Over the past several decades, academics have identified numerous variables that seem to predict future expected returns. This has led to a proliferation of so-called “factors” identified in the literature, and created what John Cochrane has labeled the “factor zoo.”

Now we we have a zoo of new factors.

–The Journal of Finance 2010 Presidential Address

Enter the zoo at your own risk — the animals all look pretty, but they might end up killing you!

In this post we discuss how to conduct basic factor analysis. Previously, we wrote this post on “anomaly chasing” and how many anomalies suffer from data mining.

While some academics like to chase new anomalies, others have focused on why certain limits to arbitrage may prevent these market inefficiencies from being arbitraged away by traders. Such limits to arbitrage can take many forms.

Questioning Assumptions

For example, in studying the anomalies, researchers often make assumptions that turn out to be unrealistic in the real world. For example, some research has focused on how price impact and transaction costs can reduce returns to factor-based strategies:

These studies suggest that strategies identified in academia don’t always translate directly into profitable trading strategies, because sometimes the assumptions used — such as costless trading — don’t hold up in the real world (although some research suggests trading costs can’t explain everything). Of course, there are many other assumptions worth examining.

In a new paper, “The costs and benefits of long-short investing: A perspective on the market efficiency literature,” by Beaver, NcNichols and Price (note: Professor Price is a member of our advisory team), the authors turn a critical eye on a number of additional assumptions that academics use when they study anomalies and trading costs.

The paper examines:

  • The costs and benefits of long/short investing, as compared with long-only investing
  • How combinations of/diversifying across various long/short strategies, and long-only strategies affects performance
  • Strategy profitability after assessing an opportunity cost of capital

Data and Strategies

In order to conduct their analysis, the authors use a sample of firms in Compustat listed on the NYSE, AMEX, and Nasdaq for the period 1992-2011, and choose five anomalies:

  • Book-to-market ratio (BM)
  • Operating cash flow, scaled by assets (CF)
  • Accruals, scaled by assets (AC)
  • Unexpected earnings, which is change in earnings of quarter t and quarter t-4 deflated by quarter t-4 (UE)
  • Change in net operating assets, scaled by assets (?NOA)

Portfolios are formed quarterly, and held for twelve months. In order to mimic the approach taken by academics, the authors create two portfolios of stocks: 1) a long portfolio and 2) a short portfolio.

While the long book is straightforward, the creation of a short in the real world is significantly more complex than you might think from reading an academic paper.

Long-Short Strategies (and Especially Short Books) Are Murder in the Real World

Running a short book poses numerous challenges in the real world, and the authors dissect these difficulties and contrast them with the traditional academic treatment.

For instance, to create short positions, one needs to locate and borrow shares; this in itself is problematic, since sometimes shares are simply not available to borrow. Another difficulty is that short positions cannot be held indefinitely; sometimes shorts get recalled by the lender (this happened to me in 2008!). Although these issues are reduced in large, liquid firms, they can be magnified for smaller, illiquid firms.

Another big assumption from the academic studies is a “zero-cost” trading assumption, which is really several assumptions rolled into one. Studies assume that when shares are sold short, the proceeds are available to fund the long portfolio. In the real world it doesn’t work like this. In the real world, when shares are sold short, investors need to post collateral (usually equal to ~50% of the value of the short position), although they earn an interest rebate from the lender. The authors find rebates are very important for assessing strategies. Yet rebates are affected by the stocks selected. For instance, shares that are easy to locate for borrowing might have a low rebate fee, while shares that are harder to locate might have a higher rebate fee. Banks also charge fees for taking a short position.

Bid-ask spreads are also an important issue that is often glossed over or ignored in academic papers. Any rebalancing requires selling at the bid price and buying at the ask price, and bid/ask spreads can be wide, depending on market conditions or size/liquidity of stocks traded.

When it Comes to Alpha, Size Matters

Many of the considerations above are affected by the size/liqudity of the stocks traded. Clearly, the creation and maintenance of a short book (and also a long book), becomes more challenging to the extent a portfolio contains small stocks. As discussed above, liquidity considerations include the ability to borrow securities, short recalls, rebate fees, and bid-ask spreads. As it turns out, the anomalies in the literature often assume an easy, more or less frictionless ability to invest in small stocks. And academics assume a lot of small stocks are investable.

The chart below sets forth the percentage of stocks in anomaly deciles with low stock prices:

Long-Short Strategies
The results are hypothetical results and are NOT an indicator of future results and do NOT represent returns that any investor actually attained. Indexes are unmanaged, do not reflect management or trading fees, and one cannot invest directly in an index. Additional information regarding the construction of these results is available upon request.
Long-Short Strategies

Note that, when considering all stocks, significant portions of the anomalies are assumed to be invested in small stocks. The percentage of stocks <$5 in the extreme portfolios (deciles 1 or 10) ranges from 14% to 65%. This has significant implications for anyone interested in pursuing any of these strategies. Within a larger stock universe, this effect is not as pronounced.

Cost of Capital

Because long/short strategies require that funds be provided, there is an opportunity cost of capital associated with running them. What is this cost of capital? How should you think about it?

Under CAPM, if a hedge strategy has a beta of zero, this suggests the risk-free rate is appropriate. Yet clearly in the real world, investors must consider non-market risk. This implies the cost of capital for hedge strategies is something higher than the risk-free rate.

Many have suggested that a higher cost of capital is appropriate in the real world because hedge fund returns are correlated with market returns, and are not offering real “alternative” exposures. For instance, Cliff Asness points out here that “hedge funds are generally net long about 40% of the stock market.”

Perhaps the market return is a useful benchmark. If the expected return for a hedged strategy is higher or lower than for long-only equities, then this may have implications for the cost of capital (and survivability) of a hedge fund.

The cost of the long position may also be relevant (the cost of the long position is calculated by subtracting short position returns from long-only alpha).

The authors use these

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