Tag Archives: opinion

How Big Is Managed Futures’ AUM, Exactly?

By The Alts Team We tweeted the other day that Managed Futures mutual funds had seen 20 straight months of inflows, and that got us to thinking it was high time to do our annual look at how many assets there are under management in the managed futures industry. Now, for those who don’t know – we have a bit of a problem with the usual numbers reported as assets under management in the space by BarclayHedge, who include the world’s largest hedge fund Bridgewater in the managed futures asset total. In our opinion, this does a disservice to investors, vendors, and business people in the industry trying to gauge the size of the space and where they fit into it. Add to that the fact that Winton is a $30 Billion+ manager who tends to dominate the asset raising in the space, and it’s not too big of a stretch to say the majority of assets as reported by BarclayHedge are from just two firms (Bridgewater and Winton). That’s led us to pick apart the numbers a bit and report what the “real” assets and asset growth look like without those two stalwarts (one of which is not managed futures based at all). Without further ado, here’s what the rest of the space looks like: What about the Growth in assets: Here’s where things get interesting, because while stripping out Bridgewater and Winton in years past showed a shrinking industry (the “field”) without those two big dogs, 2015 showed quite the opposite. The so-called “field” added around $18 Billion in 2015 (22% growth), although we can see from the graphic that assets are still down from their 2008 levels with the growth just negative since then. Assets of “the field” grew by 22% in 2015. Assets of “the field” is still down $4 Billion since ’08. “The field” raised $22 Billion in the final 3 quarters of ’15. AQR is, for now, a member of our ‘field’, but at $10.9 Billion and $2.6 billion raised in 2015, may need to be split out in the near future. What’s the takeaway? The larger takeaway is that investors who seemingly forgot about the 2008 financial crisis and how well managed futures do in such periods are starting to remember where they put the diversification keys… and are starting to put real money to work with real managers , not just the Wintons and AQRs of the world – who need more assets like a hole in the head. Here’s to more growth ahead, not just from investors allocating funds, but from the managers multiplying those funds via their trading strategies as well.

Black-Scholes Pricing Model: Is The Hedging Argument Correct?

Black-Scholes Pricing Model: Is the Hedging Argument Correct? Preface Many are familiar with the works of Myron Scholes and Fisher Black in the late 1970s. Their contributions revolutionized the way we price options. Out of the many sections of their proof, the most interesting one in my opinion is the hedging argument given midway through the paper. The reason for which I find it so intriguing is due to the fact that it is the one section that is criticized the most. This leads us to a now popularized question, is such argument valid? Flashback Time As we pull out the proof written more than four decades ago, we notice that the traditional Black-Scholes hedging argument strictly assumes that: markets are frictionless, there is no arbitrage, there is a constant interest rate denoted as “r”, no dividends are paid out and that the stock price process respects the Geometric Brownian Motion. Let’s not forget that GBM (Geometric Brownian Motion) is a continuous time-stochastic process that models stock prices in the Black Scholes Model and other similar works. Click to enlarge If we denote the following as a European Call Price process: We must then further assume the following: As being in conjunction with some “C^2,1″ function C (S, t). When applying Itô’s Lemma we observe the following: Click to enlarge Let us also not forget that Itô’s Lemma is an identity to find the differential of a time-dependent function of a stochastic process. Now let’s consider a portfolio with the goal of long one call and short the following shares. (The goal is therefore what the portfolio consequently consists of.) If we short shares , then we must presume the following: By extracting the textbook argument we can observe the following steps: STEP 1. (**Highlighted**) STEP 2. Click to enlarge STEP 3. Click to enlarge Recalling that arbitrage is not part of the environment of the model we may equate coefficients on ” dt” yields the Black Scholes PDE. (We don’t need to go as far as to solve PDE) Click to enlarge This brings to mind a fascinating question, was the previously highlighted step (Step 1) correct? Gains Process Solution? Let’s remember that the tradition argument that if: Then: Although this seems appropriate, if we integrate by parts, we are then required to obtain the second equation as: Click to enlarge In order to maintain the strategy, two terms must be added representing additional investment. Both terms are differentials processes which have unbounded variation. We therefore cannot claim that ” dHt” is riskless. Since the math to find PDE takes too long I referred to Peter Carr’s solution to this problem in his 1999 paper discussing the proposed question. Carr had found that by doing the math right, PDE could not be found. Carr as well as many other critics, use this position in order to claims that perhaps the Black Scholes Model is wrong. The popular belief is that if the result is right, but the derivation is wrong, then the argument cannot stand. Many have proposed however, that it is possible to derive PDE by a more complicated means and achieve “tenure” therefore making the argument safe from derivations. Although this seems like a solution we must not forget that there are some that believe the contrary. Others have argued that the derivation is indeed correct since the number of shares held is referred to being “instantaneously constant”. (Sort of like instantaneous speed or velocity) In the eyes of mathematicians this two sided argument is difficult since the total variation of the number of shares held by any finite time interval must be in fact infinite. From Carr’s response, it can actually be observed that the number of shares is changing so fast that the ordinary rules of calculus do not apply. (Crazy Right?) So Is the Derivation Right..? No, well kinda… I believe that the derivation is in fact wrong since it is only correct up to some discrepancy or “typo”. If we assume the hedge portfolio value at time ” t” represented by: Then the gain “gHt” in the hedge portfolio is observed as: Click to enlarge It can be thought that “gHt” is riskless and therefore should grow at the risk-free rate in order to cancel out arbitrage. (Risk Free Rate is usually US Treasury Bill Yield) In Carr’s examples, equating coefficients on “dt” does in fact yield the Black Scholes PDE. To make the theoretical world “error free” for derivatives, the above argument replaces the need of computing a total derivative with the financial operation of determining a gain. The portfolio in question of an option and a stock is not self-financing. This is like the positions with regard to riskless assets. Essentially by showing that the gains between two non-self-financing strategies are always equal under no arbitrage, the derivative value of the security can be determined. So why say no? I believe that the solution does bring validity but also brings forward inconsistency. This inefficient manner of providing the solution takes away from the integrity of the model. I do not disagree with the hedging argument, I simply criticise the need for extra material to prove a factor that should be safeguarded in pricing models such as BSM. Disclosure: I/we have no positions in any stocks mentioned, and no plans to initiate any positions within the next 72 hours. I wrote this article myself, and it expresses my own opinions. I am not receiving compensation for it. I have no business relationship with any company whose stock is mentioned in this article.

