Chicago Board of Trade

CBOT_PatioAfter the R/Finance conference, we had the opportunity to visit the Chicago Board of Trade Building. Brian Peterson, one of the conference committee members, gave us a tour of the building and took us up to the rooftop lounge for beers.


During the days of open outcry, the building housed the trading floor with pits for each commodity. With all trading being conducted electronically, the pits have been removed. Depictions of the Roman god of grain, Ceres, are displayed inside as well as a 31 ft statute on top of the building.

As you enter the building, there is the Ceres restaurant and an empty hallway where the

pits were located. WarholA wall of original Warhols is located further inside. I included some pictures of the Art Deco elevator doors and mailboxes but there is much more to see.

CBOT MailboxesCBOT_Elevator

Ordinary Least Squares

Let’s estimate a stock’s beta and alpha using the CAPM. First prepare the data by calculating stock returns and market returns. Subtract the risk-free rate from both and form a data.frame called “urdata” where ExRet is the excess return on the stock and MktRP is the risk premium on the market. Next, specify the formula for the estimated model and call it “m2”. Use the lm() function to estimate the model and assign the results to a variable called “ols”. Finally, use summary() to see the regression results.


If you are using a lot of fixed effects, try using coef(ols)[1:5,] to get the first 5 rows of coefficients.

The Econometric Cycle

Quick results but assumptions are probably violated

Use Nonparametric Techniques
Results are not general enough because my sample isn’t big enough or lacks certain characteristics

Everything is a State Space Model!
Too many parameters → I don’t own a quantum computer.

Think more; use less parameters → Thinking is hard.

OLS is pretty robust


This code is an implementation of Volume Synchronized Probability of Informed Trading by Easley, Lopez de Prado, and O’Hara (2012) published in the Review of Financial Studies. Easley et al. argue that the CDF of VPIN indicates order flow toxicity. This is their explanation of the flash crash in 2010. You can see slides to my R/Finance 2014 presentation on the topic.

This version of the code is not particularly fast and they are plenty of opportunities for a better programmer than me to tune it up for speed.

#### VPIN calculation #########################################################
require(data.table); require(fasttime); require(plyr)
# Assuming TAQ data is arranged in 1 year stock csv files
stock=fread('/TAQ_data.csv'); stock=stock[,1:3,with=FALSE]
# Now we have an xts data frame called 'stock' with a DateTime index and... 
# two columns: Price and Volume
# Vbucket=Number of volume buckets in an average volume day (Vbucket=50)
VPIN=function(stock,Vbucket) {
  timeDF$dP2=(1-timeDF[,'Next'])*timeDF[,'dP1'] + timeDF[,'Previous']
  timeDF[,'Vtick']=timeDF[,'Vtick']-diff(timeDF[,'Vtick']); timeDF[1,'Vtick']=0; timeDF[,'DateTime']=row.names(timeDF)
  timeDF=timeDF[,c('VPIN')]; return(timeDF)

Here is what the original file looks like:

1993-01-04 09:35:25,10.375,5300,40,0,,N
1993-01-04 09:36:49,10.375,25000,40,0,,N
1993-01-04 09:53:06,10.375,100,40,0,,N
1993-01-04 10:04:13,10.375,200,40,0,,N
1993-01-04 10:04:20,10.375,100,40,0,,N
1993-01-04 10:24:42,10.375,1000,40,0,,N
1993-01-04 10:25:19,10.375,600,40,0,,N
1993-01-04 11:31:04,10.5,10000,40,0,,N
1993-01-04 12:13:09,10.5,200,0,0,,M
1993-01-04 12:13:38,10.5,200,0,0,,M

Benchmark Investing Stock Selection

A particular insurance company’s investment department measures stock performance against the S&P500 index on an annual basis. The portfolio is long only with no derivatives. The portfolio manager eases into new positions and takes smaller positions outside of the index. The department operates on a monthly trading schedule where all trades for the next month are set within the last week of the current month. Regardless of how much the portfolio outperforms its benchmark, full bonuses are paid based on the trailing three years of performance. This compensation plan is ridiculous for any institutional or individual investor paying for active management and the following is a short example of why that is true.

