## Arbitrage Opportunities in Cryptocurrency Markets Tuesday, 10 July, 2018

**Authors:** Makarov, Schoar

**Title: **Trading and Arbitrage in Cryptocurrency Markets

**Link:** https://papers.ssrn.com/sol3/papers.cfm?abstract_id=3171204

**Abstract:**

This paper studies the efficiency and price formation of bitcoin and other cryptocurrency markets. First, there are large recurrent arbitrage opportunities in cryptocurrency prices relative to fiat currencies across exchanges that often persist for several days or weeks. These price dispersions exist even in the face of significant trading volumes on many of the exchanges. The total size of arbitrage profits just from December 2017 to February 2018 is above of $1 billion. Second, arbitrage opportunities are much larger across than within the same region; they are particularly large between the US, Japan and Korea, but smaller between the US and Europe. But spreads are much smaller when trading one cryptocurrency against another, suggesting that cross-border controls on fiat currencies play an important role. Finally, we decompose signed volume on each exchange into a common component and an idiosyncratic, exchange-specific one. We show that the common component explains up to 85% of the variation in bitcoin returns and that the idiosyncratic components of order flow play an important role in explaining the size of the arbitrage spreads between exchanges.

**Notable quotations from the academic research paper:**

"While significant attention has been paid to the dramatic increase in the volume and price of cryptocurrencies, and many commentators have highlighted their price volatility, there has not been a systematic analysis of the trading and efficiency of cryptocurrencies markets. In this paper we attempt to fill this gap.

In the following we document a number of stylized facts about cryptocurrency markets. First, we show that there are large arbitrage opportunities in bitcoin prices across exchanges that open up recurrently across different exchanges and often persist for several hours, and in some instances even days and weeks. These price dispersions exist even in the face of significant trading volumes on the exchanges. We construct an arbitrage index to show the maximum deviations in the price of bitcoin versus USD at different intervals. The index is calculated each second (each minute in the beginning of the sample), as the ratio of the maximum price of bitcoin on any exchange to the minimum price of bitcoin on any other exchange where bitcoin is traded. On an average day the arbitrage index is 1.05 in 2017. But there are several months where the arbitrage index shoots up to 1.5. For example, in December 2017 and January 2018 there were more than 15 days, where the maximum difference in bitcoin prices across exchanges was more than $3000.

To provide a sense of the magnitude of the money left on the table, we calculate the daily profits that could have been achieved in this market. We find that the daily amount of arbitrage prots between these markets was often more than $5 million a day, and for several days in December 2017 and January 2018, the daily profits reached $30 million. The total size of arbitrage profits in the period December 2017 - February 2018 is estimated to be at least $1 billion under the most conservative assumptions.

Second, we show that arbitrage opportunities are much larger across countries (or regions) than within the same country. We recalculate our arbitrage index separately for each country where there are several significant cryptocurrency exchanges. We find that the average size of the arbitrage index within US, Europe, Japan and Korea has an average value of around 1.01 to 1.03, compared to a value of 1.15 to 1.6 for the total arbitrage index. Similarly, the daily average price ratio between the US and Korea from December 2017 until the beginning of February 2018 was more than 15 percent; and reached 40 percent for several days. This has been noted in the popular press as the "Kimchi premium". Similarly, the average price difference between Japan and the US was around 10 percent, and between US and Europe about 3 percent. The results suggest that regions which are more closely integrated show smaller cross-region arbitrage spreads. Note, however, that even the within country arbitrage spreads are still large by comparison with more traditional asset markets. For example, Du, Tepper, and Verdelhan (2016) show that deviations from the covered interest rate parity in the currency market after the 2008 financial crisis range between 9 and 23 basis points on average on annualized values. These are an order of magnitude smaller than the ones observed in cryptocurrency markets.

Our findings suggest that there are significant barriers to arbitrage between regions and to a lesser extent even between exchanges in the same country. We show that mere transaction costs cannot explain these results since their magnitudes are small in comparison to the arbitrage spreads we document. The governance risk of cryptocurrency exchanges is also unlikely to explain these arbitrage spreads. First, the exchange risk would have to be correlated within a region to explain the large crossborder arbitrages we observe. Second, one would expect that the exchange risk would be correlated with trading volume and bid-ask spreads. This is not supported by the data, since we find large heterogeneity in the liquidity of exchanges within a region but nevertheless arbitrage spreads are small between them.

