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Term: Total Value to Paid-In Capital (TVPI) - Finance"TVPI (Total Value to Paid-In Capital) measures a fund's total relative performance. It is a multiple showing the sum of cash given back to investors plus the current worth of remaining assets, divided by the actual money investors put into the fund." - Total Value to Paid-In Capital (TVPI) - Finance TVPI matters because private market returns are not fully captured by cash alone. A fund can distribute little in the early years and still show strong underlying value, while another can hand back cash quickly yet leave weak residual assets behind. TVPI is designed to combine both sides of that picture into one multiple, making it a central shorthand for how much value a private equity or venture capital fund has created relative to the money investors have actually paid in. In practical terms, TVPI answers a simple question with a lot of nuance hidden inside it: for each unit of paid-in capital, how much total value exists today? That total value is the sum of cumulative distributions already returned to investors and the current value of remaining holdings, usually measured as residual net asset value. The denominator is paid-in capital, meaning actual capital called and contributed, not merely capital committed on paper. Core definition and formula The standard formula is . In some sources, residual value is described as remaining NAV, unrealised value, or the fair value of the still-held portfolio. The same identity is often expressed as , where DPI captures realised cash returned and RVPI captures the unrealised balance still in the fund. That decomposition is analytically useful because it prevents the headline multiple from becoming a black box. If a fund has returned in cash and still holds assets worth of paid-in capital, its TVPI is . The number looks strong, but it also reveals that most of the outcome still depends on assets that have not yet been sold. What the metric means in substance TVPI is often described as the total return multiple or overall fund value multiple because it blends realised and unrealised performance into one figure. A TVPI of means the fund has, on a combined basis, merely matched the money investors have put in. A figure above indicates value creation, while a figure below implies capital destruction on a total-value basis. In the private funds context, this matters because the timing of returns can vary dramatically. Early in a fund's life, DPI may be low because few exits have occurred, yet RVPI may be high if the portfolio has appreciated. Later in the life of the fund, the balance may shift: DPI rises as exits happen, while RVPI falls as the remaining portfolio is sold down. TVPI sits across both phases and gives LPs a way to compare funds that are at different stages of maturity. Why the denominator matters One subtle but important point is that TVPI is built on paid-in capital, not committed capital. That distinction matters because LPs usually commit more than is called at any one time, and committed but uncalled capital has not yet been deployed into assets or fees. Using paid-in capital keeps the metric tied to the capital base that has actually entered the fund and has therefore been exposed to performance outcomes. This also explains why TVPI is best understood as a fund-level multiple rather than a time-adjusted return measure. It does not say when value was created, only how much value exists relative to what has been contributed. That is why analysts often pair TVPI with IRR, which does incorporate timing, and with DPI, which focuses on actual cash returned. How practitioners read it In due diligence, TVPI is often treated as the broadest single performance snapshot. LPs use it to gauge whether a manager has generated value overall, whether or not that value has yet been realised as cash. GPs may also use it as a headline figure because it can present a stronger picture than DPI alone when the portfolio still contains meaningful unrealised gains. Yet the metric only becomes genuinely informative when read alongside its components. A high TVPI with a low DPI means the fund's reported success is still largely paper value. A high TVPI with a high DPI is more robust because much of the multiple has already been converted into cash. Conversely, a modest TVPI can still be attractive if it is driven by a strong DPI in a fund that has already returned capital early. Schools of thought and debates There are two broad ways of interpreting TVPI. The first treats it as a convenient summary of economic value, especially for comparing funds in the same vintage, strategy, or stage of life. The second treats it more sceptically, as a valuation-dependent multiple that can flatter portfolios whose remaining assets are marked aggressively. Both views are valid, and the tension between them is part of why the metric remains debated. The main criticism is that TVPI contains unrealised value, and unrealised value depends on marks. Those marks may be disciplined and conservative, or they may be optimistic and slow to adjust. For that reason, a fund with a very strong TVPI may still be carrying latent write-down risk if market conditions deteriorate or if exit assumptions prove too aggressive. There is also a methodological debate about whether TVPI is too blunt to stand alone. Supporters argue that it is the right level of aggregation for fund reporting because LPs need a broad measure of how much value the manager has created. Critics argue that it can obscure the composition of that value, especially when a fund has returned relatively little cash but is carrying a large residual stake that may or may not monetise at the stated value. Mathematical interpretation and related metrics TVPI is a simple ratio, but its interpretation is richer than the formula suggests. If denotes cumulative distributions, residual value, and paid-in capital, then . The related metrics are and , which yields the identity . That identity is more than notation. It shows that TVPI is a full-value measure, DPI is a realised-return measure, and RVPI is the unrealised balance still waiting to be proven. In practice, these three metrics let investors separate cash already earned from value that remains contingent on future exits. Why the term still matters TVPI remains important because private markets are still characterised by lumpy exits, long holding periods, and valuation marks that matter long before cash is distributed. Public market investors can often look at a quoted price and know exactly where they stand. Private market investors cannot. TVPI gives them a disciplined way to track the combined effect of distributions and residual assets while the fund is still alive. It also remains central because it fits the needs of LP reporting. A single multiple is easier to communicate than a full ledger of cash flows and marks, yet it is still rich enough to connect realised and unrealised performance. For that reason, TVPI is often the first number an LP scans, even if it should never be the last number they use. Ultimately, the value of TVPI lies in its balance. It is more complete than DPI, because it includes assets still on the books. It is more grounded than an abstract growth story, because it is anchored to capital actually paid in. And it is more decision-useful than a raw valuation figure, because it tells investors how much of that valuation has already been converted into realised economic return.