Imagine that we need to improve performance over the next month or so and identify two stocks for possible purchase. Both have sufficient liquidity with attractive fundamentals and good management but one is a small cap stock outside of the index and the other is a large cap stock in the S&P500. Using multiple valuation methods, we determine that the small cap stock is cheaper than the large cap stock and therefore has a higher expected return. The small cap value stock is also likely to have greater price volatility than the large cap index name. This is intuitive if we assume that over the long term, all stocks revert to some constant information ratio. With a greater expected return, we would assume greater price volatility relative to the large cap stock.

If this were your portfolio and you wanted to maximize long run returns, you would prefer to buy the small cap stock. Unfortunately, this is not what the portfolio manager or equity analyst would like to do. The portfolio manager is primarily concerned with risk. He believes that initiating a new position in a small cap stock is riskier than adding to an existing position in the large cap stock in the index and he is right in the sense that it will increase tracking error due to the higher price volatility of the small cap stock combined with being outside of the index. He is also wrong in the sense that a larger tracking error is only a problem if you are buying more stocks with negative alpha than with positive alpha. I will also be generous in assuming that the portfolio manager does not believe that holding a stock in the past reduces uncertainty in future returns. This is a industry wide problem to be addressed another day. The equity analyst will also prefer the large cap stock to the small cap stock even if his/her compensation is completely performance based. The reason for this is that the position size that the portfolio manager is willing to take is insufficient to provide any meaningful performance improvement. Therefor, it is better to get a small performance boost from a larger position in an index stock than a minimal performance improvement from the small cap stock.

Ultimately, this results in a mediocre enhanced index fund run by overpaid managers. People who make their career on this business model will argue that the portfolio is a broadly diversified, actively managed, low risk, blah blah blah. I usually don’t catch the rest due to the amount of quacking emanating from their non-indexed index portfolio. The bottom line is that if over 90% of your investments are inside the benchmark index and your tracking error is infinitesimal, you are running an index fund and should be paid accordingly. For more articles on the unintended consequences of performance benchmarks, please refer to Beating the Market Part 1 and Part 2.

Value Creation

I hear a lot of opinions on how economic value is created. Some of these opinions are supported by secondhand anecdotal evidence and most of them are used to support various political or social positions. Some of the most absurd theories on value creation even come from wealthy and/or successful people so someone without a business education may be forgiven for believing that this is a philosophical question that can only be answered through a belief in some set of principles. I would like to articulate why there is an objective reality to value creation. It has very little bearing on any political or social position and absolutely nothing to do with faith.

Value is created through the decision making process. This process need not be rational; the only thing that matters is success. As in warfare, winning by skill, preparation, accident, luck, or for the wrong reasons are all sufficient. Unfortunately, in this framework, there is an objective definition of success and it requires two ingredients. The first ingredient is an understanding of the money generated from a new venture and the second is understanding the price of the money necessary to start and maintain the project. Success is defined as a project that generates a rate of return greater than the cost of the money that is required for the project. That is it. Full stop.

While the concept is simple, there is also an objective methodology for calculating success. Future cash flows must be discounted at the cost of capital which is the rate at which you obtain the capital necessary to start and run the business. Oftentimes this rate is uncertain so the best estimate is used and the results are tested to see if changes in this rate affect the decision to go ahead with the project. The internal rate of return is the constant rate at which a series of positive and negative cash flows can be discounted such that the net present value of these cash flow are zero. This can also be described as the discount rate at which the manager is financially indifferent to taking on a new project. If that discount rate is greater than your cost of capital then you undertake the project.

Whether managers know this process or not, this is the only method of creating economic value. Improving on this process requires either lowering your cost of capital by getting money at a lower interest rate or by increasing the present value of the cash flows generated from the project. This can be achieved by reducing the investment in the project, getting the cash flows earlier, or increasing the growth rate in cash flows.