Our analysis suggests that the most important factors that impede arbitrage are cross-border capital controls on at currencies. In further support of this interpretation we find that arbitrage spreads are an order of magnitude smaller in two way cryptocurrency trades (say bitcoin to ethereum) on the exact same exchanges where we see big (and persistent) arbitrage spreads relative to at currencies. We show that the arbitrage spread between bitcoin and ethereum in Korea versus the US is low, around 1.03 on average. But over the same time period the spread of bitcoin to Korean Won is more than 20 percent. Similar low arbitrage spreads between bitcoin and ethereum exist between the US and Japan or Europe. At the same time the price of ethereum (or ripple) to at currencies, shows similarly large arbitrage spreads as the bitcoin market. Since the main difference between fiat and cryptocurrencies is that capital controls cannot be enforced on cryptocurrency transactions our finding suggest that controls on at currency contribute to the large arbitrage spreads we find across regions.

Nevertheless, industry reports suggest that while capital controls are binding for retail investors large institutions are able to avoid these constraints, see for example a recent IMF working paper by Baba and Kokenyne (2011). Thus, capital controls should not impose insurmountable constraints to arbitrage across regions, but they add to the cost of arbitrage. They may be the reason why arbitrageurs are unable to scale up their trading strategies with the intensity of noise trader activity in a timely fashion. We observe a recurring pattern of arbitrage spreads opening up across different exchanges and times which might be the result of a delayed equilibration between noise traders

and arbitrage capital.

In the second part of the paper, we ask how arbitrage opportunities arise in the first place. Previous research in other asset classes attributes the price pressure of net order flow to price discovery, but in the cryptocurrency market it is less obvious whether there are any traders who are more informed than others and what the nature of the information is. Nevertheless, we show that a strong positive relationship also exists between net order flows and prices in the cryptocurrency market. A common way to estimate the impact of net order flow is to regress returns over a particular time period on the signed volume of trades during the same period. The complication in the bitcoin market is that the same asset is traded simultaneously on multiple exchanges. When forming their demand investors might not only look at prices on their own exchange but also take into account prices on the other exchanges where bitcoin is traded. Therefore, we build on the approach used in traditional financial markets and decompose signed volume and returns on each exchange into a common component and an idiosyncratic, exchange-specifiic component.

We use factor analysis to extract the common factors from data at 5-minute, hourly, and daily frequencies. The common component of signed volume explains about 50% of the variation in returns at 5-minute and hour level, and up 85% at daily level. The price pressure at the daily level is mostly permanent. Buying 10,000 bitcoins raises returns by about 4%.

To investigate the role of signed volume in explaining price deviations across exchanges, we show that exchange-specific residuals of signed volume are significant at explaining variation in exchange-specific residuals of returns at 5-minute and hour level. We also show when the price on any exchange deviates above(below) from the average price on other exchanges, subsequent returns on this exchange are predicted to be lower(higher) than the returns on other exchanges. Furthermore, the predictive power of the local average price index is higher for exchanges in this local market. **These results show that arbitrage spreads open up in periods when there are differential price
pressures through idiosyncratic signed volume on one exchange relative to another. The arbitrage spreads are not arbitraged away immediately but they do predict subsequent relative returns on exchanges.** This lends further support to our interpretation that cryptocurrency prices are the result of a balance between the idiosyncratic sentiments of noise traders and the efforts of arbitrageurs to equilibrate prices across exchanges.

"

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## The Impact of Volatility Targeting on Equities, Bonds, Commodities and Currencies Tuesday, 3 July, 2018

**Authors:** Harvey, Hoyle, Korgaonkar, Rattray, Sargaison, Hemert

**Title: **The Impact of Volatility Targeting

**Link:** https://papers.ssrn.com/sol3/papers.cfm?abstract_id=3175538

**Abstract:**

Recent studies show that volatility-managed equity portfolios realize higher Sharpe ratios than portfolios with a constant notional exposure. We show that this result only holds for “risk assets”, such as equity and credit, and link this to the so-called leverage effect for those assets. In contrast, for bonds, currencies, and commodities the impact of volatility targeting on the Sharpe ratio is negligible. However, the impact of volatility targeting goes beyond the Sharpe ratio: it reduces the likelihood of extreme returns, across all asset classes. Particularly relevant for investors, “left-tail” events tend to be less severe, as they typically occur at times of elevated volatility, when a target-volatility portfolio has a relatively small notional exposure. We also consider the popular 60-40 equity-bond “balanced” portfolio and an equity-bond-credit-commodity “risk parity” portfolio. Volatility scaling at both the asset and portfolio level improves Sharpe ratios and reduces the likelihood of tail events.