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Global Advisors News Brief - August 15 2026Read the full brief at the link Headlines for the last 24hrs
Time window: 2026-08-14T05:00:33.115Z to 2026-08-15T05:00:33.115Z |
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Quote: David Frankel - Founder Collective"[AI] is the wave of our lives. I feel that way, by the way. If I look at internet, SaaS, mobile, AI, nothing looks the same. And will there be roadkill from this wave? Oh my God, there's going to be a lot." - David Frankel - Founder Collective AI is compressing product cycles, inflating capital intensity and widening the gap between companies that can turn capability into distribution and those that cannot. That is why the current wave can be both transformational and destructive at the same time: the technology improves quickly, but the market clears far more brutally, leaving a long tail of funded businesses unable to justify the prices paid for them . Why the boom feels bigger than prior waves Frankel places AI ahead of the internet, SaaS and mobile as a force in his investing lifetime, not because every company in the category will be a winner, but because the ceiling on the best outcomes is higher and the pace of change is faster . The historical comparison matters. Over the past 25 years, he argues, there have been fewer than 100 sustainably large technology companies above roughly $10 billion in value, and the median of the top 500 companies created in that period is around $2.6 billion . That means the modal outcome in every great wave has still been middling relative to the rare giants. AI is likely to repeat that pattern, only with greater speed and more capital chasing the same small set of large wins . The implication is uncomfortable for founders and investors alike. A great technology shift does not guarantee broad success for the companies formed around it. It can instead create a narrow funnel in which a handful of businesses become generational, while the rest become what Frankel calls roadkill . The phrase is stark, but the underlying mechanism is familiar: when a category becomes the focus of intense consensus, valuations rise faster than the underlying certainty of durable differentiation. The market begins to treat participation in the wave as a substitute for competitive edge, even though participation alone is not enough . The seed market problem is really a maths problem Frankel's scepticism about frothy seed pricing is not emotional; it is arithmetic. If the entry valuation rises sharply, the eventual winner must be far larger, or much faster, for the fund maths to work. He pushes back directly against the idea that price no longer matters in AI. In his view, price always matters, because the required exit multiple changes with the starting point . An uncapped note, a lofty cap, or a seed round priced as if it were a later stage all compress the margin of safety and make even a good company a less attractive venture investment . This explains why he is wary of the current fashion for large seed rounds led by multi-stage funds. Those firms can write big cheques, but their involvement often changes the power dynamics for everyone else. Frankel describes a recurring pattern in which a startup takes money from a prominent platform, only to discover later that the internal champion has left, the company is no longer strategic, and the founder is left looking for a second source of support . That is why he sees Founder Collective's smaller cheques as useful not because they dominate the round, but because they remain relevant after momentum investors move on . Discipline is becoming a strategic differentiator The venture market increasingly rewards fund size, access and speed, yet Frankel still argues for discipline at seed. He does not deny that larger platforms can win, especially when a company is already on the path to being one of the very biggest . What he disputes is the notion that scale alone is enough to produce durable venture outperformance. Mega-funds need the very largest outcomes because their fixed costs and cheque sizes require huge capital returns, whereas a boutique seed fund can still generate excellent returns from a more modest, but genuinely elite, company . That distinction gives context to his comments on Founder Collective's strategy. The firm has always been willing to sacrifice some upside by staying small, avoiding management-fee maximisation and keeping a framework that favours founder quality over momentum . He admits that this discipline has caused the firm to miss certain businesses that later became obvious successes, but he treats those misses as the cost of not turning the firm into a size-driven machine . The argument is not that larger funds are wrong in all cases. It is that a small fund can still be a rational, coherent business when it is built around seed economics rather than later-stage asset gathering . Why founder quality still outranks category fashion Even in an AI cycle, Frankel insists that the real edge lies in founder quality, complementary teams and deep domain knowledge . The most interesting startups are not necessarily the ones that declare themselves AI companies first; they are often the ones where people with long industry experience can now use modern tools to attack a persistent pain point. A veteran SAP consultant, for example, who has spent years inside a broken workflow may suddenly be able to build a platform that was previously too expensive or too difficult to create . The capability is new, but the insight is old. That combination is more durable than theme-chasing . Frankel also gives unusually high priority to the relationship between founder and market. He wants a founder who can sell, a technical co-founder who can do what he calls magic, and a partnership marked by trust rather than sameness . That emphasis matters because AI lowers the barrier to building, but not the barrier to convincing, distributing and retaining customers. A model can be copied, but trust, timing and judgement remain hard to replicate. In that sense, AI may actually increase the value of operators who understand a niche deeply enough to see what the market has missed . AI changes the size of the company, not just the size of the market One of the most important strategic shifts in the discussion is the claim that AI enables meaningful businesses to be built by very small teams . That is not just a story about lower headcount; it is a story about a new operating baseline. With coding, support, research, analytics and even some creative tasks partially automated, a startup can begin with more leverage than earlier generations could access . This resembles the effect cloud computing had on infrastructure, but higher up the stack: the product can be launched without assembling the same volume of human labour first . The same logic helps explain why Frankel does not expect mass unemployment, despite expecting significant labour disruption. He anticipates a widening divide between those who learn to use AI well and those who do not . That divide may be especially sharp between younger workers who are already using voice, model-based tools and code assistants, and older workers whose workflows are more fixed . The labour market consequence is not a simple replacement story. It is a reallocation story in which routine tasks disappear, service expectations rise and high-trust human judgement becomes more valuable in the situations where mistakes are expensive . The next battleground is not only models Frankel is also explicit that today's