned: “October, this is one of the peculiarly dangerous months to speculate in stocks.” The others “are July, January, September, April, November, May, March, June, December, August, and February.” 

Since the 1980s, finance academics have systematically investigated seemingly calendar-related returns. The list of alleged patterns includes day of the week (“Monday effect”), month of the year (“January effect”) and Christmas, New Year, Easter, etc. (“holiday effect”).

According to Investopedia.com (25 March 2025), “’sell in May and go away’ is a well-known saying in finance based on stocks’ supposedly underperforming during the six months from May 1 to October 31.”

It elaborates: “The Stock Trader's Almanac popularized the idea ... that investing in stocks as represented by the Dow Jones Industrial Average from November to April (the ‘winter’ period) and switching to fixed-income investments the other six months (‘summer’) would have ‘produced reliable returns with reduced risk since 1950.’” In the U.S., this supposed pattern is also and more widely known as the “Halloween effect.”

What might underlie it? The old English saying “sell in May and go away, and come on back on St Leger’s Day” refers to the past custom of aristocrats, bankers and merchants: during the late spring they’d leave London and spend the next several months on holiday. St Leger’s Day refers to the St Leger’s Stakes. It’s a horse race which takes place in mid-September, and is the last leg (the 2000 Guineas Stakes is the first and The Derby is the second) of the British Triple Crown which has occurred annually since 1776.

Past Research

Australian Research Focusing upon Australian Data

Philip Gray and Irene Tutticci (“Australian Stock Market Anomalies,” Journal of Investment Strategies, vol. 2, no. 2, 2007) reviewed the evidence in Australia relating to seasonality effects. Although they didn’t specifically examine the “sell in May and go away” effect (they concentrated upon the “January effect” and end of financial year tax-related effects), they found that “at the aggregate market level, it is difficult to conclude that seasonalities exist. Despite apparent graphical ‘evidence,’ there is no statistical evidence of (such effects).”

Shane Oliver (“The ’best’ and the ‘worst’ months for shares,” 3 May 2024) purports to show a seasonal pattern in American and Australian equities “after the longer-term fundamentally driven trend is removed” (he doesn’t specify its size or how he removed it). “Breaking the year into two six-month periods,” he adds, “also reflects this historic pattern. Since 1985, the average total return (i.e., from price gains and dividends) from U.S. shares from end November to end May has been 90% more than from end May to end November. Globally and in Australia and Asia it has been three or more times bigger, according to AMP analysis.”

Oliver also compares “the seasonal pattern” in 1985-1999 to the one in 2000-2023: “it looks like (it has) weakened a bit, with average gains in April, July and December falling in the more recent period. However (these) are still the strongest months of the year, and October looks stronger (mainly because the October 1987 share crash drops out of the data). A broad seasonal pattern still remains with September being confirmed as the weakest month of the year on average.”

Yet his conclusion is curiously inconclusive: the seasonal effect is “not always reliable, but don’t ignore the time of the year.” “Seasonal patterns,” he says, “have weakened slightly over time. Such influences can also be overwhelmed when contrary fundamental influences such as market or company factors are strong, so they don’t apply in all years.”

Overseas Academic Research

Academic research mostly concerns other countries, but key studies incidentally analyse Australian data. Sven Bouman and Ben Jacobsen (“The Halloween Indicator, ‘Sell in May and Go Away:’ Another Puzzle” (The American Economic Review, vol. 92, no. 5, 2002) is regarded as the seminal study. It was certainly the first which concluded that seasonal effects exist in many global stock markets. In 36 of the 37 developed and emerging markets which they analysed, using data from 1973 to 1998, Bouman and Jacobsen estimated that returns in November-April were, on average and after taking transaction costs into consideration, higher than in May-October.

They also concluded that this effect tended to be strongest in Europe, was robust over time and had been noticeable for a very long time – most remarkably, they uncovered evidence of a “sell in May” effect in Britain as early as 1694. Finally, they tried “some alternative explanations ... but none of them (apart from sell stocks just before the northern summer holidays, and forget about them over the next six months) seems to provide an explanation for the puzzle.”

Given these results, they proposed that investors and speculators 

1. buy a proxy of the S&P 500 Index in November and hold it until May;
2. sell the stocks in May, buy “risk-free” instruments like U.S. Treasury bills, and hold them until November;
3. sell the cash-equivalents in November, and repurchase the index;
4. repeat steps 1-3 every year.

