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By Philip van Doorn

Even a slow-growing sector can include rapidly growing companies that are putting up big numbers

Robinhood is expected to increase revenue at a compound annual growth rate of 15.5% from 2025 through 2027, based on consensus estimates among analysts polled by LSEG. But investors seem to have higher expectations based on the stock’s valuation and the company’s annualized revenue-growth rate of 47.4% from 2022 through 2024.

No doubt you have gotten used to the flow of warnings about how expensive the S&P 500 has become. But there are always sectors that trade at low valuations to the full U.S. large-cap benchmark index.

The cheaper sectors reflect investors’ and analysts’ expectations for slower growth than what they expect to continue to see in the information-technology sector. But even in lower-valued sectors there are companies expected to put up big numbers over the next two years.

We are going to screen the three sectors of the S&P 500 that are least expensive based on a commonly used valuation measure. First let’s look at the 11 sectors of the S&P 500 SPX. Here they are, sorted by ascending forward price/earnings ratios, with the full index at the bottom.

   Sector or index           Forward P/E  Forward P/E to 10-year average  Two-year estimated revenue CAGR through 2027  Two-year estimated EPS CAGR through 2027 
   Energy                           14.8                             64%                                          2.4%                                     17.5% 
   Financial                        16.2                            119%                                          5.8%                                     11.2% 
   Healthcare                       17.1                            105%                                          5.7%                                     11.0% 
   Materials                        19.3                            110%                                          5.0%                                     16.5% 
   Utilities                        19.8                            111%                                          5.2%                                      8.9% 
   Communication Services           21.2                            126%                                          7.5%                                     10.4% 
   Consumer Staples                 21.4                            108%                                          4.4%                                      7.5% 
   Industrials                      23.9                            126%                                          6.3%                                     16.0% 
   Consumer Discretionary           28.5                            118%                                          6.7%                                     14.4% 
   Information Technology           29.6                            134%                                         12.7%                                     19.5% 
   Real Estate                      36.4                             90%                                          6.9%                                     11.2% 
   S&P 500 Index                    22.7                            121%                                          6.5%                                     13.9% 
                                                                                                                                                    Source: LSEG 

You might need to scroll the table or flip your screen to landscape to see all of the columns in the table.

The forward price/earnings ratios are based on Wednesday’s closing prices for stocks and consensus 12-month earnings-per-share estimates for companies among analysts polled by LSEG, weighted by market capitalization. The second data column shows the current P/E valuations relative to 10-year average valuations, based on rolling stock prices and 12-month EPS estimates. So the full S&P 500 is trading at a 21% premium to its 10-year average valuation.

In fact, all sectors of the S&P 500 are trading at premium valuations to their 10-year average P/E, except for the energy and real-estate sectors, according to LSEG’s data.

Among the three least expensive sectors based on current forward P/E, the financial sector may appear pricey, since it is trading at a 19% premium to its 10-year average P/E, but it is still the second-cheapest sector based on current P/E. On this basis, the financial sector trades at 71% of the valuation of the full S&P 500. Over the long term, this level of discount for the financial sector to the full index has been typical.

The right-most columns of the table show projected compound annual growth rates (CAGR) for revenue and EPS. The three cheapest sectors by forward P/E (energy, financials and healthcare) all have projected revenue CAGR from 2025 through 2027 lower than the full S&P 500’s projected 6.5%. The energy sector’s projected EPS CAGR of 17.5% exceeds the full index’s projected EPS CAGR of 13.9%. These are both attractive figures and reflect expectations for continuing improvements in efficiency and profit margins. Oil and natural-gas producers in the energy sector have shown discipline during the years following the decline in oil prices form mid-2014 through early 2016 – a period during which U.S. producers suffered in the wake of high production that softened prices. In more recent years, the U.S. oil and gas producers have been careful not to expand production quickly and have focused on increasing dividends to shareholders and on stock buybacks. Reduced share counts resulting from the buybacks boost EPS, and the projected EPS CAGR shows analysts expect this action to continue.