**Notable quotations from the academic research paper:**

"One of the key features of volatility is that it is persistent, or “clusters”. High volatility over the recent past tends to be followed by high volatility in the near future. This observation underpins Engle’s (1982) pioneering work on ARCH models. In this paper, we study the risk and return characteristics of assets and portfolios that are designed to counter the fluctuations in volatility. We achieve this by leveraging the portfolio at times of low volatility, and scaling down at times of high volatility. Effectively the portfolio is targeting a constant level of volatility, rather than a constant level of notional exposure.

While most of the research has concentrated on equity markets, we investigate the impact of volatility targeting across more than 60 assets, with daily data beginning as early as 1926. We find that Sharpe ratios are higher with volatility scaling for risk assets (equities and credit), as well as for portfolios that have a substantial allocation to these risk assets, such as a balanced (60-40 equity-bond) portfolio and a risk parity (equity-bond-credit-commodity) portfolio.

**Risk assets exhibit a so-called leverage effect, i.e., a negative relation between returns and volatility, and so volatility scaling effectively introduces some momentum into strategies. That is, in periods of negative returns, volatility often increases, causing positions to be reduced, which is in the same direction as what one would expect from a time-series momentum strategy.** **Historically such a momentum strategy has performed well. **

**For other assets, such as bonds, currencies, and commodities, volatility scaling has a negligible effect on realized Sharpe ratios.**

We show that volatility targeting consistently reduces the likelihood of extreme returns (and the volatility of volatility) across our 60+ assets. Under reasonable investor preferences, a thinner left tail is much preferred (for a given Sharpe ratio). Volatility targeting also reduces the maximum drawdowns for both the balanced and risk parity portfolio.

In Figure 3, we further compare unscaled and volatility-scaled returns, where the latter uses a volatility estimate based on a half-life of 20 days. In the top-left panel, we plot the cumulative return, which shows that the volatility-scaled investment generally outperformed, except during the middle part of the sample period. The impact of volatility scaling is illustrated in the top-right panel, where we depict the rolling 1-year realized volatility for both unscaled and volatility-scaled 30-day overlapping returns. The realized volatility of volatility-scaled returns is much more stable over time. This is also evident from the vol of vol metric (i.e., the standard deviation of the rolling 1-year realized volatility) reported in the legend: 4.6% for unscaled returns versus 1.8% for volatility-scaled returns. Finally, in the bottom-left and bottom-right panels we show the lowest 1% and 5% of the 1-month (30-calendar days) return distribution.19 Very negative returns of, say, -10% or worse are more common for unscaled returns.

To summarize, Figure 3 illustrates the two main ways volatility scaling has helped an Equities All US investment: first, it improves the risk-adjusted performance, and second, it reduces the left tail.

"

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## Returns to Investors in Initial Coin Offerings Monday, 25 June, 2018

**A very interesting research paper we recommend to read to all cryptocurrency traders and investors:**

**Authors:** Benedetti, Kostovetsky

**Title: **Digital Tulips? Returns to Investors in Initial Coin Offerings

**Link:** https://papers.ssrn.com/sol3/papers.cfm?abstract_id=3182169

**Abstract:**

Initial coin offerings (ICOs), sales of cryptocurrency tokens to the general public, have recently been used as a source of crowdfunding for startups in the technology and blockchain industries. We create a dataset on 4,003 executed and planned ICOs, which raised a total of $12 billion in capital, nearly all since January 2017. We find evidence of significant ICO underpricing, with average returns of 179% from the ICO price to the first day’s opening market price, over a holding period that averages just 16 days. Even after imputing returns of -100% to ICOs that don’t list their tokens within 60 days and adjusting for the returns of the asset class, the representative ICO investor earns 82%. After trading begins, tokens continue to appreciate in price, generating average buy-and-hold abnormal returns of 48% in the first 30 trading days. We also study the determinants of ICO underpricing and relate cryptocurrency prices to Twitter followers and activity. While our results could be an indication of bubbles, they are also consistent with high compensation for risk for investing in unproven pre-revenue platforms through unregulated offerings.