apparent winners are not guaranteed to remain so. He argues that technology platforms rarely stay on top forever, and that the next disruption could come from China, from open models, or from a computing shift that is not yet mainstream . His photonic-computing comments are especially revealing because they show how he thinks about the stack: the model layer is important, but chips, energy and data-centre architecture may be equally decisive over time . If optical or photonic chips materially reduce energy cost, then current assumptions about what constitutes an unassailable advantage could change quickly . That broader view also explains his concern about US research spending and regulation. He sees public R and D, universities and agencies such as DARPA as the upstream source of future commercial breakthroughs, and worries that underinvestment could erode American advantage . At the same time, he views China's faster experimentation and lighter practical constraints as a serious competitive force, especially in areas that require rapid iteration . The strategic tension is clear: if the best ideas come from open-ended research but the fastest deployment happens elsewhere, then national advantage will depend on whether the US can preserve both invention and implementation . Why the most useful venture metric is liquidity, not paper value Frankel's attention to secondary sales and DPI is another sign of how pragmatic his framework has become . In a market where companies can remain private for years while still changing shape underneath investors, paper gains can become misleading . He is more interested in real cash returned than in theoretical value, and that is why he is open to partial liquidity when a company is clearly successful . The point is not to be anti-growth. It is to recognise that waiting for a perfect exit may be inferior to realising some return while preserving upside . This concern dovetails with his comments on the speed of innovation cycles. If products can be made obsolete before liquidity arrives, then the venture business becomes more dependent on timing, optionality and fund construction . Smaller funds can still work, but only if they remain disciplined about entry, selective about ownership and realistic about how much of the portfolio will actually become meaningful . Frankel's position is therefore not nostalgic. It is adaptive. He is willing to accept that AI will create enormous wealth, but he refuses to confuse that fact with an assumption that every investor, fund or startup in the category will share it . The long view: transformation and destruction are linked The deepest thread in Frankel's view is that technological revolutions always produce both creation and elimination. AI will likely make software more abundant, teams smaller, scientific work faster and services more accessible . It will also compress the life expectancy of companies, intensify competitive pressure and expose valuations that were justified more by narrative than by economics . That is why he can sound both enthusiastic and severe in the same breath. The opportunity is real, but so is the waste . For founders, the practical lesson is to build something with genuine edge rather than merely joining the category. For investors, the lesson is to respect price, preserve discipline and treat current leaders as temporary rather than permanent . For the broader market, the lesson is simpler still: AI is not just a growth story. It is a sorting mechanism. The companies that understand their customers, own a real workflow and adapt faster than the model cycle can become extraordinary. The rest may help prove just how ruthless a great wave can be .
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![“[AI] is the wave of our lives. I feel that way, by the way. If I look at internet, SaaS, mobile, AI, nothing looks the same. And will there be roadkill from this wave? Oh my God, there's going to be a lot.” - Quote: David Frankel - Founder Collective](https://globaladvisors.biz/wp-content/uploads/2026/08/20260812_19h00_GlobalAdvisors_Marketing_Quote_DavidFrankel_GAQ.png)
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Term: Recurrent neural network (RNN) - Artificial intelligence"A recurrent neural network (RNN) is a type of artificial intelligence model designed to process sequential data by saving a short-term memory of past inputs. Unlike standard networks that treat each piece of data independently, an RNN feeds the output of a step back into the network as input for the next step." - Recurrent neural network (RNN) - Artificial intelligence Sequential data creates a modelling problem that plain feedforward networks handle awkwardly: the meaning of each new input depends on what came before it. A recurrent neural network meets that problem by carrying forward a hidden state, so the model can use a short-term representation of earlier inputs when processing the current step. That design makes RNNs especially relevant wherever order matters, from speech and text to sensor streams and other time-based sequences . The practical meaning is straightforward. Rather than treating each token, frame, or observation as independent, an RNN updates an internal memory as it moves through the sequence. The same set of parameters is reused at every step, which lets the network apply a consistent rule to arbitrarily long inputs without increasing the parameter count with sequence length . In applied settings, this is why RNNs were long associated with language modelling, transcription, translation, sentiment analysis, and forecasting tasks that depend on temporal context . How the mechanism works At each time step , an RNN receives an input vector and a previous hidden state , then computes a new hidden state . A common compact specification is , with an output such as . Here maps inputs to the hidden layer, carries recurrent information forward, maps the hidden state to outputs, and , are bias terms . This formulation matters because the hidden state acts as the model's working memory. The network does not store a perfect record of the past; it compresses past information into a fixed-size state that is updated repeatedly as new data arrives. In effect, the RNN is unrolled across time into a chain of identical cells, each using the same weights but a different time index, which is the standard way to understand how recurrence and parameter sharing fit together . Training usually relies on backpropagation through time, in which the unrolled network is treated as a deep structure spanning all time steps. Gradients are propagated through the sequence so that the model can learn how earlier inputs influenced later errors . This training method is one reason RNNs were powerful but also difficult to optimise in practice, because long chains of repeated transformations can make gradients shrink or grow too much as they move backward through time . Why RNNs were important The main appeal of an RNN is that it builds sequence awareness directly into the architecture. That makes it suitable for language, where a word's meaning depends on previous words, and for time series, where current values are shaped by trends and lags in the past . RNNs therefore became a natural choice for machine translation, speech recognition, text generation, handwriting synthesis, and forecasting problems where the order of observations cannot be ignored . Another advantage is flexibility over input length. Because recurrence reuses parameters at every step, the same network can process short sequences and long sequences without redesigning the architecture for