The rapid growth of sales and earnings for the largest technology companies in the S&P 500 has increased the index’s weighting toward a small number of stocks. Success is rewarded in an index weighted by market capitalization, but this has also led to a high level of concentration.

The S&P 500 is now 39.9% concentrated in its largest 10 companies, according to analysts at Ned Davis Research. That is close to the peak concentration of 40.3% in September, which was the highest concentration for the S&P 500 since at least 1972.

Some investors might not realize how much of their portfolios are focused on Big Tech. The $677 billion SPDR S&P 500 ETF Trust SPY tracks the S&P 500 by holding all of its stocks. The ETF is 29.5% concentrated in five companies: Nvidia Corp. (NVDA), Microsoft Corp. (MSFT), Apple Inc. (AAPL), Alphabet Inc. (GOOGL) (GOOG) and Amazon.com Inc. (AMZN).

Screening the cheapest sectors of the S&P 500 for growth stocks

There are index funds tracking each of the sectors of the S&P 500. Among exchange-traded funds, the three sectors we are screening are tracked by the Energy Select SPDR ETF XLE, the Financial Select SPDR ETF XLF and the Health Care Select SPDR ETF XLV. But you might also want to drill down into individual stocks.

To screen these sectors, we combined the S&P 500 energy, financial and healthcare sectors for a list of 157 stocks. Then we cut the list to 151 companies covered by at least five analysts polled by LSEG, and for which consensus revenue and positive EPS estimates were available from the calendar year 2025 through calendar 2027. We used calendar-year estimates as adjusted by LSEG if necessary for companies whose fiscal years don’t match the calendar.

Among the 151 remaining companies in the energy, financial and healthcare sectors, these 10 have the highest projected revenue CAGR from 2025 through 2027 based on consensus estimates among analysts polled by LSEG:

   Company                         Ticker   Two-year estimated revenue CAGR through 2027  Two-year estimated EPS CAGR through 2027  Forward P/E 
   Blackstone Inc.                BX                                               26.1%                                     27.2%         25.8 
   KKR & Co.                      KKR                                              24.4%                                     26.1%         19.0 
   Insulet Corp.                  PODD                                             17.7%                                     24.7%         57.7 
   Apollo Global Management Inc.  APO                                              17.2%                                     19.1%         14.2 
   Eli Lilly & Co.                LLY                                              17.1%                                     27.6%         27.6 
   Fifth Third Bancorp            FITB                                             16.9%                                     16.2%         11.4 
   Brown & Brown Inc.             BRO                                              15.8%                                     11.5%         18.9 
   Robinhood Markets Inc.         HOOD                                             15.5%                                     17.6%         61.5 
   Arthur J. Gallagher & Co.      AJG                                              15.4%                                     17.4%         20.9 
   Dexcom Inc.                    DXCM                                             14.7%                                     22.9%         28.0 
                                                                                                                                   Source: LSEG 

No companies in the energy sector made the list.

All of these companies have projected revenue CAGR more than twice the 6.5% projection for the S&P 500. For EPS, all but Brown & Brown have higher CAGR projections than the S&P 500’s 13.9%.

(MORE TO FOLLOW) Dow Jones Newswires

10-23-25 1129ET

Copyright (c) 2025 Dow Jones & Company, Inc.

The DIFC recently announced that it had enacted an amendment to the Data Protection Law, following an earlier consultation in March.

Summary

The right for data subjects to claim compensation for damage they have suffered by reason of a contravention of their rights under data protection law is established in GDPR based countries, upon which the DIFC Data Protection Law is modelled. Claims of this nature have become increasingly common over the past five or six years in those jurisdictions.

• The introduction of a private right of action through the DIFC courts for data subjects whose rights under the law have been contravened; and
• A widening and clarification of the scope of the application and extraterritorial scope of the law, which applies to:
  • A Controller or Processor who processes personal data and is incorporated in the DIFC, regardless of whether or not the processing takes place in the DIFC; and
  • A Controller, Processor or Sub-processor, processing personal data in the DIFC regardless of their place of incorporation as part of stable arrangements.