**Notable quotations from the academic research paper:**

"The traditional sources for seed and early-stage funding have recently been supplemented with crowdfunding: raising money from many small investors, in small amounts, over the Internet. Early on, crowdfunding was provided in exchange for future rewards or deals on products (e.g., Indiegogo, Kickstarter), and more recently for securities (equity crowdfunding). Advances in the blockchain technology have also led to a new hybrid form of crowdfunding: token offerings, also known as initial coin offerings (ICOs), which are the subject of this paper.

Tokens are cryptocurrencies, digital currencies for which all records and transaction data are protected by cryptographic methods. Entrepreneurs issue branded tokens to raise capital to create an online platform or ecosystem, in which all transactions require the use of that native token. In the 16 months since January 2017, over 1,000 startups successfully raised a total of about __$12 billion__ using ICOs.

The closest analogue to the ICO is the Initial Public Offering (IPO) of equity. In addition to selling a different asset, two key differences between ICOs and IPOs are: (1) ICO firms are much younger and smaller, typically in the earliest stage of a firm’s life cycle, and (2) ICO firms do not use an underwriter to help determine value and attract buyers. As a result, it is not clear how two well-known characteristics of the IPO market, underpricing and post-IPO underperformance translate to ICOs and listed tokens.

In this paper, we study the market for crypto-tokens, focusing on how entrepreneurs determine the price for tokens, the returns to investors from buying tokens during an ICO and selling them once they are listed on an exchange, and the returns to investors from investing in tokens on the listing date and holding them for various fixed time horizons. We also use data from Twitter accounts of cryptocurrency firms to investigate the relationship between Twitter followers and activity, and market prices, and to measure the attrition rate of crypto-companies after completion of the ICO. Our paper aims to provide a comprehensive analysis of how startups in this industry transition and perform from birth, through the offering, to the listing, and beyond.

Figure 3 illustrates that most tokens were sold below their market price, but also, that many tokens were overpriced, and declined in value. The red-dashed line, which is the best fit line, is above the x-axis for the entire sample period, indicating that the average (log) return is positive,** but it has a negative slope, suggesting that underpricing of tokens has declined over time (i.e., returns to ICO investors have been declining).**

Table 3 shows the average returns to investing in an ICO. We start by calculating returns to investors in 416 ICOs that went on to list, in less than 60 days, and report the results in Column (1) of Table 3. The average of equal weighted returns to investing in listed ICOs is a statistically significant 179% and 167% (in Bitcoin), with a very similar 173% and 162% (in Bitcoin) value-weighted average. From the sellers’ point of view, crypto-companies are, on average, issuing tokens for less than half of their true market value, leaving significant money on the table.

For Columns (2) and (3), we also include (in addition to the 416 listed ICOs) another 471 ICOs that reported raising capital but did not list within 60 days. Since there are no available market values for these tokens in the aftermath of the ICO, we impute returns under two different scenarios. In Column (2), the average imputed return to unlisted tokens is -50%. Unlisted tokens investments are not a total loss if the raised capital is refunded due to inadequate funds, if there is an over-the-counter market for them, or if the tokens are listed on an exchange which is not included in CMC. With imputed returns of -50% to unlisted ICOs, average ICO returns are unsurprisingly lower than in Column (1), 57% and 52% (in Bitcoin) for equal-weighted averages and 105% and 98% (in Bitcoin) for value-weighted averages, but still positive and statistically significant. In Column (3), we look at worst-case scenario, imputing -100% to all ICOs that raised capital but did not list within 60 days. **Under this scenario, the equal-weighted average returns are 31% and 26% (in Bitcoin)** and are no longer significant at the 5% level, but the value-weighted returns remain larger in magnitude and significant at 90% and 82% (in Bitcoin).

For Columns (4) and (5), we include an additional 732 ICOs that neither reported raising capital nor were listed within 60 days. Again, we calculate and report average equal-weighted investor returns after imputing -50% (in Column (4)) and -100% (in Column (5)) returns to unlisted ICOs. Since these ICOs raised little or no capital, they do not change the value-weighted returns we calculated and displayed in the last two rows of Columns (2) and (3). **When including these ICOs, equal-weighted returns are reduced to 9% (6% in Bitcoin) with a -50% imputed return, and -28% (-31% in Bitcoin) with an imputed return of -100%.** These are the returns to a naïve investor who invests across all ICOs, even those that didn’t report raising capital, and they provide a lower bound to naïve investor returns. However, they are not at all a realistic estimate of returns, even for naïve investors, because many of the ICOs that don’t report raising capital (and many of those that report raising capital but do not list) either refunded the capital they raised because of inadequate funds or they planned an ICO but never actually began collecting funds.