each possible length . That property helped RNNs become a general-purpose tool for variable-length sequence data, which is one reason they appeared in early voice assistants and other systems that had to absorb streams of language or audio . Core debates and technical limits The same mechanism that gives RNNs memory also creates their biggest weakness. In standard forms, the hidden state must compress everything relevant from the past into a single vector, so distant information can be lost or diluted as the sequence grows longer . This makes plain RNNs less reliable on tasks that require very long-range dependencies, such as tracking a subject introduced many steps earlier in a paragraph or a regime change that began far back in a financial series . That limitation led to several schools of thought. One camp treated the plain RNN as the cleanest expression of sequential modelling and tried to improve it with better optimisation and feature engineering. Another camp moved towards gated variants, such as long short-term memory networks and gated recurrent units, which were designed to preserve information more effectively across long spans. A third camp eventually shifted attention to attention-based architectures, especially transformers, which avoid step-by-step recurrence and instead model dependencies more directly across positions. The result is not that RNNs were wrong, but that their inductive bias is most useful when recency, order, and local continuity are more important than very long-distance recall . There is also a conceptual debate about what 'memory' means in an RNN. In strict terms, the model does not remember in a human sense; it stores a learned summary in the hidden state and updates that summary according to its parameters . For some tasks, that summary is enough. For others, especially those involving richer context or complex cross-token relationships, the compressed state becomes a bottleneck rather than a strength . What the term means in practice today In modern AI, RNNs remain important as a teaching model and as a practical baseline for sequential learning. They clarify the logic of state, recurrence, and temporal dependence in a way that makes later architectures easier to understand . In production systems, they are less dominant than they once were, but they still matter where compute constraints, streaming data, or established legacy pipelines favour compact recurrent models over larger attention-based systems . The term also matters because it describes a broader design principle rather than a single fixed implementation. Any system that feeds its prior state forward to influence later predictions is using recurrence in some form, even if the exact cell structure differs across variants . That is why RNNs remain a reference point in machine learning discussions: they sit at the intersection of sequence modelling, memory, optimisation, and architectural trade-offs, and they explain why order-sensitive data demands more than ordinary static classification .
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Global Advisors News Brief - August 14 2026Read the full brief at the link Headlines for the last 24hrs
Time window: 2026-08-13T05:00:33.075Z to 2026-08-14T05:00:33.075Z |
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Quote: David Frankel - Founder Collective"Are we headed for another dot crash? Definitely. It's not a question of if. When, nobody knows." - David Frankel - Founder Collective The central tension is between technological truth and financial timing. AI can be transformational and still leave a trail of mispriced companies, inflated expectations and broken portfolios, because capital markets reward narrative far faster than they reward durable economics. David Frankel's warning lands in that gap: the technology may be real, the opportunity may be enormous, and the crash may still be unavoidable . Why the warning matters Frankel's position is not that AI is a mirage. He treats it as the most consequential technology wave of his venture career, with the capacity to produce a small number of genuinely giant companies while destroying a much larger number of hopeful entrants . That matters because the market tends to flatten very different kinds of company into the same theme. A startup using AI well, a startup built around AI infrastructure, and a startup merely borrowing AI language for fundraising can all look identical in a pitch deck, even though their economics and survival prospects are radically different . The background to that view is historical concentration. Frankel repeatedly returns to the idea that venture outcomes are not normally distributed in the way many current investors would prefer. Dealroom's summary of the discussion notes his argument that the most valuable companies of the last quarter century were exceedingly rare, and that the median value of the top 500 companies created over that period was about $2.6 billion . In practical terms, that means the AI wave does not need dozens of $10 billion winners to look impressive; it only needs a handful. But it also means that most of the capital already deployed into the category will not be rewarded at the same level. The crash can be real without invalidating the technology Frankel's most important distinction is between a good technological thesis and a bad market structure. He does not argue that AI progress will stop. He argues that valuations, round structures and investor behaviour are likely to outrun what the underlying businesses can support . That is why he is willing to say a dot-com style crash is coming, while also insisting that the underlying wave is still the opportunity of a generation . In his framing, the crash is not a rebuttal to AI; it is a consequence of everyone trying to own the same future at once. This is a familiar pattern in technology cycles. First comes a genuine capability shift. Then capital floods in. Then investor discipline weakens because no one wants to miss the next category-defining company. Then the market starts financing too many lookalikes at prices that assume all of them will become category leaders . Frankel's language is blunt because he thinks the distortion is already visible. He suggests that a large share of today's AI startups are effectively roadkill in waiting, not because they are useless, but because the market is treating a very narrow top tier as if it were broadly available . Seed investing has become a different business The quote also makes more sense when placed inside the economics of seed venture. Frankel argues that small funds can still work because their return requirements are different from those of larger firms . A boutique seed fund can be made whole by owning a meaningful stake in an outcome that would barely move a mega-fund. By contrast, bigger platforms increasingly need exposure to the very largest companies in order to justify their own scale . That is why he sees seed as crowded but not dead: the stage still works if the fund size, entry price and ownership model remain coherent . His scepticism is aimed at a specific intermediate category: the enlarged seed fund that is too big to be nimble and too small to dominate later rounds . Those firms often depend on access, branding and reserve power, but Frankel thinks they can lose the intimacy that matters most at the point of company formation. The irony is that the current market sometimes treats capital scale as proof of strength, when in practice it can become a weakness if the firm can no longer support founders once the next financing decision arrives . Price, ownership