Correlation Graph

Earlier this week, I saw a message in my Twitter feed talking about an unusual correlation pattern between the S&P 500 and the Dow. Unfortunately, the graph produced by the Greg Mankiw recommended site was grossly inaccurate showing periods of zero correlation between the indices. A few lines of code using the Quantmod package in R can easily replicate the functionality of the site and a prudent analyst can simply load a more reliable data source before arriving at any conclusions. This script takes data from Yahoo finance but you can easily use Google finance or load your own data.

The Effects of Venture Capital Strategy


Highland Capital and Tallwood Venture Capital represent two strategies of venture capital investing. Highland represents the traditional diversified portfolio strategy where many unrelated investments are made and little operational support is provided by the investor. Tallwood represents the focused portfolio strategy where fewer investments are made in a specific industry and investors are able to provide a greater amount of time and operational support to their firms. Neither of these firms is absolute in their strategic focus. Highland provides some support to some of its investments in the form of office space and access to other industry leaders. Highland also has focused teams in specific industries and cannot simply invest in any firm. While I will discuss a hybrid approach later in the paper, the number of focused sectors and number of investments in each sector results in a strategy that is indistinguishable from a diversified strategy.

Tallwood only has two executives in residence to assist partners in providing technical advise for its portfolio. Clearly, this is insufficient to provide constant support to their firms however this paper will discuss relative differences in strategies rather than absolute examples of either strategy. I will explain why this difference matters to investors, how it affects investment selection within the firm, and the type of firms that are most likely to receive funding from each strategy. Given the extremely high exits necessary to compensate for a large number of losers, a diversified strategy is interested in funding companies that have a low probability of success and a high-expected growth rate. A high probability of success would not allow for a large enough equity stake given a limited amount of equity and a low growth rate does not provide a sufficiently high exit valuation. Increasing an investor’s focus on an industry allows for investing in ideas that may have a smaller market potential but greater probability of success.

Investor Motivation

From the investor’s point of view, venture capital should provide superior risk adjusted returns with a liquidity premium when compared with public markets. Without this return, there is no incentive to invest. The problem lies with describing risk in statistical terms in order to get a precise quantitative answer rather than business terms that usually results in a more qualitative answer.

Investing in a venture capital firm requires a lockup period where the investor cannot withdraw the investment or may withdraw but at a severe penalty. This is to protect other investors in the fund from being forced to contribute more capital than planned or to sell illiquid investments at a discount. As compensation for being unable to quickly withdraw their investment, an investor requires a liquidity premium. Without this liquidity premium, investors would be better off buying assets such as stocks with the same returns and no penalty for selling early. Endowments that have too much of their portfolios allocated to illiquid assets may not be able to support their liquidity needs when a financial crisis causes the value of their stocks and bonds to fall. When the liquidity risk is not considered, venture capital returns may be overstated.

While venture capital may be an unappealing investment based on overestimated returns and underestimated risk, there may be opportunities to make a rational investment by choosing a successful fund manager. If an investor will need to accept a lockup period of up to 10 years, the initial manager selection is critical. There is a substantial risk that one of the partners may retire or leave the firm and support staff typically has a higher turnover so the selection process will need to focus on strategy rather than personality. Knowing this, the question then becomes what strategy produces above average returns in the venture capital industry?

Venture Capital Industry Concerns 

According to Fred Wilson, venture firms need average exit multiples of three to meet the returns required by investors. The average industry exit multiple was 1.6 which is approximately a ten percent annual IRR. According to the article, another unnamed industry analyst estimated that venture capital would need to decrease by 50% in order to generate adequate risk adjusted returns before coming to the conclusion that the venture capital model doesn’t scale. This conclusion seems justified when we compare the expectation of a 10% return in 2010 with the expectation of a 25% to 35% return in 1998 and the realized return of 8.2% as of the third quarter of 2010 but does not take into account a strategy change in the venture capital industry.

