Capital Asset Pricing Model, Part Three – Other Assumptions

In Parts One and Two of our examination of the Capital Asset Pricing Model (CAPM), we evaluated two major assumptions:

1)     Market returns are properly modeled by a normal distribution

2)     Beta (systematic risk) is the sole source of priced risk for an asset or portfolio of asset

As you recall, we found several weaknesses in both assumptions as they may apply to hedge funds. This time, we’ll examine the remaining assumptions underlying CAPM, and see if each is reasonable when applied to hedge fund trading.

CAPM assumes:

  • Frictionless trading – there are no expenses associated with trading. Obviously, this assumes away such costs as commissions and taxes.  The higher the trading volume, the more unreasonable this assumption becomes.  For some high-volume, low-unit-profit strategies, frictional costs can make the difference between a profit and a loss, so traders are constantly looking for the best deal available. Hedge fund managers can use leverage to ramp up returns (albeit at higher risk) so as to overwhelm an otherwise decisive cost prohibition. Then there are the meta-costs inherent to hedge fund investing, including management fees, profit fees, exit penalties, and liquidity restrictions.
  • Traders are price-takers – no one purchase (sale) is of sufficient size to move the ask (bid) price of the security. This in fact only makes sense for highly liquid securities, such as shares in the S&P 500.  For less liquid securities, it is not uncommon for a sizable single trade to move prices. Because of leverage, hedge funds may be able to buy or sell huge blocks of shares that do indeed move the current equilibrium price.
  • Unrestricted short selling – CAPM assumes there are no limits on short selling.   Until 2007, covered shares in the U. S. could only be shorted on an uptick (a trade at a higher price). The uptick rule was eliminated in 2007, but a modified version was reinstated in 2010. In this new version, circuit-breakers kick in if the stock’s price declines by 10% or more from the prior day’s closing price. At that threshold, short selling in the security is permitted only if its price is above the current national best bid; the safety measure remains in effect for the remainder of the day and the entire following day. Uncovered, or naked, shorting is not permitted in the U. S. – you must own or control the shares you short.  The prohibition on naked shorting is not as controversial as that on covered shares. Many academics argue that restrictions on covered shorting do little to limit downside moves and in any event are easily circumvented, especially by hedge funds, which can “manufacture” an uptick with little effort. The prohibition against naked shorting is a clear violation of CAPM’s assumption.
  • Homogenous behavior – all investors have equal access to all material information and evaluate risk and return in the same manner (homogenous expectations). Furthermore, it is assumed that all investors use the same, unchanging time horizons, and that it is not possible to change portfolios within the estimated time horizon.  Hedge fund positions, however, typically have a very short holding period. In addition, edge fund behavior departs from the homogenous in the use of leverage, derivatives, and shorting.
  • Liquidity premiums – CAPM makes no provision for a risk premium arising from the relative illiquidity of small-capitalization stocks, despite much research to the contrary. Hedge fund strategies that buy small-cap and simultaneously short large-cap shares seek to profit from liquidity risk.
  • Risk-adverse investors – investors must be paid, in terms of a higher expected return, to take on additional risk. However, many hedge fund managers are risk junkies, using leverage, derivatives, and shorting to pile on the risk (and hoped-for returns). Such behavior clearly violates an underlying CAPM assumption, resulting in a distorted perception of beta.
  • Continuously divisible shares – CAPM assumes you can trade fractional shares, which is untrue but probably not very material.  Possibly more material are the higher costs associated with odd-lot trading (lots not in 100-share multiples), but this usually affects individual investors more than it affects hedge funds.  However, certain hedge fund strategies, such as delta hedging, may require the trading of odd lots of securities.
  • Market portfolio – it is assumed the market portfolio contains all assets from all markets. Each asset is weighted by its relative contribution to the market portfolio’s total value.  Obviously flawed, this is even more detached from hedge fund strategies which specialize on a tiny segment of the market portfolio. This begs the question: to what is beta correlated?
  • Single portfolio optimization – investors only optimize the totality of their holdings. Behavioral theorists disagree, pointing out that many investors mentally compartmentalize their holdings by differing objectives.  We’ll have more to say about this in a future article.

The bottom line is that CAPM is a rough-and-ready simplification of trading markets, and is certainly not a good fit to hedge fund trader behavior.  The most important inadequacy of CAPM is that it fails to recognize that certain investors want exposure to only certain risks rather than general exposure to market risk.  This results in imperfect risk sharing, in which systematic risk premia for specific risks exist and can be captured. These are, in effect, risk-specific betas that can be isolated through hedging techniques. These risks cannot be fully diversified away by all agents in the marketplace, and so can persist for a long enough time to be profitable for the suitably positioned trader.

Now that we’ve looked at CAPM’s assumption, we’ll explore the model’s equations next time.

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Copyright 2011 Eric Bank, Freelance Writer

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