and the mathematics of dilution Frankel is also pushing back against the idea that price no longer matters if the company is a future winner. His objection is simple: it is still a ratio problem. The higher the entry valuation, the larger the outcome required to generate the same return . That means uncapped notes, oversized seed rounds and momentum pricing all compress the margin for error. A company can be excellent and still be a bad venture investment if the entry price is too aggressive . This is why he is comfortable missing some deals. Founder Collective's model is explicitly disciplined, even if that means leaving upside on the table . The firm may invest smaller cheques, act as a back-pocket insurer for founders and accept that some later growth will accrue to larger funds . Frankel would rather preserve a framework than become a momentum investor by default. That choice is not cost-free, and he admits it can look foolish in retrospect . But it keeps the firm aligned with the type of outcome it can actually monetise. What changes inside the company There is another layer to the warning: AI changes company formation itself. Frankel argues that more people can now start companies, but fewer possess the entrepreneurial stamina required to build them through a full cycle . That distinction matters because an AI-enabled market lowers the friction to launch, yet does not lower the emotional cost of persistence. Many teams can look like founders at the start, but far fewer can sustain the pressure, ambiguity and constant reinvention demanded when the tide turns . He also sees AI reducing the minimum size of a viable company. Very small teams can now do work that previously required much larger organisations, and that will create new forms of efficiency as well as new forms of concentration . But the stronger consequence may be psychological rather than operational. If a tiny team can now ship like a much larger one, investors may start demanding compressed growth timelines from everyone else, even where that makes no strategic sense . The market then mistakes AI speed for universal speed, and penalises companies that are strong but not spectacular. Why incumbency may be shorter than it looks The crash warning also reflects Frankel's broader belief that no current leader is safe for long. He expects today's apparent AI incumbents to be challenged by new model architectures, Chinese competitors, open-source systems and eventually shifts in compute itself . That is one reason he is interested in photonic computing and other technologies that could change the cost base beneath Nvidia's current dominance . The message is not that one company will definitely lose, but that every layer of the stack is provisional. That same logic shapes his view of regulation and state capacity. Frankel worries that the United States may underinvest in basic research, while China may continue to compress experimentation cycles through faster deployment and looser constraints . If that is true, then the next turn in AI may not merely be a better model, but a different industrial geography. The market implication is stark: a company that looks dominant in one cycle can become just another historical footnote if the capital, policy and research environment changes underneath it. Why the warning is also a strategy note Frankel's phrasing sounds like a prediction, but it also functions as guidance. If a crash is coming, then investors should care less about being seen in the hottest rounds and more about whether the business can survive a changed financing environment . That pushes the best capital towards founders with domain knowledge, real product edge and enough discipline to build through volatility rather than merely ride it . It also rewards firms that can remain active when valuations are less fashionable and liquidity is more constrained . The deeper strategic point is that AI is not a single market. It is a series of overlapping markets: models, tooling, infrastructure, application layers, professional services, data, workflow software and compute . Some of those layers will see spectacular concentration. Others will be commoditised. Some will expand because costs fall. Others will contract because new tools displace old ones. Frankel's warning cuts through the fantasy that all of these outcomes can be financed at once and still produce acceptable returns. In his view, the wave is real, but the market's current enthusiasm is too broad to be sustainable . That is why the phrase 'another dot crash' should be read less as a prophecy of technological failure and more as a statement about discipline. In periods of intense innovation, capital often confuses participation with conviction. Frankel is arguing for a harder standard: if the next decade will reward a small number of extraordinary companies, then the burden on investors is to identify genuine edge, price it honestly and accept that most of the category will not make it through intact .
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Term: Analysis of Variance (ANOVA) - Statistics"ANOVA stands for Analysis of Variance. It is a statistical test used to check if the average values (means) of three or more groups are different from each other. Instead of running multiple t-tests - which increases the chance of a false-positive error - ANOVA looks at the data all at once to see if the group differences are real or just random luck." - Analysis of Variance (ANOVA) - Statistics Group comparison becomes fragile the moment the analyst moves beyond two samples, because repeated pairwise testing inflates the probability of a false positive. ANOVA addresses that problem by asking a single omnibus question: do the observed differences among group means exceed what would be expected from ordinary sampling variation alone? The method is built around variance partitioning, so it compares how far group averages sit from the overall mean against how much spread remains inside each group . That framing matters in practice because the test is designed to separate signal from noise when the explanatory variable is categorical and the outcome is numerical. In the standard one-way case, there is one factor with multiple levels and one response variable, and the null hypothesis states that all population means are equal. A significant result does not prove that every group differs from every other group; it only shows that at least one mean is inconsistent with the rest . How ANOVA works The mechanical idea is simple even if the bookkeeping is not. ANOVA decomposes total variation into a between-group component and a within-group component, then forms an F ratio from the corresponding mean squares. In symbolic form, a one-way model is often written as , where is the observation in group , is the grand mean, is the effect of group , and is the residual error . The test statistic is usually expressed as , where is the between-group mean square and is the within-group mean square . If the groups are genuinely different, the numerator should be large relative to the denominator, because the group means will be pulled apart more than can be explained by random scatter within groups. The resulting value is then compared with an distribution with suitable degrees of freedom to obtain a p-value . Another way to see the logic is through the sum of squares. The total sum of squares is partitioned into between-group and within-group parts, often written as . The between-group term measures how far each group mean sits from the grand mean, while the within-group term measures how far individual