Important points to note

Data subjects can claim for mere distress

They do not need to prove that they have suffered a recognised psychiatric injury as a result of the infringement. This reduces the barrier to entry as expert medical evidence is not required in order to issue a claim.

The data subject can claim compensation from both the Controller or the Processor

This is important for Processors to bear in mind as whilst the bulk of the responsibility generally sits with the Controller e.g. notifying the Commissioner and affected data subjects of a personal data breach, this amendment makes clear that Processors will be held liable in circumstances where their unlawful actions, or inappropriate security measures result in harm to data subjects.

A Controller or Processor is not liable if they can prove that they are in no way responsible for the event giving rise to the damage

The burden lies with the Controller or Processor to demonstrate this when seeking an exemption from liability.

For example, if an organisation utilises the services of a third party payment provider, and as a result of a compromise of that payment provider’s systems, the organisation’s customer data is exposed, they may have a defence under Article 64A(4) if they had performed appropriate due diligence before selecting the payment provider (the Processor) and had a valid data processing agreement in place.

In these circumstances the Controller may be able to evidence that the event giving rise to the damage sits squarely with the Processor (albeit the Processor may have their own defence under this Article, for example if this incident was caused by the exploitation of a zero-day vulnerability for which there was no patch yet) and thereby escape liability.

We expect to see a gradual increase in data subject claims as individuals become more informed about their rights and how to exercise them.

We simulate the dynamics of VCG pools using a kinetic simulation that is based on the Gillespie algorithm. In the simulation, oligomers can hybridize to each other to form complexes or dehybridize from an existing complex. Moreover, two oligomers can undergo templated ligation if they are hybridized adjacent to each other on a third oligomer. At each time $t$, the state of the system is determined by a list of all single-stranded oligomers and complexes as well as their respective copy number. We refer to the state of the system at the time $t$ as the ensemble of compounds ${\mathcal{E}}_t$. Given the copy numbers, the rates $r_i$ of all possible chemical reactions $i\in \mathcal{I}$ can be computed. To evolve the system in time, we need to perform two steps: (i) We sample the waiting time until the next reaction, $\tau$, from an exponential distribution with mean $(\sum _{i\in \mathcal{I}}{r}_i{)}^{-1}$, and update the simulation time, $t\to t+\tau$. (ii) We pick which reaction to perform by sampling from a categorical distribution. Here, the probability to pick reaction $i$ equals $r_i/(\sum _{i\in \mathcal{I}}{r}_i)$. The copy numbers are updated according to the sampled reaction, yielding ${\mathcal{E}}_{t+\tau }$. Steps (i) and (ii) are repeated until the simulation time $t$ reaches the desired final time, $t_{\text{final}}$. A more detailed explanation of the kinetic simulation is presented in Göppel et al., 2022; Rosenberger et al., 2021.

Our goal is to compute observables characterizing replication in the VCG scenario based on the full kinetic simulation. In the following derivation, we focus on one particular observable (yield) for clarity. The results for other observables are stated directly, as their derivations follow analogously. Recall the definition of the yield introduced in the Results section,

