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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EquitesLab Out-Of-Sample Test of F-Score and Equity Reversal Strategy Thursday, 7 June, 2018
We would again like to present a very interesting cooperation, this time with a guys from EquitiesLab.
They too started to analyze some of Quantpedia's suggested strategies. The first article (https://www.equitieslab.com/f-score-and-short-term-reversals/) analyzes a combination of a well-known fundamental Piotrovski's F-Score strategy with a Short-Term Reversal (see Combining Fundamental FSCORE and Equity Short-Term Reversals for details). Combined strategy shows nice outperformance since year 2000. A long-short strategy trails a strong S&P 500 performance during last few years, but it can be expected in such strong bull market. However, probably the most interesting feature is strategy's outperformance during crisis years like 2001, 2002, 2008 and 2011:
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Currency Management with FX Style Factors Tuesday, 5 June, 2018
A new financial research paper has been published and it is related to:
#5 - FX Carry Trade
#8 - FX Momentum
#9 - FX Value - PPP Strategy
Authors: Lohre, Kolrep
Title: Currency Management with Style
Link: https://papers.ssrn.com/sol3/papers.cfm?abstract_id=3175387
Abstract:
Currency hedging is often approached with an all-or-nothing mentality: either full hedging of all foreign exchange (FX) positions or no hedging at all. As a more nuanced alternative, we suggest systematically harvesting the benefits of the FX style factors carry, value and momentum. In particular, we demonstrate how these factors can expand the opportunity set of traditional asset allocation when pursuing either FX factor-based tail-hedging or return-seeking strategies.
Notable quotations from the academic research paper:
"There are good reasons to believe that the optimal currency hedge lies between the two extremes of a full hedge and no hedge at all. We believe that it pays off to have a closer look at currency style factors for determining a beneficial currency allocation.
FX style factors vis-à-vis multi-asset classes We will now demonstrate the mean-variance properties of FX style factors relative to traditional asset classes. Figure 1 depicts a mean-variance diagram of the three FX style factors carry, value and momentum, as well as five traditional asset classes as given by US equity, US Treasuries, US corporate bonds (investment grade and high yield).
First, we inspect the investment opportunity set of traditional multi-asset investors based solely on the latter five asset classes. In particular, we take the perspective of a EUR investor who is fully hedging USD/EUR exposure. The left chart in figure 2 shows the ensuing mean-variance allocations along the efficient frontier for the five multi-assets only. Going from left to right, we learn that a more defensive investor would have allocated towards government
bonds, whereas the latter allocation for less riskaverse investors gives way to investment grade and high yield credit positions.
Second, adding the three FX style factors to the mix would significantly expand investors’ opportunity set. The ensuing efficient frontier including FX styles shifts considerably to the northwest compared to the multi-asset-only allocation. Obviously, the inclusion of the FX carry and value factors is expanding the portfolio return perspective. Still, judging from the corresponding mean-variance allocations, we learn that all three FX style factors crucially enhance the tail-hedging capabilities of any multi-asset investor, as demonstrated by their large portfolio weights in the minimum-variance portfolio. While FX momentum does play a role, especially for very defensive allocations, we see that FX value is beneficial across the whole spectrum of risk profiles. Likewise, allocation to the FX carry trade replaces some of the high yield allocation, reflecting its close association with genuine equity and credit risk. and commodities."
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Short-Term Return Reversals and Intraday Transactions Tuesday, 29 May, 2018
A new financial research paper has been published and is related to:
#31 - Short Term Reversal in Stocks
Authors: Miwa
Title: Short-Term Return Reversals and Intraday Transactions
Link: https://papers.ssrn.com/sol3/papers.cfm?abstract_id=3174484
Abstract:
I examine whether a short-term reversal is attributed to past intraday or overnight price movements. The results show that intraday returns significantly reverse in the following week, while overnight returns do not, indicating that the short-term reversal is attributed to past intraday price movements. In addition, the reversal of intraday returns is stronger for more illiquid stocks and during more volatile market conditions, while the reversal is unaffected by fundamental news. This result supports the view that short-term reversals are attributable mainly to price concessions for liquidity providers to absorb intraday uninformed transactions, rather than intraday price reactions to fundamental information.
Notable quotations from the academic research paper:
"In this study, I advance the understanding of drivers of short-term return reversals by a careful examination of when temporal price mispricing or concessions, resulting in short-term reversals, accrue. In particular, I decompose short-term return reversals into reversal of overnight return and that of intraday returns.
Though I am the first to decompose short-term return reversals in this way, such a decomposition is natural, because these two periods differ along several key dimensions. Fama (1965) shows that volatility is higher during trading hours (intraday) than it is during non-trading hours (overnight), and Kelly and Clark (2011) suggest that overnight stock returns are, on average, higher than intraday returns. Thus, decomposing return reversals into overnight and intraday return components could yield new and important information on the drivers of the short-term return reversal.
I find that short-term return reversal is mainly attributed to reversal of lagged intraday returns. In other words, intraday returns significantly reversed in the following week, while overnight returns do not. These results hold strongly in each international sample (i.e., US stocks, Japanese stocks, UK stocks, and Eurozone stocks). Even after excluding one-day returns in order to avoid the bid-ask bias, the strong intraday return reversal remains. Furthermore, this finding is robust to a variety of controls and risk-adjustments.
The two competing explanations for short-term reversals raise the question of whether the reversal of intraday returns results from a reaction to new information which occurs intraday, or from a price concession to absorb intraday transactions.
I attempt to address this question in two steps. I first examine whether the negative association between intraday returns and subsequent returns is stronger arounf fundamental news. If a reversal of intraday returns is attributed to a price reaction to fundamental news which occurs intraday, the negative association should be strengthened by the existence of fundamental news.
Then I analyze whether a reversal of intraday returns is stronger when liquidity providers request higher compensation. To this end, I examine whether the reveral of intraday returns is associated with a volatility index.
The analysis reveals that reversals of intraday returns are not stronger around news, indicating that the overreaction explanation is not plausible for the short-term reversals. On the other hand, reversals of intraday returns are stronger for illiquid stocks and when the volatility index is higher. These results support the view that reversals of intraday returns are attributed to price concessions that enable liquidity providers to absorb intraday transactions. The finding supports the lliquidity explanation."
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