observations sit from their own group mean. This partition is why ANOVA is often described as a model of variation rather than simply a test of means . Why variance, not direct mean comparison The choice to work through variance is not a cosmetic one. If one were to compare several means by running many t-tests, each test would carry its own chance of error, and the overall false-positive rate would rise quickly. ANOVA avoids that by pooling the comparison into one test, which preserves the intended type I error rate much more effectively than an uncorrected battery of pairwise tests . That is why the method is usually treated as the first gate in a wider inferential workflow rather than as the final word on which specific groups differ. This also explains a common misunderstanding. ANOVA does not directly tell the analyst which treatments, categories, or conditions differ from each other. A significant omnibus result only justifies further investigation, usually with post hoc procedures that adjust for multiple comparisons. In applied work, this distinction is crucial: the test answers whether there is evidence of any difference, while follow-up analysis answers where that difference lies . Assumptions and their practical meaning Classical ANOVA rests on three core assumptions: independence of observations, approximately normal residuals within each group, and equal variances across groups. These are often presented as technical requirements, but they have ordinary practical meanings. Independence means one measurement should not mechanically determine another, normality concerns the shape of the error distribution in each group, and homogeneity of variance means the groups should have roughly comparable spread . The equal-variance condition is especially important because the ratio implicitly assumes that any within-group variation is measuring the same underlying error scale across groups. When that assumption is badly violated, the nominal p-value can be misleading, particularly if sample sizes are also uneven. In such cases, analysts may use a robust alternative such as Welch's ANOVA, transform the response, or model the structure differently rather than forcing the classical test to fit the data . Major schools of thought Historically, ANOVA is associated with Fisher's experimental design tradition, where randomisation, replication, and blocking are central to credible inference. In that school, the method is not merely a computational test but part of a disciplined way of structuring experiments so that treatment effects can be separated from nuisance variation . The appeal of that approach is its clarity: design the study well, then let the variance decomposition do the inferential work. A second tradition treats ANOVA as a special case of the general linear model. In that view, the same algebra underlies t-tests, one-way ANOVA, factorial designs, and regression with categorical predictors. This unifying perspective is attractive because it shows that the method is not a standalone ritual, but a particular parameterisation of linear modelling with indicators for group membership . It also makes extensions such as two-way ANOVA and interactions easier to understand, since the analyst is simply adding structure to the model . A third perspective is more pragmatic and less doctrinal. Here the emphasis is on whether the question asks for an ordered comparison of several means, whether the sample sizes are adequate, and whether the assumptions are plausible enough to justify the method. This school is less interested in defending ANOVA as a universal solution and more interested in using it as one tool among others, alongside robust tests, mixed models, or non-parametric alternatives where appropriate . Tensions, limitations, and common misuses One tension is that ANOVA is often described as a test of means, yet it is operationalised through variance. That wording can mislead users into thinking the procedure directly measures average differences in a simple way. In fact, the logic is inferential and indirect: means matter because their separation changes the variance structure, and the test statistic captures that change through a ratio of estimated error terms . Another limitation is that statistical significance can be overinterpreted. A small p-value indicates that the observed pattern would be unlikely if all population means were equal, but it does not say that the effect is practically important, causally identified, or stable across samples. In applied settings, the analyst still needs effect sizes, confidence intervals, diagnostic checks, and subject-matter judgement to decide whether the difference is meaningful . There is also a recurring temptation to treat ANOVA as if it were immune to poor design. It is not. If groups differ systematically in ways that were never controlled, if observations are dependent, or if variance heterogeneity is severe, the tidy algebra can produce a false sense of certainty. That is why serious use of the method begins with the design of the comparison, not with the software output . Why it still matters ANOVA remains important because many real questions are still group-comparison questions: do teaching methods produce different outcomes, do treatments differ, do factories produce products with the same mean quality, or do policy regimes lead to distinct average results? The method offers a compact answer to those questions while controlling the error rate better than ad hoc multiple testing . Its longevity comes from that combination of statistical discipline and practical usefulness. It also matters because it teaches a broader lesson about inference. Differences in raw averages are not enough; one must ask whether those differences exceed the background variation that naturally appears in data. ANOVA formalises that idea in a way that is portable across disciplines, from medicine and psychology to agriculture, engineering, and business research . The method endures because the underlying problem endures: real decisions usually depend on whether apparent differences are genuine or merely the noise of sampling.
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Global Advisors News Brief - August 13 2026Read the full brief at the link Headlines for the last 24hrs
Time window: 2026-08-12T07:00:52.108Z to 2026-08-13T07:00:52.108Z |
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Quote: Aswath Damodaran - Professor at NYU Stern School of Business"The problem with smart money is that its self-regard makes its susceptible to attributing more precision to its own convictions, than merited by the circumstances, and that, in turn, results in over reach (portfolios that are much too concentrated or levered)." - Aswath Damodaran - Professor at NYU Stern School of Business The central problem is not intelligence alone, but the way intelligence can mutate into certainty when it is rewarded by a strong narrative, rapid gains and a receptive audience. In markets, a strong view about the future can be useful only if it remains tethered to uncertainty, because the moment a trader starts treating a scenario as near-certainty, position sizes and borrowed money can rise faster than the evidence justifies. That is why the recent rise and collapse of Situational Awareness matters beyond one fund: it illustrates how a persuasive macro thesis can be converted into excessive concentration, excessive leverage and, eventually, forced liquidation . The immediate backdrop was the extraordinary ascent of Leopold Aschenbrenner, whose AI manifesto made him a conspicuous voice in the technology