Bouman and Jacobsen conclude: “a simple strategy based on the saying would outperform a buy and hold portfolio in many countries . . . and would also be a lot less risky.”

At face value, this result – and the viability of this proposed tactic – is very odd and even highly questionable. If anybody can do it, why isn’t everybody doing it? And if it’s long been widely known and offers significant reward with little risk, why hasn’t arbitrage trimmed its reward close to zero – and thereby greatly boosted its ratio of risk to reward?

The “January effect” provides an example. (It’s frequently been misinterpreted: it doesn’t state that stocks’ returns are unusually large in January; instead, returns, especially small cap stocks’ returns, rise on the last trading day in December and the first five in January.) For decades until the early 1980s, it was apparently readily exploitable; at that point, it received much publicity; as a result, since then it’s become statistically insignificant (see Arbad Cheema et al., “The Cross-Section of the January Effect,” Journal of Asset Management, vol. 24, 2023).

Assuming charitably that it once existed, common sense – predicts a similar fate for the “Halloween effect.”

Edwin Maberly and Raylene Pierce (“Stock Market Efficiency Withstands Another Challenge: Solving the ‘Sell in May/Buy after Halloween’ Puzzle,” Econ Journal Watch, vol. 1, no. 1, April 2004) criticised Bouman and Jacobsen. Firstly, “if the Halloween strategy is economically significant ... then (it) should carry over to U.S.-based index futures, in particular to the S&P 500 futures contract.”

Secondly, “on re-examination, the ... Halloween effect in the U.S. disappears after an adjustment is made for the impact of outliers, in particular the large monthly declines for October 1987 and August 1998 associated with the stock market crash and collapse of the hedge fund Long-Term Capital Management, respectively. For the U.S., the empirical evidence indicates that the Halloween effect is not an exploitable anomaly, and this is true for both spot and futures prices.”

Indeed, “for S&P 500 index futures, the Halloween strategy of “sell in May and go away” underperforms the buy and hold strategy by a wide margin.”

Most recently, Jacobsen and Cherry Zhang completed a follow-up study (“The Halloween indicator, ‘Sell in May and Go Away:’ Everywhere and All the Time,” Journal of International Money and Finance, vol. 110, no. 4, 2021). Using all available historical data, they extended Bouman and Jacobsen’s research to 108 stock markets. The result was a sample of 55,425 monthly observations including more than 300 years of British data. Returns in the November- April “winter” period were, on average, 4.5% higher than May-October “summer” returns. The “Halloween effect” was evident in 81 of 108 countries. The size of the effect varied from one country to another; it was stronger in developed and emerging markets than in “frontier” markets.

Jacobsen and Zhang also found that, globally, the effect’s strength has been increasing over the past 50 years. They concluded that a “sell in May” tactic “beat the market more than 80% of the time when employed over a five-year horizon, and more than 90% of the time over a 10-year horizon.”

Finally, in an unpublished and undated study (seemingly ca. 2012) entitled “The Halloween Indicator, ‘Sell in May and Go Away’: an Even Bigger Puzzle,” Jacobsen and Zhang “rigorously re-examine the ... puzzle and address issues raised” from the theoretical debate and statistical and other criticisms that their previous research generated.

They concluded: “the Halloween effect is prevailing around the world to the extent that mean price returns are higher for the period of November-April than for May-October in 81 out of 108 countries, and the difference is statistically significant in 35 countries compared to only 2 countries having significantly higher May-October returns ...”

Got that? Of the 108 stock markets which Jacobsen and Zhang analysed, the Halloween effect seems to appear in 81 (75% of countries) – but in only 35 (32%) is the effect statistically significant.

They also concluded: “our evidence reveals that the size of the Halloween effect does vary cross-nation ... Geographically, (it) is more prevalent in countries located in Europe, North America and Asia than in other areas.”

Crucially (see Tables 2-4 of Jacobsen and Zhang’s unpublished article), Australia isn’t merely one of the 73 countries in which the effect is NOT statistically significant: it’s also one of the 27 countries in which it’s effectively zero.