${\displaystyle {\displaystyle y=\frac{\mathrm{\#}\mathrm{n}\mathrm{u}\mathrm{c}\mathrm{l}\mathrm{e}\mathrm{o}\mathrm{t}\mathrm{i}\mathrm{d}\mathrm{e}\mathrm{s}\mathrm{i}\mathrm{n}\mathrm{c}\mathrm{o}\mathrm{r}\mathrm{p}\mathrm{o}\mathrm{r}\mathrm{a}\mathrm{t}\mathrm{e}\mathrm{d}\mathrm{i}\mathrm{n}\mathrm{V}\mathrm{C}\mathrm{G}\mathrm{o}\mathrm{l}\mathrm{i}\mathrm{g}\mathrm{o}\mathrm{m}\mathrm{e}\mathrm{r}\mathrm{s}\mathrm{u}\mathrm{n}\mathrm{t}\mathrm{i}\mathrm{l}{\tau }_{\text{lig}}}{\mathrm{\#}\mathrm{i}\mathrm{n}\mathrm{c}\mathrm{o}\mathrm{r}\mathrm{p}\mathrm{o}\mathrm{r}\mathrm{a}\mathrm{t}\mathrm{e}\mathrm{d}\mathrm{n}\mathrm{u}\mathrm{c}\mathrm{l}\mathrm{e}\mathrm{o}\mathrm{t}\mathrm{i}\mathrm{d}\mathrm{e}\mathrm{s}\mathrm{u}\mathrm{n}\mathrm{t}\mathrm{i}\mathrm{l}{\tau }_{\text{lig}}}.}}$

As we are interested in the initial replication performance of the VCG, we compute the yield based on the ligation events that take place until the characteristic timescale of ligations ${\tau }_{\text{lig}}=k_{\text{lig}}^{-1}\approx {10}^{12}{t}_0$. In principle, we would like to compute the yield based on the templated ligation events that we observe in the simulation. Unfortunately, for reasonable system parameters, it is impossible to simulate the system long enough to observe sufficiently many ligation events to compute $y$ to reasonable accuracy. For example, for a VCG pool containing monomers at a total concentration of $c_{\mathrm{F}}^{\text{tot }}=0.1\mathrm{m}\mathrm{M}$ and VCG oligomers of length $L=8\mathrm{n}\mathrm{t}$ at a total concentration of $c_{\mathrm{V}}^{\mathrm{t}\mathrm{o}\mathrm{t}}=1\text{μ}\mathrm{M}$, it would take about 1700 hr of simulation time to reach $t=5\cdot {10}^{12}{t}_0$ (Figure 8). Multiple such runs would be needed to estimate the mean and the variance of the observables of interest, rendering this approach unfeasible.

Instead, we compute the replication observables based on the copy number of complexes that could potentially perform a templated ligation, that is complexes in which two strands are hybridized adjacent to each other, such that they could form a covalent bond. We can show analytically that the number of productive complexes is a good approximation for the number of incorporated nucleotides: The number of incorporated nucleotides can be computed as the integral over the ligation flux, weighted by the number of nucleotides that are added in each templated ligation reaction,

${\displaystyle {\displaystyle {\displaystyle (\mathrm{\#}\mathrm{i}\mathrm{n}\mathrm{c}\mathrm{o}\mathrm{r}\mathrm{p}\mathrm{o}\mathrm{r}\mathrm{a}\mathrm{t}\mathrm{e}\mathrm{d}\mathrm{n}\mathrm{u}\mathrm{c}\mathrm{l}\mathrm{e}\mathrm{o}\mathrm{t}\mathrm{i}\mathrm{d}\mathrm{e}\mathrm{s}\mathrm{u}\mathrm{n}\mathrm{t}\mathrm{i}\mathrm{l}{\tau }_{\text{lig}})={\int }_0^{{\tau }_{\text{lig}}}\mathrm{d}t\sum _{\text{C}\in {\mathcal{E}}_t}N(\text{C})\text{min}(L_{\text{e,1}},L_{\text{e,2}})\mathbb{1}(\text{C allows templated ligation}).}}}$

Here, $N(\text{C})$ denotes the copy number of the complex C in the pool ${\mathcal{E}}_t$. $L_{\text{e,1}}$ and $L_{\text{e,2}}$ denote the lengths of the oligomers that undergo ligation, and $\mathbb{1}$ is an indicator function which enforces that only complexes in a ligation-competent configuration contribute to the reaction flux. As only a few ligation events are expected to happen until ${\tau }_{\text{lig}}$, it is reasonable to assume that the ensembles ${\mathcal{E}}_t$ do not change significantly during $t\in [0,{\tau }_{\text{lig}}]$. Therefore, the integration over time may be interpreted as a multiplication by ${\tau }_{\text{lig}}$,

