Modern Portfolio Theory – Part Three

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Our quest continues to find out whether hedge fund alpha really exists or is just hype. Recall from last time our documentation of the Capital Market Line (CML).  The CML represents a portfolio containing some mixture of the Market Portfolio (MP) and the risk-free rate. It is a special version of the Capital Asset Line, ranging from the risk-free rate tangentially to the Efficient Frontier at the Market Portfolio, and then extending upwards beyond the tangent point.  Modern Portfolio Theory (MPT) posits that any point on the CML has superior risk/return attributes over any point on the Efficient Frontier.  Let’s ponder that for a second – just adding some T-Bills to, say, S&P 500 baskets (our proxy for the Market Portfolio) will improve the risk/return characteristics of your portfolio.

Capital Market Line

If your entire portfolio consisted only of the cash-purchased Market Portfolio (i.e. the tangent point on the Efficient Frontier), your leverage ratio would be 1 – you are unleveraged. The points on the CML below the Market Portfolio represent deleveraging: adding cash to your portfolio.  You are lowering risk and expected return when you deleverage. If you borrowed and sold TBills, and used the proceeds to buy additional Market Portfolio, your new portfolio would be leveraged, and would be a point on the CML above the tangent. Leveraging increases your risk and expected return. If you disregard the effects of borrowing (or margin) costs, then all points on the CML share the maximum Sharpe Ratio, a popular formula for expressing risk/return.

In MPT, a portfolio on the CML is as efficient as it gets. Notice that the only risk associated with the CML is market (diversifiable) risk, our old friend beta.  Alpha is completely absent from MPT (it is diversified away), implying that asset selection and timing, over the long run, do not result  in returns superior to buying and holding the Market Portfolio. Which sort of knocks the pins out from under hedge fund managers: what are they offering besides access to higher leverage (that is, higher beta)?

It’s a loaded question, because MPT is subject to numerous criticisms:

  • Hedge funds allow access to markets for which there is no reasonable proxy of a Market Portfolio (for example: risk arbitrage)
  • MPT takes a simplified view of markets, and is a less than perfect model. MPT assumes that the Efficient Market Hypothesis is true (at least in its weak form) and that there are no frictional costs (i.e. commissions, taxes, etc). To the extent that MPT does not coincide with reality, perhaps there are ways to consistently beat the Market Portfolio.
  • MPT assumes that investors are risk-adverse, rational, and well-informed. They want to be paid for undertaking additional risk.  However, many investors are risk-seeking, and are likely to take more aggressive positions even if MPT says those positions are inefficient.
  • MPT assumes that asset returns are normally distributed random variables and their correlations are fixed forever over time. However, in real life, improbable returns occur more frequently than predicted (the so-called “fat tails” problem).
  • MPT relies on past performance to help predict future performance, in a probabilistic way. There is thus no structural explanation for results, which makes predictions less useful in the real-life chaos that is the market.
  • Other unrealistic assumptions include divisibility of shares into fractions, unlimited credit to borrow at the risk-free rate, investors do not move security prices (they are “price-takers”), all information is available to all investors at the same time, and investors perceive all information in an unbiased way.

Bottom line: due to its imperfections, MPT is not the death of alpha (but it’s certainly no friend either).

How would one measure the effect of adding a risky asset to the Market Portfolio? The Security Characteristic Line is a graph that plots expected return of the MP versus that of the additional asset, and therefore indicates the beta of the asset.  Unless the additional asset had a beta of 1, the resulting portfolio would be inefficient in terms of MPT.

Security Characteristic Line

Having devoted three posts to MPT, I note in passing that in a recent blog, E. Derman points out that the ease of looking up a stock’s beta is an “indication of how successfully modern portfolio theory, right or wrong, has influenced what you can buy in the way of information”.

Armed with an understanding of the Market Portfolio, the Capital Market Line, and beta as depicted on the Security Characteristic Line, we are ready to discuss the Capital Asset Pricing Model, which we’ll do in our next installment.

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Copyright 2011 Eric Bank, Freelance Writer

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