The Short-Term Seasonality of Australian Stocks’ Returns, 1875-2025

The Sydney Stock Exchange’s Research and Statistical Bureau published a pamphlet by D. McL. Lamberton, entitled “Security Prices and Yields 1875–1955,” in 1956. It provided monthly estimates of Australian stocks’ overall level and dividend yield during these years. Much more recently, a couple of studies have contended that Lamberton likely overestimated the market’s dividend yield; for this reason, I’ve excluded dividends from these data. Thomas Mathews, a researcher at the RBA, extended and elaborated Lamberton’s and others’ data (for details, see “A History of Australian Equities,” RBA Research Discussion Paper – RDP 2019-4).

I’ve taken Mathews’ data and merged them, together with data from the ASX (1975-2005) and Standard & Poor’s (2005-2005), into series which estimate the All Ordinaries Index before its creation in January 1980. I thus possess increasingly reliable data over the 150 years from 1875 to 2025. The data for 1875-1925 ignore dividends and don’t adjust returns for the Consumer Price Index; the period 1925-1975 uses the RBA’s estimates since the January quarter of 1923 to adjust the Index’s returns for CPI; and the period 1975-2025 incorporates dividends (that is, total returns) and adjusts for CPI.

All of these data quantify the market’s closing level on the final trading day of the month; accordingly, six-month returns run from July to January, August to February, etc.

For each of the three series, I calculated the Index’s six-month return; I then sorted the data into 12 groups: returns for July-January, August-February, ... and June-December. I then computed the mean return for each group; Figure 1 plots the results.

Since 1975, CPI-adjusted six-month total average returns have peaked in November-May (average of 6.0%), have generally decreased during the next five months, troughed in May-November (1.75%) and then risen during the succeeding months, peaking again in November-May.

Figure 1: All Ordinaries Index, CPI-Adjusted, Six-Month Total Returns since 1875

Do these results suggest that over the past half-century Australian equities’ CPI-adjusted, total six-month returns have been seasonal? Do they thereby imply that the “sell in May” tactic can generate a return that’s superior to a B&H strategy?

Selling in May crystallises the average high return over the previous six months (6.0%), and foregoes the average low return during the next six months (1.8%). Using the proceeds from the sale of stocks by buying Australian bank bills in May and holding them until November, has, as we’ll see in Figure 8, provided an average six-month CPI-adjusted total return of 2.7% since 1975. This action swaps an average low return (1.8%) for the May-November period and substitutes an average higher one (2.7%).

Notice the repeated use of the word “average” in the preceding paragraph. Under the crucial assumption that each of the November-May returns since 1975 have been uniform (or, at least, are approximately 6% – which, as we’ll subsequently see, is clearly untrue), that’s an average 12-month CPI-adjusted total return of 1.027 × 1.06 = 8.9%. Buying stocks and holding them over the next 12 months would generate an average “real” 12-month total return of 8.4%.

Given this false assumption, and net of the costs of the transactions, tax and general bother, is the short-term outperformance of S&S significant?

Seasonal effects also seemed to appear in 1875-1925. The Index’s six-month return (unadjusted for dividends and CPI) crested in January-July (average of 4.1%), ebbed steadily thereafter, troughed in July-January (mean of 0.3%) and then increased during the next six months. During the half-century to 1925, the seasonal effect seemed to be very regular – much more so than since 1975 – but was a bit askew; it was more a case of “sell in July and go away.”

Finally, and whether or not the series is adjusted for CPI, in 1925-1975 the seasonal effect is the polar opposite of the one in 1875-1925: the six-month return peaks in July-January and troughs in January-July.

Let’s recall why these seasonal effects purportedly occur. According to Jacobsen and Zhang, “while it seems unlikely that we will ever find a smoking gun, the circumstantial evidence we report confirms more recent empirical evidence ... that vacations are the most likely explanation. At least, the vacation explanation is consistent with all empirical evidence to date.”

I don’t buy it: were Australian investors’ holiday habits in 1875-1925 versus 1925-1975, and again in 1925-1975 versus 1975-2025, polar opposites? Were apparently seasonal returns in Australian markets in 1875-1925 and 1975-2025 reactions to summer holidays in the northern hemisphere – but those in 1925-1975 were responses to summer holidays in the southern hemisphere?

Bearing in mind that the two series before 1975 are less reliable than the one since 1975, this sharp disparity of results – indeed, these flat contradictory results – make no sense.

Are These Short-Term “Seasonal Effects” Actually Merely Random Fluctuations?

There’s strong evidence that they are; in other words, there’s no evidence that they reflect anything other than chance. Random fluctuations are irregular variations – in this case of the All Ordinaries Index’s returns – around a mean. They have no identifiable cause and are trendless; hence they’re effectively unpredictable.