(6)

${\displaystyle {\displaystyle {\displaystyle (\mathrm{\#}\mathrm{i}\mathrm{n}\mathrm{c}\mathrm{o}\mathrm{r}\mathrm{p}\mathrm{o}\mathrm{r}\mathrm{a}\mathrm{t}\mathrm{e}\mathrm{d}\mathrm{n}\mathrm{u}\mathrm{c}\mathrm{l}\mathrm{e}\mathrm{o}\mathrm{t}\mathrm{i}\mathrm{d}\mathrm{e}\mathrm{s}\mathrm{u}\mathrm{n}\mathrm{t}\mathrm{i}\mathrm{l}{\tau }_{\text{lig}})\approx {\tau }_{\text{lig}}⟨\sum _{\text{C}\in \mathcal{E}}N(\text{C})\text{min}(L_{\text{e,1}},L_{\text{e,2}})\mathbb{1}(\text{C allows templated ligation})⟩,}}}$

where $⟨\dots ⟩$ denotes the average over realizations of the ensembles ${\mathcal{E}}_t$ within the time interval $t\in [{\tau }_{\text{eq}},{\tau }_{\text{lig}}]$. This average corresponds to the average number of complexes in a ligation-competent configuration. Note that, at this point, we made the additional assumption that no templated ligations are taking place between $[0,{\tau }_{\text{eq}}]$. This assumption is reasonable, as (i) the equilibration process is very short compared to the characteristic timescale of ligation, and (ii) the number of complexes that might allow for templated ligation during equilibration is lower than in equilibrium (we start the simulation with an ensemble of single-stranded oligomers). Both aspects imply that the rate of templated ligation is negligible during the interval $[0,{\tau }_{\mathrm{e}\mathrm{q}}]$.

In order to compute the average over different realizations of ensembles $\mathcal{E}$ (as required in Equation 6), we need to sample a set of uncorrelated ensembles that have reached the hybridization equilibrium, which can be done using the full kinetic simulation. The simulation starts with a pool containing only single-stranded oligomers and reaches the (de)hybridization equilibrium after a time ${\tau }_{\text{eq}}$. We identify this timescale of equilibration by fitting an exponential function to the total hybridization energy of all complexes in the system, $\mathrm{\Delta }{G}_{\text{tot}}$ (Figure 9A). In the set of ensembles used to evaluate the average in Equation 6, we only include ensembles for time $t>{\tau }_{\text{eq}}$ to ensure that the ensembles have reached (de)hybridization equilibrium. To ensure that the ensembles are uncorrelated, we require that the time between two ensembles that contribute to the average is at least ${\tau }_{\text{corr}}$. The correlation time, ${\tau }_{\text{corr}}$, is determined via an exponential fit to the autocorrelation function of $\mathrm{\Delta }{G}_{\text{tot}}$ (Figure 9B). Besides computing the expectation value (Equation 6), we are also interested in the ‘uncertainty’ of this expectation value, that is in the standard deviation of the sample mean ${\sigma }_{⟨X⟩}$. (We use $X$ as a short-hand notation for $\sum _{\text{C}\in \mathcal{E}}N(\text{C})\text{min}(L_{\text{e,1}},L_{\text{e,2}})\mathbb{1}(\mathrm{C}\mathrm{a}\mathrm{l}\mathrm{l}\mathrm{o}\mathrm{w}\mathrm{s}\mathrm{t}\mathrm{e}\mathrm{m}\mathrm{p}\mathrm{l}\mathrm{a}\mathrm{t}\mathrm{e}\mathrm{d}\mathrm{l}\mathrm{i}\mathrm{g}\mathrm{a}\mathrm{t}\mathrm{i}\mathrm{o}\mathrm{n})$). The standard deviation of the sample mean, ${\sigma }_{⟨X⟩}$, is related to the standard deviation of $X$, ${\sigma }_X$, by the number of samples, ${\sigma }_{⟨X⟩}=(N_s{)}^{-1/2}{\sigma }_X$. Moreover, based on the van-Kampen system size expansion, we expect the standard deviation of $X$ to be proportional to $V^{-1/2}$, such that ${\sigma }_{⟨X⟩}\propto (N_{s}V{)}^{-1/2}$.