debate and whose fund then channelled that worldview into public markets . The strategy was simple enough to understand and difficult to execute safely: own the companies most exposed to the build-out of AI infrastructure, and short those most vulnerable to disruption from it . In principle, such a trade can work if the direction of technological change is right and the market is slow to absorb it. In practice, it becomes dangerous when the manager starts treating a theme as if it were a settled fact rather than a probabilistic call . Conviction as a market force Conviction is often praised in investing because without it, capital stays idle. Yet conviction is not the same as insight. It is the willingness to act on an estimate of value, a view about how the market will correct, and a belief that the correction will happen inside the investor's time horizon . When those three elements align, conviction can be productive. When they drift apart, conviction becomes a lever that magnifies error. The important distinction is between being right about a broad direction and being right about the path, timing and scale of the move. Markets punish confusion between those things, especially in fast-moving sectors such as AI where expectations can reprice sharply from week to week . The fund's early success helped create the conditions for overconfidence. Returns reportedly surged at a pace that made the strategy appear more precise than it really was, and that kind of feedback can narrow an investor's tolerance for ambiguity . Strong paper gains are psychologically dangerous because they can be mistaken for proof that the underlying model is robust. The danger is greater when the thesis itself is already seductive: AI spending was real, semiconductor demand was real, and the market had genuine reasons to bid up the enabling infrastructure . When a sound macro intuition is packaged inside a concentrated portfolio, the very fact that it has worked for a while can tempt the manager to add more size and more leverage, just when humility is most needed . Why the structure mattered What made the episode fragile was not only the direction of the bet, but the financing of it. Reports indicated leverage of up to 400%, meaning a relatively modest adverse move in the underlying holdings could produce a much larger fall in equity value . That is the arithmetic of borrowed money: if assets rise, returns are amplified; if they fall, losses are accelerated. Once margin pressure arrives, the problem stops being theoretical. Forced selling replaces debate. A manager who may still believe in the thesis is required to unwind positions at exactly the wrong time, handing the market the power to determine the exit price . This is why the comparison with less levered investing is so important. A concentrated book can survive if it is funded conservatively and the thesis has time to mature. But a concentrated and levered book has to be correct not only on substance, but on tempo. Aschenbrenner's public portfolio was heavily exposed to AI infrastructure names, including semiconductors and related beneficiaries, while also carrying shorts against software and other areas thought to be on the wrong side of the transition . When the trade moved against him and funding tightened, the fund was forced to sell most of its public holdings to Citadel, turning a thesis-driven portfolio into a distressed transaction . What the episode reveals about AI investing The wider lesson is that AI investing contains a structural asymmetry. The upside story is easy to tell because the market can already see the capital expenditure cycle: more chips, more data centres, more power, more networking and more speculative enthusiasm around the firms enabling those layers . The harder part is knowing which companies will retain economic power once the technology diffuses. That uncertainty is not a minor footnote; it is the core risk. A manager can be directionally correct about AI and still be wrong about the timing, the beneficiaries and the price paid for the exposure . The market also introduces a momentum problem. If the relevant stocks have already been rising, then a bullish portfolio can look brilliant for reasons that have little to do with original insight. Momentum can validate a thesis in the short run, then reverse without warning . That is particularly dangerous when the trade is crowded, because a manager may believe the position is grounded in fundamental conviction when it is also piggybacking on a broader market trend. Several reports on the fund's unwinding pointed to sharp declines in the very names that had powered the AI trade, alongside pressure from shorts that moved the wrong way . In that setting, leverage does not just increase risk; it compresses time and removes room for interpretation . Reputation, pedigree and overreach The phrase smart money carries its own trap. It flatters managers into thinking that superior pedigree, access or intelligence can convert uncertainty into precision. In reality, strong credentials may improve judgement, but they can also intensify self-regard, especially after early success . Aschenbrenner's background gave him unusual credibility for a young manager: a precocious academic record, experience at OpenAI, and a public intellectual profile around AI safety and AGI timelines . Those assets helped him raise capital and shape expectations. They may also have made it easier, both for him and for his backers, to believe that the portfolio was expressing unusually deep foresight rather than a high-conviction but still vulnerable market view . That is why the collapse resonated so widely. It was not merely a story about one fund losing money. It was a reminder that markets do not reward self-belief in proportion to how compelling it sounds. They reward position sizing that survives mistakes. They reward structures that let a thesis breathe through volatility. They reward investors who can distinguish between a valuable view and an overextended one . The market can tolerate boldness, but it is unforgiving of boldness financed with too much debt. The eventual lesson is less about AI than about the old investment rule that being right is never enough if you have borrowed too much, concentrated too much and left too little room for error . Why it matters now The importance of this backstory lies in what it says about the next generation of thematic funds. AI, climate, energy transition, defence technology and other large secular narratives will continue to attract managers who believe they see the future sooner than everyone else. Some of them will be right for long enough to build real track records. The danger is that markets often allow a view to look more predictive than it is, precisely because narrative and price momentum can reinforce one another . When that happens, investors may confuse early success with durable edge, and a strategy that should have been sized for uncertainty instead becomes a vehicle for one person's confidence . For allocators, the question is not whether a manager has conviction, but whether the portfolio is built to survive the possibility that the conviction is only partly right. For managers, the challenge is to remember that a persuasive thesis about AI adoption is not a licence to ignore balance-sheet discipline. The recent collapse shows how quickly a supposedly brilliant trade can become a forced sale once leverage meets volatility . It also shows that in markets, the difference between insight and overreach is often just a matter of how much money has been borrowed to express the view .