Assuming charitably that it exists, the “sell in May” effect is so weak that it fails to come even close to standard levels of statistical significance.

Consider as an example the 49 CPI-adjusted November-May returns (Figure 2). Their mean is 5.6% and their standard deviation is 9.2%. In plain English, the annual observations fluctuate enormously around their 49-year average. Assuming that these observations derive from a normally-distributed population, we can expect that 95% (that is, 0.95 × 50 = 47.5) of these observations will fall within ± 2 standard deviations of their mean, i.e., between 5.6% - (2 × 9.2%) = -12.8% and 5.6% + (2 × 9.2%) = 24.0%, and that the remaining 5% (2.5) will lie outside these bounds.

And so it is: one lies just above the upper bound and two below the lower bound. (The other 11 series are also acceptably normal distributed and their variances are roughly equal; accordingly, standard and relatively straightforward statistical tests are appropriate.)

Figure 2: Six-Month, CPI-Adjusted Total Returns, November-May, by Year, Mean and Confidence Bounds

These observations’ trend – that is, the slope of its regression line – is slightly negative; over the years, the return has ebbed somewhat. Essentially, however, these observations fluctuate randomly around their mean. Similarly, the observations in each of the other six-month intervals also fluctuate randomly around their respective means.

Figure 3: Confidence Intervals, All Ordinaries Index’s “Real” Six-Month Total Returns, 1975-2025

Figure 3 summarises this crucial reality: it plots for each of the 12 six-month intervals what Figure 2 plotted for July-January. Three results are paramount:

1. the individual observations (returns) within each group vary enormously relative to their means; each group’s standard deviation, in other words, is large relative to its mean;
2. substantively, each of the 12 group means varies little from the overall mean; statistically, according to appropriate tests, they don’t differ significantly from the overall mean;
3. the 12 group means – including the largest (November-May) versus the smallest (May-November) – don’t differ significantly from one another.

Superficially, variations of Australian stocks’ CPI-adjusted six-month total returns might appear to be seasonal; digging below the surface, however, we cannot reject the hypothesis that their fluctuations are random.

Comparing S&S to B&H – Short-Term

Let’s now investigate another of Sven Bouman and Ben Jacobsen’s key claims. Specifically, let’s assume that 

1. in November 1974 an investor acquired a portfolio of stocks which perfectly mimicked the All Ordinaries Index, and during the next several months collected distributions and dividends;
2. in May 1975, she sold the stocks and used the proceeds purchase three-month bank bills, and held them (with one “rollover”) until November of that year;
3. in November 1975, she sold all of the bills and reacquired stocks;
4. and so on until November 2024.

Will this tactic’s short-term (12-month) return outperform a simple buy and hold approach? Given the previous section’s results, scepticism is warranted.

An Australian bank bill (also known as a bank accepted bill) is essentially a promise by a borrower – which a bank guarantees – to pay to a lender a specified amount on a given future date. Why assume that this investor switches from stocks to these bills? For retail investors, but not institutional ones, term deposits are the obvious option; and for institutions but not retail investors, a Commonwealth Government six-month debt security is the obvious option. TDs aren’t liquid (that is, tradable) and thus differ in a key respect from stocks; besides, no data of monthly TD rates exist since 1975.

Practitioners of S&S need a safe and ideally six-month instrument, and for four reasons the three-month bank bill with one “rollover” is the best candidate. Firstly, it’s unquestionably safe. Indeed, it’s as safe as a Commonwealth Government debt security: since 1975 an Australian bank has never failed to honour its obligation to pay lenders required amounts on specified dates.

Secondly, they trade on an active market and are thus very liquid (in 2018, the RBA estimated that, excluding derivatives, loans and securities referencing the Bank Bill Rate have a notional value $1 trillion). Thirdly, the Bank Bill Rate is, along with the RBA’s Overnight Cash Rate, one of this country’s benchmark rates of interest. That’s why – here’s a final reason – the RBA has tracked it since June 1969; that’s much longer than any other rate (including Australian government bond rates since 1995) which it tracks.

Bills are much safer than stocks: they guarantee, in nominal but not CPI-adjusted terms, the repayment of principal. Like stocks, however, they can also be volatile: over the past half-century their CPI-adjusted, six-month total return has fluctuated widely (Figure 4).