"

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## Are Currently Used Significance Levels for Investment Strategies Too Strict? Tuesday, 19 June, 2018

**Authors:** de Prado, Lewis

**Title: **What is the Optimal Significance Level for Investment Strategies?

**Link:** https://papers.ssrn.com/sol3/papers.cfm?abstract_id=3193697

**Abstract:**

Most papers in the financial literature estimate the p-value associated with an investment strategy, without reporting the power of the test used to make that discovery. This is a mistake, because a particularly low false positive rate (Type I error) may be achieved at the expense of missing a large proportion of the investment opportunities (Type II error). In this paper we provide analytic estimates to Type I and Type II errors in the context of investments, and derive the familywise significance level that optimizes the performance of hypothesis tests under general assumptions. Contrary to long-held beliefs, we conclude that a familywise significance level below 15% is suboptimal (excessively conservative) in the context of most investment strategies.

**Notable quotations from the academic research paper:**

"Financial researchers conduct thousands (if not millions) of backtests before identifying an investment strategy. Hedge funds interview hundreds of portfolio managers before filling a position. Asset allocators interview thousands of asset managers before building a template portfolio with those candidates that exceed some statistical criteria. What all these examples have in common is that statistical tests are applied multiple times. When the rejection threshold is not adjusted for the number of trials (the number of times the test has been administered), false positives (Type I errors) occur with a probability higher than expected.

Empirical studies in economics and finance often fail to report the power of the test used to make a particular discovery. Without that information, readers cannot assess the rate at which false negatives occur (Type II errors). Suppose that you are a senior researcher at the Federal Reserve Board of Governors, and you are tasked with testing the hypothesis that stock prices are in a bubble. At first, you apply a high significance level, because before making a claim that might trigger draconian monetary policy actions you want to be extremely confident. At a 99% confidence level, you cannot reject the null hypothesis that stock prices are not in a bubble. When you report your findings to the Board, the chairperson asks what is the power of the test. Surprised by the unexpected request, you promise that you will report the test’s true positive probability in the next meeting. Back at your office, you are shocked to realize that, unbeknownst to you, the test’s power is only 50%. In other words, the test is so conservative that it misses half of the bubbles. At the next meeting, the chairperson shakes his head while explaining that, from the Fed’s perspective, missing half of the bubbles is much worse than taking a 1% risk of triggering a false alarm.

In contrast, hedge funds are often more concerned with false positives than with false negatives. Client redemptions are more likely to be caused by the former than the latter. Also, investors know that performance fees incentivize managers to avoid false negatives, hence a “safety first” principle calls for investors to focus on avoiding false investment strategies. Although this is a valid argument, it is unclear why investors and hedge funds would apply arbitrary significance levels, such as 10% or 5% or 1%. Rather, an objective significance level could be set such that Type I and Type II errors are jointly minimized. In other words, even researchers who do not particularly care for Type II errors could compute them as a way to introduce objectivity to an otherwise subjective choice of significance level.

The purpose of this paper is threefold: First, we provide an analytic estimate to the probability of selecting a false investment strategy, corrected for multiple testing. Second, we provide an analytic estimate to the probability of missing a true investment strategy, corrected for multiple testing. Third, we derive the significance level that maximizes the performance of a statistical test used to detect investment strategies.

WHAT IS A REASONABLE SIGNIFICANCE LEVEL FOR INVESTMENT STRATEGIES?

For the particular numerical example presented earlier, where π§πΌ≈2.4978 and the true Sharpe ratio was assumed to be ππ ∗≈0.0632 (annualized Sharpe ratio of 1.0), the harmonic mean between confidence and power is maximized at πΌπΎ∗ ≈0.3051 and π½≈0.4224, where β≈0.6309. Exhibit 2 plots β (y-axis) as a function of πΌπΎ (x-axis).

The reader may be surprised to learn that the optimal significance level is so high, compared to the standard 5% false positive rate used throughout the academic literature. The reason is, at the standard significance level of πΌπΎ=0.05, the test is so powerless that it misses over 71.55% of strategies with a true Sharpe ratio below 1! It is therefore optimal to give up some confidence in exchange for more power, even if that means accepting a false positive rate as high as 30.51%.

