These essays discuss discrepancies in modern portfolio theory (MPT) that can be resolved by technical analysis.

In portfolio theory, asset classes’ correlations with other asset classes, their standard deviation of returns, and their expected returns are the only inputs needed to create a “global market portfolio,” which can be defined as the an optimal portfolio, whose cumulative weightings of all asset classes maximize the expected return per unit of risk. Of the three variables, two are the result of similar statistical operations. Holding an asset class in isolation, it is comprised of a standard deviation and an expected return. As such, these two variables are a corner stone of MPT. The two essays that follow present issues surrounding these variables.

**Essay I: The New Liquidity Premium**

The standard deviation of returns is one definition of risk for an asset class. Assuming this is a valid definition, there still remains an inadequacy in its *measurement.*

Rationally, and academically, one can state that the probability of an established company’s price going to zero is very low; moreover, a diversified portfolio not only renders that possibility inconsequential but is itself incapable—barring the end of civilization— of losing its entire value. The unincorporated issue is that it is not only possible, but to a degree probable, that portfolios, diversified or not, can lose significant value. Why? Trading. Trading, in any of its forms: portfolio rebalancing, strategic management, tactical management, active management, sector rotation, arbitrage, hedging, high frequency trading, value investing, speculation. Every single portfolio, even those in the realm of theory, subjects itself to changes, trades. Investing can be passive, but it cannot be immutable.

Trades result in cumulative transaction costs, cumulative trading losses, and possibly, cumulative permanent capital impairment. Examples of permanent capital impairment are leveraged investors (Bears Sterns) or short term capital losses due to speculation. The aggregate permanent capital impairment, based on all portfolios, is probably significantly high. Trading can create excess gains, but a safe assumption is that on a net basis, wealth is destroyed. Effectively, the inadequacy of the standard deviation’s measure is that since it does not account for the effects of trading on returns, it is drastically deflated. Inevitable trading losses and gains increase the standard deviation of returns. Instead of using an index, such as the Russell 3000, as a benchmark, a more accurate one would be an index of portfolios tracking the Russell 3000.

On the other hand, highly illiquid asset classes, such as private equity, real estate, and certain hedge funds, should be given an illiquidity discount! These require a holding period of several years. For these investments, because transactions and the dynamics of ever changing supply and demand are mitigated, the expected returns are usually more purely tied to their economic reality. The standard deviations do not need to be adjusted, but the expected return would decrease due to the illiquidity discount; in other words, in this paradigm, rational investors would be being willing to pay more, or accept lower returns, for illiquid investments.

In summary, the ease with which a portfolio or its components can be traded, its liquidity risk or, liquidity premium, affects both its volatility and expected returns. (Traditionally, liquidity is viewed as mitigating risk because it results in lower bid-ask spreads and the ability to trade in size.) The expected returns are affected in two ways: one is by an expected loss (or gain) in value due to trading, and the other is due to an increase in the discount rate due to the liquidity premium as defined in this essay. In the context of portfolio theory, the standard deviation of liquid asset classes should increase. The net effect of liquidity on expected returns is less clear because it is comprised of both a liquidity premium (resulting in higher required rates of return) and expected net trading losses. Altering these asset classes’ variables will result in different weightings for the global market portfolio.

Now that the effects of trading on standard deviations and returns have been established, the question remains: how can the effects be measured or predicted? The most significant impact of trading on these variables is likely to be from capital losses. Fortunately, potential capital losses would be at their highest and at their most easily detectable simultaneously: during sentiment extremes. At such extremes, the “majority” is depicted as being largely invested or not-invested in an asset class whose price is about to undergo a profound trend reversal. The potential capital losses resulting in the trend change would be compounded for those who bought at overbought levels or sold at oversold levels.

One could observe such behavior among individual and institutional investors, who have discretion regarding in what asset classes their funds are invested. The following weekly chart (courtesy of stockcharts.com) depicts the ratio of an Aggregate Bond Index to the Russell 3000 Index, plotted against the 10 week moving average on the CBOE Equity Put-Call Ratio, a well established sentiment indicator.

Note that the relative strength line has a high correlation with the put-call ratio, indicating that at extremes in sentiment, the outperforming asset class may begin underperforming.

As you can see, the technical tools of relative strength and sentiment analysis can help predict potential capital losses resulting from a trend reversal of a favored asset class. I propose a “Permanent Capital Impairment Index” be devised, based on such studies, which can be used to adjust expected returns and standard deviations.

**Essay II: The Equity Risk Premium**

When determining the value of a company using fundamental analysis, the inputs required are expected cash flows, expected growth, and a discount rate, which can be broken down into a T-bill’s yield plus and an equity risk premium (ERP). The discount rate, all else equal, has an enormous effect on valuation. Of the five inputs stated above, all are objectively measurable, except for the equity risk premium.