Particularly noteworthy, for reasons that’ll become clear in the next section, is the high volatility of bills’ returns in the 1970s and 1980s, and their relatively steady returns (except during the GFC and COVID-19) since the turn of the century.

Figure 4: Australian 90-Day Bank Bill, CPI-Adjusted Total Six-Month Return, January 1975-March 2025

The mean return has been 2.3%, but its standard deviation is 10.3%. A sharp rise of rates of interest or CPI, or expectations of rate rises or higher consumer price inflation, as occurred frequently during the 1970s and 1980s and in 2022, can cause bank bills’ total return to plunge; conversely, a sharp decrease of rates of CPI, or expectations to that effect, as also occurred throughout the 1970s and 1980s and in 2009, can cause their total return to soar.

Importantly, in two respects I’ve deliberately weighted the scale in favour of S&S.

Firstly, and highly unrealistically, I’m assuming that transaction costs are zero: the sale of stocks and bank bills incurs no brokerage or capital gains tax. These costs are far greater for the buyer and switcher because he transacts twice per year, whereas the buyer and holder rebalances just once. Secondly, and perhaps more importantly, S&S is more bothersome than B&H. It requires much more time and effort, which I’m ignoring.

Given my assumptions, how do the CPI-adjusted, 12-month total returns of a B&H investor (who owns a portfolio that mimics the All Ordinaries Index) and a S&S investor (who owns stocks during one half of the year and bank bills during the other) compare? I’ve made the calculations not just for investments in November-November, but also for the other 11 six-month intervals. Table 1 summarises the results.

Table 1: Two Strategies and 12 Intervals, January 1975-December 2024

On average (bottom row), B&H generates a higher return than S&S. In two of the 12 intervals (marked in red), however, S&S appears to generate a higher return than B&H. Indeed, “sell in April and go away” generates a higher return than “sell in May and go away” – and the average returns for these two intervals exceed B&H’s return in any.

But as we’ve already seen, the crucial questions to ask of any comparison of group means include: “how much to the underlying observations fluctuate? Given this dispersion, is the difference of means significant?”

Figure 5 answers the first question: it plots the actual outperformance (summarised in the last column of Table 1) of B&H versus S&S for each of the November-May intervals. The year-by-year results differ markedly. Moreover, B&H mostly underperformed in the 1970s and 1980s, but (except and unsurprisingly during the GFC) has mostly outperformed since ca. 2000.

Hence the trend is mildly positive; over time, in other words, the underperformance of B&H has trended from underperformance towards outperformance.

Figure 5: 12-Month Outperformance of B&H versus S&S, November-May, 1975-2024

Given the variability of the year to year results in Figure 5, has B&H significantly underperformed S&S? Using standard statistical tests, the answer is “no.” Moreover, and unsurprisingly, none of the 11 other comparisons of B&H versus S&S (including October-April) is statistically significant.

Finally, what does a comparison of the maximum outperformance of S&S (June-December) versus its maximum underperformance (October-April) tell us? Figure 6, which plots these two series, addresses this question. Particularly since the turn of the century, the returns are, substantively and statistically, indistinguishable.

In short, the random fluctuation of equities’ 12-month returns is so strong that no S&S tactic significantly outperforms B&H. Accordingly, the converse is true: no short-term B&H strategy outperforms S&S.

Figure 6: Outperformance of B&H versus “Sell and Switch,” Oct-Apr and Jun-Dec Periods, 1975-2024

Comparing S&S to B&H – Medium-Term

Thus far I’ve established – as I have elsewhere– that on a CPI-adjusted, total return basis, the All Ordinaries short-term returns are essentially random. Accordingly, so too are the returns of B&H and S&S. But as I’ve also demonstrated elsewhere, over time random fluctuations (“noise”) cancel one another and systematic ones (“signal”) emerge. What, then, are B&H’s and S&S’s medium-term (five-year) cumulative results?

In order to interpret my results, it’s essential to establish several key facts. The first has long been well-known: consumer price inflation in Australia was very high in the 1970s and 1980s, and since then has fallen gradually and cumulatively drastically.