Highland Capital represents the traditional diversified venture capital strategy. As Peter Bell noted in his presentation, the success of any investment is viewed as a random process and Highland’s partners are generalists that follow a top down approach to individual investments. The partner first determines an attractive industry; one that is in the growth period of the industry S-curve. High growth companies command higher valuations at exit and are easier to market to the public market or an acquirer. Since there is little disagreement in the industry on what the high growth industries will be, venture firms will tend to over invest in attractive industries.

According to Zider, a venture capital investment has an estimated 10% probability of success, which implies that the average venture capital firm has excess capital to allocate to investments. The exact proportion of the remaining 90% that is required to obtain the winning 10% cannot be determined with certainty without making some assumptions. In Highland Capital’s case, the assumption is that venture investors are not skilled in selecting investments. This assumption supports the diversification strategy also limiting the amount of time each partner can devote to an individual investment. A generalist who invests in a diversified portfolio has little incentive to choose the best firm in an attractive industry with time being a limited resource. This conclusion is based on the assumption of limited equity in quality firms seeking capital and limited time combined with excess funds with which to invest.

In Tallwood’s case, the firm has a focused portfolio strategy where the top down approach can only be applied in a limited manner. If investments are limited to the semiconductor industry and are smaller in number, Tallwood can pursue a bottom up investment strategy where more time is spent evaluating whether the particular investment is attractive as opposed to evaluating whether an industry is attractive. Time constraints become more relaxed relative to a diversified strategy since there are fewer investments to track. The focused portfolio strategy assumes that partners have some expertise in selecting investments and advising companies. Without this assumption, there would be no incentive to limit the number of investments or the industry in which to invest.

An alternative to the diversified and focused portfolio strategies is for a single venture capital firm to have multiple partners where each partner or team of partners is focused on a particular industry or technology. This hybrid strategy can mimic the results of either the diversified or focused portfolio depending on the number of investments made by each partner and the resources available for each partner or team to support their investments. A partner with few investments has an incentive to select best in class companies and provide operational support while a partner with many investments will provide little to no support and assume success is a random process. In the former example, the hybrid strategy will mimic a focused strategy while in the latter case; the strategy will be similar to a diversified strategy.

Financial Theory

The assumptions I have made regarding diversified and focused portfolio strategies in the venture capital industry are supported by the work of Fisher Black and Robert Litterman in their model of portfolio optimization. The Black Litterman model was original applied to currencies but it can be applied to any investment. The main idea of this model is to optimize a portfolio not just on expected return but also on the deviation between market expected returns and the investor’s expected return. In essence, invest more money when the investor believes that he/she has an edge over the market.

The diversified strategy is diversified because partners believe that they do not have more skill at selecting investments than the market. Under the Black Litterman model, we would expect these firms to exhibit “herding” behavior investing in the same firms and industries and, as Peter Bell confirmed, this is what we observe in the industry. Focused funds believe that they have an edge over other investors and overweight those firms as described by the model. This results in fewer investments and more resources to support each investment.

Returning to the argument of the amount of excess capital necessary to secure a 10% success rate, the focused fund must assume that either they have a higher success rate than diversified funds or they have higher returns from their winners. Without one or both of these assumptions, there would be no incentive to remain limited to a focused strategy. If we assume that one or both of these possibilities are true, a focused firm has the opportunity to invest in firms where the expected return is lower than that required of a diversified fund. This occurs because of the secondary weighting of the difference between investor expectations and market expectations described by the Black Litterman model. The two components of expected return, possible returns weighted by probabilities of success, have some interesting implications regarding the type of investments that each strategy will prefer.

Impact on Funded Companies

In the case of Highland, a diversified portfolio results in many companies receiving funding with each project receiving little to no operational guidance. Given the extremely high exits necessary to compensate for a large number of losers, the type of ideas that get funding are those that have a low probability of success, a high growth rate, and a high expected return. Knowing that there is excess capital when measured against the limited amount of quality equity for the reasons discussed above, only a low probability of success will guarantee a sufficient equity stake to compensate for the large number of losers in the diversified portfolio. A high probability of success would not allow for a large enough equity stake and would not provide sufficient returns for the diversified investor.