To Be (The Market) Or Not To Be?

Key highlights After significant losses by large-capitalization and growth stocks during the 2000-2002 bear market, investors have become increasingly interested in non-market-cap index-weighting strategies that intentionally divorce a security’s index weighting from its price. Such rules-based alternatives to market-cap-weighted indexes include strategies labeled alternative indexing, fundamental indexing or, more commonly used, smart beta. Vanguard believes strongly that, by definition, smart beta indexes should be considered rules-based active strategies because their methodologies tend to generate meaningful security-level deviations, or tracking error, compared with a broad market-cap index. Our research shows that such strategies’ “excess return” can be partly (and in some cases largely) explained by time-varying exposures to various risk factors, such as size and style. Place “the market” in front of a mirror and what would you see? A perfect reflection of that market-same size and shape, nothing added, nothing taken away. If you wanted the reflection to show something different from the market-something better?-you’d need to place something different in front of the mirror. That’s the puzzle of smart beta, whose providers often suggest that they’re “like the market,” only better. If you’re looking to get different returns from, for example, the U.K. stock market, “you have to look different in some way, shape, or form,” said Don Bennyhoff, senior investment analyst in Vanguard Investment Strategy Group. “The first thing smart beta providers do is modify what the market looks like, based on their own active choices and biases.” Recent research by Bennyhoff and his colleagues Christopher Philips, Fran Kinniry, Todd Schlanger, and Paul Chin found that the rules-based methodologies employed by alternatives to market-cap-weighted indexes tend to generate meaningful tracking error compared with broad market-cap indexes. The methodologies may weight securities differently from their market-cap weighting. Or they may exclude securities that feature in a benchmark and include securities that aren’t part of the benchmark. “In our opinion,” Bennyhoff said, “these rules-based strategies are active, which means they’re not asset-class beta or ‘the market’ in the traditional sense.” The sources of outperformance “These strategies tend to result in portfolios that emphasize smaller-cap or value stocks, which have performed very well since the early 2000s,” Bennyhoff said. “So the question is, ‘Are these higher returns the result of higher risks?’ There is rigorous debate about that topic. But when we look at risk-adjusted returns, the excess return tends to go away, and maybe that’s a meaningful finding.” Moreover, as the figure below shows, smart beta strategies’ exposures to risk factors change over time. Non-market-cap-weighted strategies’ exposures to risk factors are time-varying 60-month rolling style and size exposure of alternative index versus broad developed-equity market, 1999-2014 Source: Illustration by Vanguard, based on data from MSCI, FTSE, S&P Dow Jones Indices, and Thomson Reuters Datastream. Figure displays 60-month rolling inferred benchmark weights resulting from tracking error minimization for each index across size and style indexes. Factors are represented by the following benchmarks: fundamental-weighted-FTSE RAFI Developed 1000 Index; equal-weighted-MSCI World Equal Weighted Index; GDP-weighted-MSCI World GDP Weighted Index; minimum volatility-MSCI World Minimum Volatility Index; risk-weighted-MSCI World Risk Weighted Index; dividend-weighted-STOXX Global Select Dividend 100 Index. “We’re not saying that paying attention to factors or tilting on value or small-cap is necessarily a bad thing,” Bennyhoff said. “Whether they pay off in the future as they’ve paid off in the past remains to be seen. But instead of putting together a strategy where the factor exposure is a by-product of the weighting scheme or the security-selection scheme, maybe it should be the primary focus .” And if you’re looking to capture the risk and reward of an asset class, Bennyhoff says, “the only way you can reflect that aggregate capital invested in the asset class is through market-cap weighting.” Interested in an overview of smart beta and other rules-based active strategies? Read our research brief . Notes: All investing is subject to risk, including possible loss of the money you invest. Diversification does not ensure a profit or protect against a loss. There is no guarantee that any particular asset allocation or mix of funds will meet your investment objectives or provide you with a given level of income. Past performance is no guarantee of future returns. The performance of an index is not an exact representation of any particular investment, as you cannot invest directly in an index.