Figure 7: Consumer Price Index, Annualised Percentage Change, June 1923-March 2025

Using data compiled by the RBA, Figure 7 plots the CPI’s annualised percentage change since the June quarter of 1923. It’s average 4.2% per year. Except in the year to December 1951, when it reached its all-time high (23.9%), it was highest in the year to March 1975 (17.7%).From March 1974 until December 1995, its 10-year CAGR was at least 5% per year; in contrast, with very few exceptions since September 1998 its 10-year CAGR has not exceeded 3.0%.

The second key point is virtually unknown by stock market investors: bank bills’ six-month, CPI-adjusted total returns since 1975 have been seasonal (Figure 8). Specifically, they were strongly – and, in key respects, statistically significantly – seasonal from 1975 to 1999; since 2000, however, their seasonality has disappeared.

Figure 8: Bank Bills, Six-Month, CPI-Adjusted Total Returns since 1975

It’s not hard to conjecture why: bank bills often finance business’ working capital, and businesses in industries such as agriculture or tourism rely upon them to finance short-term inventory, etc., in cycles which fluctuate seasonally. Perhaps the overall importance of seasonal industries has ebbed since the turn of the century; if so, then so too has the seasonality bank bills’ CPI-adjusted six-month returns.

A third point has also been forgotten: throughout the 1980s and 1990s, bank bills’ yields net of CPI’s annual rate of growth were very high (Figure 9). From 1981 to 1999 they averaged 5.8%. In sharp contrast, from 1975 to 1990 the All Ordinaries Index’s dividend yield was, net of CPI, very low – indeed, it was negative (average of -2.7%).

During these years, in other words, bank bills were a comparatively safe yet very high-yielding; stocks, on the other hand, were much riskier yet very low-yielding.

Figure 9: Yields Net of CPI, Monthly, January 1974-March 2025

More recently, as CPI’s annual rate of increase has decelerated, bills’ net yield has fallen and the Index’s net yield has risen. Indeed, since 2000 the Index’s real yield (average of 1.2%) has exceeded bills’ (average of 0.9%).

Bills have ceased to be high-yielding, and stocks are no longer low-yielding.

We’re now in a position to compare and interpret the cumulative results of the B&H and S&S approaches over the medium-term. I’ve assumed that (1) in November 1974 an investor acquired a portfolio of stocks which perfectly mimicked the All Ordinaries Index, and during the next six months collected distributions and dividends; (2) in May 1975, she sold the stocks and used the proceeds purchase three-month bank bills, and held them (with one “rollover”) until November of that year; (3) in November 1975, she sold all of the bills and reacquired stocks; (4) and so on until November 1979.

It’s essential to bear in mind: we’re continuing to ignore S&S’s transaction costs and capital gains taxes. These are considerable: its annual “churn,” i.e., the rate at which the S&S portfolio’s assets are bought and sold, is 100%. I’m therefore continuing to weight the scales heavily in favour of S&S over B&H.

I’ve calculated S&S’s results in terms of a compound annual growth rate (CAGR), and also calculated the CAGR of B&H, that is, of shares purchased in November 1974 and held for the next five years. I’ve then repeated this exercise for all succeeding five-year intervals; Figure 10 plots the results; three are most noteworthy.

Firstly, from 1979 to the mid-1990s S&S mostly outperformed B&H. Clearly, however, this result stemmed not from the seasonality of stocks’ returns; to a greater extent it derived from the seasonality of bills’ returns and – and the key fact S&S entailed the sale of more risky and very low-yielding securities (namely stocks), and the switch to less risky and much higher-yielding securities (bank bills).

Figure 10: Five-Year CAGRs, Two Strategies, 1979-2024

Secondly, from ca. 2000 to ca. 2015 the two strategies mostly generated similar results. B&H clearly outperformed before the GFC, and underperformed in its wake.

Finally, since 2015 B&H has increasingly outperformed S&S. That’s because (1) B&H’s five-year CAGR has been stable and (2) S&S’s has crashed to an all- time low that’s well below zero.

Conclusions and Implications: Don’t Be Fooled by Randomness

My results update and elaborate Gray’s and Tutticci’s, as well as Jacobsen’s and Zhang’s (the latter’s results for Australia failed standard tests of significance):

1. Since 1975, stocks’ CPI-adjusted, short-term total returns have fluctuated randomly.
2. On a medium-term (five-year) basis, the outperformance of “sell in May and go away” before 2000 wasn’t a consequence of equities’ seasonality: it resulted from bank bills’ very high real yields. Since then, their yields have collapsed – and, consequently, so too has S&S’s outperformance.