Increasing an investor’s focus on an industry allows for investing in ideas that may have a smaller market potential but greater probability of success. This type of investing serves several important purposes. First, it is obviously an efficient allocation of capital that produces economic growth. Second, it provides a form of financing that is less expensive than the most speculative angel investing but more expensive than traditional debt financing. Usury laws prohibit charging an appropriate interest rate for the amount of risk that investors are exposed to even when investing in a company with a greater probability of success. This is because many firms that fit this description may not have sufficient physical assets to post as collateral. Firms with a focused strategy ensure that companies that may not change the world but may create substantial economic value receive funding.

Recent data from the National Venture Capital Association suggests that investors are on average pursuing a diversified strategy. Despite low and even negative returns the number of deals remains high while the amount invested decreases. This would suggest that venture capital investors are making numerous small investments rather than a small number of large investments. The most recent data also suggest that investors continue to choose the same sectors in which to invest. Cambridge Associates reports that 75% of its venture capital benchmark is composed of healthcare, IT, and software and that these sectors outperform other venture capital investments. This would seem to support the idea that most investors do not deviate from market expectations and under the Black Litterman model, would be best served by pursuing the diversified portfolio strategy.

If most venture firms are investing in similar companies and the returns of the industry are declining, an investor may still be able to obtain above average risk adjusted returns. One method is by choosing a venture capital manager that has sufficient expertise to beat the average venture capital return through a focused strategy. One problem with this alternative is that managers have an incentive to limit the number of investors in order to reduce the risk of missing a capital call. Investing with a focused fund of sufficient quality may not be possible for an individual investor. An alternative is to choose a venture capital manager that has a strong enough reputation and network to ensure that they are able to invest in the best firms in an attractive industry. Since the amount of equity with a high probability of success is limited and there is an excess supply of capital, it is critical that a venture firm that pursues a diversified strategy be able to invest in the best firms. Without this network and reputation, investors should not expect above average risk adjusted returns.

Cambridge Associates Private Equity and Venture Capital Funds Closed out First Half of 2010 with 5th Consecutive Quarter of Positive Returns November 2010

Ghalbouni, Joseph and Rouziès, Dominique The VC Shakeout. Harvard Business Review, Jul/Aug 2010, Vol. 88, Issue 7/8

Zider, Bob How Venture Capital Works. Harvard Business Review, Nov/Dec 1998

Beating the Market Part 2

In Part 1, I discussed some of the structural reasons why it is easy to beat the market that stem from the incompleteness of markets. The investment policy statement limits most market participants to specific assets and factors such as liquidity, bid-ask spreads, and risk management limit the remaining market participants from maintaining constant market efficiency. If we look at the largest market participants, they are typically long only institutional investors with relatively low portfolio churn rates. A good representative portfolio consists of the following five asset classes: U.S. Equities, International Equities, Fixed Income, REITs, and Alternative Investments.

Using monthly data from January 1990 through December 2009, average correlations among asset classes range from .0942 to .7708 with the highest correlation between U.S. equities and alternatives and the lowest correlation between bonds and alternatives. A moving block bootstrap of this return series shows a optimal tactical band size of around 2% assuming a constant band size across all asset classes and maximizing the information ratio.

From January 2007 through December 2009 correlations ranged from .1304 to .9209 with the highest correlation between international and U.S. equities and the lowest correlation again between bonds and alternatives. Contrast that with the period from January 2001 through December 2003 when correlations ranged from -.3830 to .8978 and the return from asset allocation was far greater. No doubt decreasing the time interval would reveal much larger swings in correlations but few institutions have substantial daily liquidity needs relative to the size of the portfolio so large tactical allocation decisions are not needed.