Using Equation 6 (as well as an analogous expression for the number of nucleotides that are incorporated in VCG oligomers), the yield can be expressed as

${\displaystyle {\displaystyle {\displaystyle y=\frac{⟨\sum _{\text{C}\in \mathcal{E}}N(\text{C})\text{min}(L_{\text{e,1}},L_{\text{e,2}})\mathbb{1}(\text{C}\mathrm{a}\mathrm{l}\mathrm{l}\mathrm{o}\mathrm{w}\mathrm{s}\mathrm{t}\mathrm{e}\mathrm{m}\mathrm{p}\mathrm{l}\mathrm{a}\mathrm{t}\mathrm{e}\mathrm{d}\mathrm{l}\mathrm{i}\mathrm{g}\mathrm{a}\mathrm{t}\mathrm{i}\mathrm{o}\mathrm{n})\mathbb{1}(L_{\text{e,1}}+L_{\text{e,2}}\ge L_{\mathrm{U}})⟩}{⟨\sum _{\text{C}\in \mathcal{E}}N(\text{C})\text{min}(L_{\text{e,1}},L_{\text{e,2}})\mathbb{1}(\text{C}\mathrm{a}\mathrm{l}\mathrm{l}\mathrm{o}\mathrm{w}\mathrm{s}\mathrm{t}\mathrm{e}\mathrm{m}\mathrm{p}\mathrm{l}\mathrm{a}\mathrm{t}\mathrm{e}\mathrm{d}\mathrm{l}\mathrm{i}\mathrm{g}\mathrm{a}\mathrm{t}\mathrm{i}\mathrm{o}\mathrm{n})⟩}.}}}$

The additional condition $\mathbb{1}(L_{\text{e,1}}+L_{\text{e,2}}\ge L_{\mathrm{U}})$ in the numerator ensures that the product oligomer is long enough to be counted as a VCG oligomer, that is at least $L_{\mathrm{U}}$ nucleotides long. Analogously, the expression for the fidelity of replication reads

${\displaystyle {\displaystyle {\displaystyle f=\frac{⟨\sum _{\text{C}\in \mathcal{E}}N(\text{C})\text{min}(L_{\text{e,1}},L_{\text{e,2}})\mathbb{1}(\text{C allows templated ligation})\mathbb{1}(L_{\text{e,1}}+L_{\text{e,2}}\ge L_{\mathrm{U}})\mathbb{1}(\text{product correct})⟩}{⟨\sum _{\text{C}\in \mathcal{E}}N(\text{C})\text{min}(L_{\text{e,1}},L_{\text{e,2}})\mathbb{1}(\text{C allows templated ligation})\mathbb{1}(L_{\text{e,1}}+L_{\text{e,2}}\ge L_{\mathrm{U}})⟩}.}}}$