Let’s be charitable and assume that this seasonal effect once existed. If so, and in the words of Benjamin Graham (The Intelligent Investor, 4^th rev. ed., 1973), its disappearance “demonstrates an inherent characteristic of forecasting and trading formulas in the fields of business and finance. Those formulas that gain adherents and importance do so because they have worked well over a period, or sometimes merely because they have been plausibly adapted to the statistical record of the past. But as their acceptance increases, their reliability tends to diminish.”

This, Graham elaborated, “happens for two reasons: First, the passage of time brings new conditions which the old formula no longer fits. Second, in stock-market affairs the popularity of a trading theory has itself an influence on the market’s behaviour which detracts in the long run from its profit-making possibilities.”

“The moral,” Graham concluded, “seems to be that any approach to moneymaking in the stock market which can be easily described and followed by a lot of people is ... too simple and too easy to last.”

Let’s now be less charitable but more realistic: it’s reasonable to question whether the “sell in May and go away” effect has ever existed. If so, here’s how I’d explain the broad pattern of results internationally: first, a replication of my methods using data from the S&P 500 Index would generate a similar conclusion – namely that the “Halloween effect” in the U.S. is a chimera; and (2) the S&P 500’s returns typically influence returns in other countries.

As a result, the mostly-random rather than seasonal effects on the S&P 500 reverberate on major indexes in other countries: what appear to be “seasonal” effects internationally is actually the influence of the S&P 500’s returns on other markets.

In Fooled by Randomness: The Hidden Role of Chance in Life and in the Markets (Thomsen, 1^st ed. 2001) Nassim Nicholas Taleb contended that, most of the time, most people – including investors – underestimate and even overlook randomness. As a result, they tend to “explain” chance outcomes in causal terms; they thereby tend to view the world as more determinate than it really is.

Marcus Padley (“Sell in May and Go Away,” Marcus Today, 30 April 2019) surmises that the apparent seasonality of stocks’ short-term returns means that “your chances of making money in the market in the six months ahead of May have been over double your chances of making money in the six months following May.” Shane Oliver reckons that “seasonal patterns certainly shouldn’t dominate an investor’s strategy. However, they nevertheless provide a reasonable guide to the monthly rhythm of markets that investors should ideally be aware of.”

Oliver’s first sentence is sensible; but his second one, and assertions such as Padley’s, doesn’t survive thorough scrutiny.

Yet it doesn’t appear that they’ve been fooled by randomness. Sensibly, Oliver seems to question the veracity of his own results. He attributes the origin of the phrase “sell in May and go away” to crop cycles – which are “not so relevant today!” He should therefore add another entry to his useful and readable collection about the psychological pitfalls of investing: “take care not to mistake random for systematic fluctuation.”

Padley is more explicit. He implies that these “seasonal” variations are random, and concludes: “I ... abhor the use of past statistics as a predictor of the future. Some newsletters-commentators-analysts make a career out of spotting past coincidences and then pass it off as prediction ... So I am naturally sceptical (about ‘sell in May and go away’).”

I am too; indeed, like the Spanish-American philosopher, George Santayana, I agree that “scepticism, like chastity, should not be relinquished too readily.” That’s why, over the past quarter-century, Leithner & Company has extensively analysed historical statistics.

We’ve NOT done so in order to predict the future – that’s a fool’s errand – but rather in order to (1) identify and thus ignore past coincidences and (2) establish and act on the basis of plausible but nonetheless fallible inferences. This article has provided an example.

Although he wasn’t referring directly to the seasonality of stocks’ returns, almost a century ago a broker, trader and publisher, Richard Wyckoff, wrote some of the wisest words on this subject. In Wall Street Ventures & Adventures Through Forty Years (1930, Fraser Publishing Co., 1985) he remarked: “many (people once) thought that the market could be beaten by mechanical methods; that is, by some means other than human judgment. (Charles) Dow suggested a few of these. (Roger) Babson had one or more. All kinds of individuals came forward with ways of beating the stock market; each was certain his method would make a fortune.”

Wyckoff’s assessment remains valid today: “... after further study, I decided that methods of this kind, which substitute mechanical plays for judgment, must fail. For the calculations on which they are based omit one fundamental fact, i.e., that the only unchangeable thing about the stock market is its tendency to change.”

Wyckoff therefore concludes: “the rigid (mechanical) method sooner or later will break the operator who blindly follows it.”

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