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Term: Hill climbing - Artificial intelligence"Hill climbing in artificial intelligence is a local optimisation technique. It continuously adjusts a candidate solution to maximise or minimise an objective function. It always moves toward immediate incremental improvements until it reaches a peak where no further local gains are possible." - Hill climbing - Artificial intelligence Search quality in hill climbing depends less on brute force than on how well the problem is shaped into a landscape of scores, neighbours and stopping rules. The method keeps only the current candidate, tests nearby alternatives, and accepts a move only if it improves the objective, which makes it a local search procedure rather than a full tree search . That simplicity is the reason it remains useful in artificial intelligence, but it is also the source of its main weakness: once no nearby move is better, the algorithm stops even if a far better solution exists elsewhere . Core mechanism In practical terms, hill climbing starts from an initial solution and repeatedly generates one or more neighbouring solutions by making small changes, such as swapping items, adjusting a parameter or modifying a state by a fixed step . An evaluation function then scores each candidate, and the algorithm moves to a neighbour only when that score is better than the current one . For maximisation, the process seeks higher values; for minimisation, the same logic is applied to a cost function by moving towards lower values, which is why sources describe hill climbing as a general optimisation technique rather than a method tied to a single type of goal . The mathematical structure is straightforward. Let the current state be and the objective be . Hill climbing evaluates neighbouring states and accepts a move when for maximisation, or for minimisation . The update rule is therefore greedy and incremental: when a better neighbour exists, otherwise the algorithm terminates . In this formulation, the meaning of the parameter set is unusually important. The neighbourhood definition determines what counts as a small move, the scoring function determines what counts as improvement, and the stopping condition determines how long the search can continue . Why the method works The appeal of hill climbing comes from its economy. It stores almost no search history, examines only the current state and its immediate surroundings, and can therefore be very memory efficient compared with methods that maintain large frontiers or full search trees . That matters in AI settings where the state space is large, the objective is expensive to compute, or the application needs a quick approximate answer rather than a provably optimal one . In such cases, a good local improvement step may deliver most of the value at a fraction of the computational cost of exhaustive search. That economy also explains why the method is often described as greedy. The algorithm never sacrifices an immediate gain in the hope of a better later outcome, and it does not backtrack once a move has been accepted . This makes it easy to implement and interpret, but it also means the search is myopic. Hill climbing can become trapped at a local maximum, a plateau where several neighbouring states have the same score, or a ridge where progress requires a sequence of sideways or temporarily worse steps . Those failure modes are not edge cases; they are the central reason optimisation researchers treat hill climbing as a useful baseline rather than a universal answer . Major variants and schools of thought Different variants try to reduce the cost of greediness or soften its rigidity. Simple hill climbing checks neighbours in a fixed order and stops as soon as it finds an improvement, which is fast but can miss a better alternative . Steepest-ascent hill climbing evaluates all neighbours and chooses the best one, which usually improves solution quality but increases per-step cost . Stochastic hill climbing samples from the set of improving moves, which introduces randomness and can help avoid some poor local traps . First-choice hill climbing tests random neighbours until it finds one that is better, which is useful when the neighbourhood is large and exhaustive comparison is expensive . These variants reflect a broader debate in AI search: should the algorithm favour speed, stability or escape from local optima. Deterministic versions are easier to reason about, but randomised versions often perform better in hard spaces where the landscape is irregular . Another division concerns whether the problem should be treated as maximisation or minimisation. In machine learning and control, for example, the same logic may be used to reduce error, loss or cost, which simply means the score is interpreted in reverse . The method therefore sits at the intersection of heuristic search, local optimisation and practical engineering judgement, with the choice of variant often more important than the label itself . Practical meaning in AI systems In real applications, hill climbing is best understood as a disciplined way to improve one candidate at a time. It is commonly used when an exact global optimum is difficult to compute, when a near-optimal solution is enough, or when the search space is too large for exhaustive methods . This makes it relevant to scheduling, path adjustment, parameter tuning, game playing and other problems where local edits can be scored quickly . The method is also pedagogically valuable because it exposes the main logic of heuristic search without hiding it behind elaborate machinery. Yet the practical meaning of hill climbing is not that it always finds the best answer, but that it offers a controlled compromise between solution quality and computational effort . A good run depends on the starting point, the shape of the objective surface and the design of the neighbourhood. A poor starting point can send the search into an inferior basin; a narrow neighbourhood can prevent meaningful movement; and a noisy objective can make the algorithm chase small fluctuations rather than real improvement . In other words, the method does not eliminate modelling judgement. It transfers that judgement into the choice of representation, scoring and move generation. Tensions and limitations The most persistent criticism is that hill climbing confuses local improvement with global progress . A state can look best among its immediate neighbours while still being far from the best overall solution, and the algorithm has no built-in mechanism for escaping such traps . This limitation is especially serious in landscapes with many peaks, flat regions or deceptive gradients, where the first locally improving path may lead to a mediocre result . Because of this, more advanced methods often borrow the hill climbing idea but add random restarts, sideways moves, simulated annealing or population-based exploration to broaden the search . There is also a conceptual tension between its simplicity and the complexity of the problems it is used to solve. On one side, the algorithm is attractive because it is transparent, cheap and easy to adapt . On the other, the very features that make it simple also make it fragile when the landscape is noisy, discontinuous or highly multimodal . That tension explains why hill climbing has survived for so long: it is not the final word in optimisation, but it remains one of the clearest ways to think about local improvement, and many stronger methods can be read as attempts to repair its weaknesses without losing its efficiency . Why it still matters Hill climbing still matters because much of AI is not about finding a single perfect solution in one leap, but about making repeated, informed improvements under constraints. That pattern appears in optimisation, search, feature adjustment, configuration tuning and many other tasks where incremental change is natural . The algorithm also remains a useful conceptual bridge between informal intuition and formal optimisation. It helps explain why local score improvements can be powerful, why they can also fail, and why the shape of a problem often matters more than the cleverness of any single move . For that reason, hill climbing is best viewed as both a method and a warning. It shows how far a simple greedy rule can go, but it also shows exactly where such a rule breaks down . In modern AI practice, that combination is valuable. It encourages compact implementations when speed matters, disciplined problem formulation when accuracy matters, and a realistic understanding that many optimisation tasks are solved not by one elegant search, but by a sequence of increasingly better local decisions .
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