Similarly, we can compute the optimal FWER πΌπΎ∗ under alternative assumptions of ππ ∗. Exhibit 3 plots the optimal πΌπΎ∗ (y-axis) under various ππ ∗ values (x-axis) and sample lengths (different lines) for the same numerical example, where ππ Μ=0.0791, πΎ=10, skewness is -3 and kurtosis is 10. The implication is that, unless you are researching a strategy with a true annualized Sharpe ratio above 1 over a period of more than 10 years of daily data, a FWER below 15% is likely to be excessively conservative.

"

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## Are Investors Becoming Better at Fund Picking? Friday, 15 June, 2018

**No, investors seem to learn from past mistake of chasing past performace but are prone to new mistakes - especially to chasing past alpha:**

**Authors:** Friesen, Nguyen

**Title: **The Economic Impact of Mutual Fund Investor Behaviors

**Link:** https://papers.ssrn.com/sol3/papers.cfm?abstract_id=3160271

**Abstract:**

This study analyzes how the determinants of mutual fund investor cash flows have changed over time, and the associated impact on investor returns. Using data from 1992-2016 we find that investor return-chasing behavior essentially disappeared starting in 2011. Investor flows have become more sensitive to expenses, past risk and alpha. Investors are paying more attention to fund characteristics that matter (e.g. risk, alpha and expenses), and less attention to characteristics that don’t (e.g. past returns). Nevertheless, the average investor dollar-weighted return is about 1.2% below the average buy-and-hold return in their underlying mutual fund nearly every year in our sample, suggesting consistently poor timing ability over the entire period. We decompose the economic impact of investor behaviors on investor returns and find that investors’ focus on alpha is actually more detrimental than their previous focus on past returns. Investors do benefit from choosing high-alpha funds (smart money), but poorly time their cash flows by investing in those funds after periods with the highest realized alphas (dumb money). The dumb money effect dominates the smart money effect for the simple reason that at the fund level, past alphas are strongly and negatively correlated with future alphas. Although past alphas are positively correlated to future alphas in the pooled cross-section of mutual fund data, this result does not hold at the individual fund level, which is the level where most mutual fund customers invest. Overall, our results suggest that mutual fund investors know that alpha is important, but have not yet learned how to effectively integrate this knowledge into their investment decisions.

**Notable quotations from the academic research paper:**

"In this study, we examine how the determinants of mutual fund investor cash flows have changed over the past twenty-five years, the economic impact of these changes on investor returns, and ask what these changes tell us about learning among these investors.

Our contributions are of three-fold: first, we document several changes in investor behaviors in the mutual fund industry over our sample period of 1992-2016: investor return- chasing behavior has essentially disappeared starting in 2011; investor flows have become much more sensitive to expenses and past risk; and that the sensitivity of cash flows to fund alpha has been steady or increasing throughout the entire period. To our knowledge, this is the first study to directly measure and report these time-trends in investor behavior.

Second, we develop and present a decomposition which captures the economic impact of each incremental change in behavior. We then estimate the economic impact and for each behavior, specifically the return- chasing, the alpha-chasing, and risk sensitivity behaviors. **Among other things, we find that investors’ focus on alpha is actually more detrimental than their previous focus on past returns.**

Third, we show that once we control for variation in average alpha levels across funds, future alphas are negatively correlated with past alphas at the fund level. The results support the presence of both a “smart money effect” (which arises from investors chasing alphas, which are positively correlated in the pooled cross-section) and a “dumb money effect” (which arises from investors chasing alphas, which are negatively autocorrelated at the fund level). The economic impact of the “dumb money” effect dominates that of the “smart money” effect. **Paying attention to alpha in the current manner is worse than not paying attention to alpha at all.**

The claim that future alphas are negatively correlated with past alphas is at odds with the findings of several studies, including a study done by Elton, Gruber, and Blake (2011), which reports a positive correlation between past and future alphas. **We show that while past and future alphas are positively correlated in the pooled cross-section, this relationship breaks down at the fund level, where most retail investors actually invest. At the fund level, past alphas are strongly and negatively correlated with future alphas, regardless of the time-horizon or factor-model used.** **This is why chasing past alphas is detrimental to investor returns.**

"

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