The one method for defining and forecasting an asset class’ risk premium is using modern portfolio theory itself. For example, the ERP is neatly expressed in a formula: Equity risk premium equals the global portfolio’s risk premium divided by its standard deviation, multiplied by the correlation between equity and the global portfolio returns, again multiplied by the standard deviation of equity returns. It’s a mouthful, but the equation itself is not important. What is important, vital even, is that this concept contains

a subtle, circular logic:

*The risk premium of an asset class comprises that asset’s **expected return. The risk premium of an asset class is **derived from a global market risk premium, as stated in the **equation above. The global market risk premium is derived **from asset classes’ expected returns (and standard **deviations).*

This circular logic is not obvious because of the intricacies and various facets of modern portfolio theory. Regardless, the equity risk premium remains in a nebulous state.

If you dig deep enough, you discover that there is no consensus on how to determine this abstract ERP. Except for the method discussed above, at best, one can define all the other variables and solve for an implied ERP with simple algebra. Evidence for the difficulty this concept presents is a 95 page paper titled, Equity Risk Premiums (ERP): Determinants, Estimation, and Implications, written by Aswath Damodaran, professor of finance at Stern School of Business. In it, he states, “determinants of equity risk premiums [include] macroeconomic volatility, investor risk aversion and behavioral components” (p. 86). Although the author manages to exclude technical terms in his explanation, no doubt, investor risk aversion and behavior have equivalent principles in the technical realm.

The frequency and rate at which market prices fluctuate on a daily, weekly, and monthly basis, cannot be accounted for as consensus adjustments to cash flow or growth expectations; these long term variables simply don’t move that quickly or greatly, and daily snippets of information are not material enough. (Even on a long term basis, changes in PEs have accounted more for stock market fluctuations than changes in earnings.) The fundamental analyst must resort to a changing ERP. But what is more likely, that a sharp increase in volatility is due to the equity risk premium undergoing nuclear fission, or because of panic selling? Panic selling is irrefutably observable and common sense, yet only acknowledged by technical analysis. If the ERP were more clearly definable, it could be more accurately estimated. If that were the case, the range of possible fair values of a stock, or stocks in general, would narrow and volatility would decrease. However, prices do fluctuate drastically over all time frames, and those fluctuations are predicted using technical analysis, regardless of whether it is a viable theory. (The argument that PE ratios are technical in nature has been posed before; it is simply a loose version of the same argument that this essay has applied to the ERP. More accurately stated, PE ratios are not technical, rather, an element of the PE ratio, the ERP, is technical.)

Ironically, a yearly plot of the implied ERP spanning fifty years, below, presents a clear technical picture: acceleration due to a “trading range” break out; a very gratifying double top in 1979—shortly before the 80s boom—and 2008, from which prices more than doubled. The dot-com boom had an unprecedentedly low ERP of 2%, meaning that investors only required a yearly return of 2% over treasuries to take on the risk of owning equities.

*From Equity Risk Premiums (ERP): Determinants, Estimation, and **Implications, page 64.* The technical drawings are my own.

Just as with the CBEO Volatility Index, charting the implied ERP would benefit the financial community. A weekly basis is probably the most granular the data should be before it obscures into noise.

To summarize, the equity risk premium component of expected returns, a crucial element of MPT, cannot satisfactorily and comprehensively be defined by its own theory or by fundamental analysis. Technical analysis thereby stands as either a theoretical substitute or amended to the theory.

**The Common Conclusion**

Some of the assumptions of modern portfolio theory are so drastic that they can’t even be challenged. They rely fully on the inherent protection granted to assumptions. To list a few, to which I have added exclamation marks:

- All asset classes are infinitely divisible!
- All investors are rational!
- All investors define risk and return the exact same way!!
- All investors share the exact same expectations for what the standard deviations and returns for each asset class will be!!!

The two essays presented here have challenged the basic, seemingly objective variables of modern portfolio theory, revealing subtler deficiencies. The first essay concluded that liquidity should alter the standard deviation and expected returns because of trading effects. These effects can be best predicted by sentiment based technical analysis. The second essay argued that changes in an essential component of expected returns, the equity risk premium, are best explained by the supply and demand dynamics that technical analysis studies.

Modern portfolio theory serves a great purpose, with which no current theory can contend. It standardizes investing. Investors with no interest or desire to invest based on fundamental or technical analysis can do so with a method that can, to a degree, protect their capital. Financial institutions can easily perform this service, and nearly anyone can learn and understand how to apply MPT to client portfolios. Without such standardization, investing would be chaotic, and much more unnecessary wealth destruction would occur. The value of the ideas presented in this essay is that they can be applied to improve portfolio theory through better estimates of standard deviations and expected returns. Thereby, modern portfolio theory becomes a platform that can integrate technical and fundamental analysis.