If you made it this far, you are no doubt wondering why you should care about this. The biggest concern is setting tactical asset allocations for policy statements or how much to deviate from your target allocation. The full 20 year period suggests that periods of higher correlations result in an optimal tactical band size of around 2% to maximize the portfolio information ratio while shorter periods of lower correlations could be used to justify taking more risk. This should be considered when setting the investment policy statement and compensation packages for investment managers if the information ratio is a meaningful measure for you. If total return is the most important metric, larger band size always increases the potential return but has a diminishing effect as correlations increase. This means that the biggest risk takers are not going to receive the benefits of asset diversification when they need it most. In order to produce sufficient returns to justify active management expense, asset selection becomes more important as the economies of scale decrease. In other words, the smaller the portfolio, better asset selection and fewer holdings are needed to justify the expense of active management. Small portfolios cannot rely on index funds and good rebalancing discipline so hiring a portfolio manager that does not engage in asset selection is a waste of money.

Disclaimer: There are clearly many problems with this analysis such as the arbitrary time periods, disclosure of initial allocations, and the simplicity of the rebalancing rule. Unfortunately, I cannot write a complete post at this time without straining any working relationships despite the fact that these results are easily replicated, however; since I am not being compensated for my work, I consider it to be my own.

Beating the Market Part 1

In 1975, John Bogle started the first index mutual fund on the theory that active management does not produce consistently superior returns to justify the added expense. Is this argument consistent with the Efficient Market Hypothesis? I will argue that the idea of “passive management” is misleading due to the practical nature of implementation. There exist only varying degrees of active management with different costs, risks, and expected returns. While it is necessary to question what strategies are worth the cost, the question of active or passive management assumes that there is an identifiable difference between the two choices. If you believe that there is a passive strategy, please leave a detailed description so that I can reply with the active management components that it contains.

The primary problem with measuring performance is that you must first define “the market”. However you define the market, it must be investable directly through an index fund, ETF, or individual assets and this is where the problem occurs. Suppose that you track every company listed on every exchange and you decide to hold a proportional number of shares in each to construct a market capitalized weighted average. In order to maintain the proper weightings, you must constantly buy and sell stocks that are often illiquid. Assuming that the trading fairy solves the liquidity problem, there are still practical limits on what to define as a sufficient change in the market that would justify rebalancing. If we assume that all international equities are part of the market, do currency fluctuations trigger a rebalance? If we segment the market by national boundaries, how do we account for multinational companies or companies where the majority of assets and primary operations are located in another country? In order to answer these questions, indices are created and maintained by various organizations such as Standard and Poor, Dow Jones, or MSCI. The rules are never perfect but if the index is successful, we can infer that industry considers it to be good enough. The rule set can be interpreted as a policy portfolio because it defines what assets will be held, under what conditions assets will be exchanged, and the frequency and methodology of rebalancing. The goal of active management is to simply construct a better rule set than the index.

If you are an asset manager that is benchmarked to one of these indices, you typically have several advantages over the index. The first is the frequency with which you can alter the portfolio enabling you to react faster to new information. The second is the portfolio construction methodology. An index rule set must be predictable which means that the rules that govern whether an asset is included must limit discretion and focus on objective measures such as market capitalization or industry. While a manager may be constrained, they are typically allowed more freedom to choose assets that do not conform to the index inclusion criteria. The manager may also choose assets based on criteria that has been proven to produce superior performance. Few indices are rebalanced based on fundamental business performance. Finally, by underweighting assets, the manger can effectively short an asset relative to the benchmark. This allows the manager to outperform the index regardless of market direction.

Given these advantages, the ability to beat an index using an enhanced index strategy is the result of sufficient work combined with prudent risk controls. The difficulty arises when you determine the amount of outperformance necessary to justify the added expense of active management. While scale certainly matters, the overriding factor is the correlations between individual assets in the case of a single asset class portfolio or the correlations between asset classes in a multi-asset class portfolio. Correlations among asset classes are typically lower than correlations between assets in the same asset class, so the value add of active management is greater for asset class selection than individual asset selection within a diversified portfolio. In a concentrated portfolio, each asset represents a greater portion of asset class selection relative to asset selection. Producing superior returns from a concentrated portfolio requires greater skill in individual asset selection because each asset must outperform its asset class in order to beat a multi-asset class benchmark.

In Part 2 I will discuss some practical examples of active management in a multi-asset class framework using data over the past 20 years, how this relates to the EMH, and what it means to investors.