Multiplying fidelity and yield results in the efficiency of replication,

${\displaystyle {\displaystyle {\displaystyle \eta =\frac{⟨\sum _{\text{C}\in \mathcal{E}}N(\text{C})\text{min}(L_{\text{e,1}},L_{\text{e,2}})\mathbb{1}(\mathrm{C}\mathrm{a}\mathrm{l}\mathrm{l}\mathrm{o}\mathrm{w}\mathrm{s}\mathrm{t}\mathrm{e}\mathrm{m}\mathrm{p}\mathrm{l}\mathrm{a}\mathrm{t}\mathrm{e}\mathrm{d}\mathrm{l}\mathrm{i}\mathrm{g}\mathrm{a}\mathrm{t}\mathrm{i}\mathrm{o}\mathrm{n})\mathbb{1}(L_{\text{e,1}}+L_{\text{e,2}}\ge L_{\mathrm{U}})\mathbb{1}(\text{product correct})⟩}{⟨\sum _{\text{C}\in \mathcal{E}}N(\text{C})\text{min}(L_{\text{e,1}},L_{\text{e,2}})\mathbb{1}(\mathrm{C}\mathrm{a}\mathrm{l}\mathrm{l}\mathrm{o}\mathrm{w}\mathrm{s}\mathrm{t}\mathrm{e}\mathrm{m}\mathrm{p}\mathrm{l}\mathrm{a}\mathrm{t}\mathrm{e}\mathrm{d}\mathrm{l}\mathrm{i}\mathrm{g}\mathrm{a}\mathrm{t}\mathrm{i}\mathrm{o}\mathrm{n})⟩}.}}}$

The ligation share of a particular type of templated ligation $s(\text{type})$, that is, the relative contribution of this templated-ligation type to the nucleotide extension flux, can be represented in a similar form as the other observables,

${\displaystyle {\displaystyle s(\text{type})=\frac{⟨\sum _{\text{C}\in \mathcal{E}}N(\text{C})\text{min}(L_{\text{e,1}},L_{\text{e,2}})\mathbb{1}(\text{C allows templated ligation of given type)}⟩}{⟨\sum _{\text{C}\in \mathcal{E}}N(\text{C})\text{min}(L_{\text{e,1}},L_{\text{e,2}})\mathbb{1}(\text{C allows templated ligation)}⟩}.}}$

As all observables are expressed as the ratio of two expectation values, $\mathcal{Z}=⟨X⟩/⟨Y⟩$, we can compute the uncertainty of the observables via Gaussian error propagation,

${\displaystyle {\displaystyle {\displaystyle {\sigma }_{\mathcal{Z}}=\sqrt{\frac{{\sigma }_{⟨X⟩}^2}{⟨Y{⟩}^2}+\frac{⟨X{⟩}^2{\sigma }_{⟨Y⟩}^2}{⟨Y{⟩}^4}-\frac{2⟨X⟩{\sigma }_{⟨X⟩,⟨Y⟩}^2}{⟨Y{⟩}^3}}.}}}$

Since the variances, ${\sigma }_{⟨X⟩}^2$ and ${\sigma }_{⟨Y⟩}^2$, as well as the covariance, ${\sigma }_{⟨X⟩,⟨Y⟩}^2$, are proportional to $(N_{s}V{)}^{-1}$, the standard deviation of the observable mean, ${\sigma }_Z$, scales with the inverse square root of the number of samples and the system volume, that is ${\sigma }_Z\propto (N_{s}V{)}^{-1/2}$. Therefore, the variance of the computed observable can be reduced by either increasing the system volume or increasing the number of samples used for averaging. Both approaches incur the same computational cost: (i) Increasing the number of samples, $N_s$, requires running the simulation for a longer duration, with the additional runtime scaling linearly with the number of samples. (ii) Similarly, the additional runtime needed due to increased system volume, $V$, also scales linearly with $V$ (Figure 8). One update step in the simulation always takes roughly the same amount of runtime, but the change in simulation time per update step depends on the total rate of all reactions in the system. The total rate is dominated by the association reactions, and their rate is proportional to the volume. Therefore, the change in simulation time per update step is proportional to $V^{-1}$. The runtime, which is necessary to reach the same simulation time in a system with volume $V$ as in a system with volume 1, is a factor of $V$ longer in the larger system. With this in mind, it makes no difference whether the variance is reduced by increasing the volume or the number of samples. For practical reasons (post-processing of the simulations is less memory- and time-consuming), we opt to choose a moderate number of samples, but slightly higher system volumes to compute the observables of interest. The simulation parameters (length of oligomers, concentrations, hybridization energy, volume, number of samples, characteristic timescales) used to obtain the results presented in Figure 2 are summarized in Table 1.