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Return Series Behavior & Risk Tolerance

As you know, volatility in many financial markets has increased over the past year. It seems that the ‘volatility’ of TV, radio, and print-media news has also increased. This letter is an update on our investment views.

About six months ago, as U.S. equity prices continued to decline, we sent you a letter indicating that the fallout from the residential housing mortgage crisis was spreading to other financial markets. The mechanism for transmitting this contagion was the banking system. In a nutshell, as the banks’ aggressive home loan portfolios came under pressure, regulators demanded that banks shore up their balance sheets. Many money-center banks had large loans out to hedge funds. Sad to say, some hedge funds chose to maintain double-digit rates of return by levering their investment positions. Financial leverage can turn mediocre investment results into attractive returns—but only at the cost of increasing investment risk. As the banks called the hedge fund loans, the funds had to unwind their investment positions by selling securities. Some hedge funds were leveraged 30 to 1, and had to sell large amounts of securities to raise a sufficient amount of cash to repay bank loans. Some hedge funds went bankrupt [proving, yet again, that there is no riskless investment that can forever generate double-digit returns]. Equity prices continue to decline as leverage is wrung out of the system. Given a long-term view, we suggested that this was a good thing despite the obvious fact that nobody enjoys periods of price decline.

At SCLC we note that clients who are at the threshold of retirement; or, who are currently drawing on their portfolio for retirement income, feel especially vulnerable. Lacking labor income, financial assets often represent the primary source of wealth earmarked to sustain an adequate standard of retirement living. The financial news during 2008 seems particularly disconcerting. At various times, economists forecasted a period of price deflation (led by declines in housing prices) or a period of price inflation (led by advances in energy prices). Some prognosticators indicated that the U.S. economy would lose jobs (especially in manufacturing) while others predicted job creation (“green technology” job explosion). Depending on which night you listened to the 6 o’clock news, the U.S. either was bankrupt (with a huge trade deficit vis-à-vis China) or was increasing exports substantially (as an adjustment to international purchasing power parity). Financial markets are weak / “fundamentals” are solid; we are on the verge of a great depression / we are experiencing a normal business cycle; price declines are to be expected and are part of normal economic conditions / it’s different this time because we’ve never had a terrorist threat, a housing crash and energy shocks at the same time.

As the financial news and opinion business operates at full volume, SCLC notes that discussions tend to devolve into statements reflecting merely the intensity of subjective beliefs. A subjective belief cannot be verified by mathematics (the classical laws of probability) or by empirical experiment (repetition over many trials). Despite the inability to verify the true probability structure of subjectively held beliefs (“I am 100% convinced that there is a UFO base on the dark side of the moon,” “I am 100% convinced that the Red Sox are a better team than the Yankees,” “I am 100% convinced that the U.S. economy is about to collapse into oblivion”), those who hold such beliefs are nevertheless deeply influenced by them. Rather than cynically dismissing intensely held opinions, one must, in general, recognize that there is a probability greater than zero that such opinions may, in fact, be correct! At this point, let us be perfectly clear—SCLC does not know the future of the global economy.

However, rather than retreat further into subjectivism, whether it tends towards optimism or despair, it is useful to take stock of the basic characteristics of a portfolio’s wealth generating process—how does a diversified portfolio behave; and, just as importantly, can I tolerate such behavior? To frame this discussion, I include a one-page graph of four investment behaviors. The behaviors are very different; and, as you can see, range from the unruly behavior of the ‘white noise’ return series (think of a two-year old or a rebellious teenager), to the calm and comforting behavior of the ‘deterministic’ return series.

Let’s take a closer look (psychoanalyze?) at the behavior of the time series of returns (to open the graphics, please scroll to the bottom where a link is located). Each graph has a y-axis that starts the return series at a zero value. If the series moves upwards, it represents positive returns; if downwards, it represents negative returns. The x-axis implicitly represents time. We motivate our discussion by trying to arrive at a conclusion about the time series that is least likely to drive us nuts over the long run.

The first series [‘white noise’] moves constantly under and over the zero line. Given the intensity of subjectively held beliefs and the contradictory nature of current economic predictions, it seems as if investing in financial assets is a white-noise process. The Dow is up 200 Monday and down 300 Tuesday. This conclusion is probably not true, however, because a white-noise process has a long-term expected return of zero. Unless you want to argue that anyone who invests in financial assets is crazy (we do not rule out this possibility!), investors must have some expectation of gain when placing money at risk. A white-noise process does not offer such an expectation; and, therefore, we rule it out as a valid description of expected behavior for a globally diversified portfolio.

The second series [‘deterministic’] manifests behavior very different than that of a white-noise process. A deterministic series provides investors with a positive and risk-free rate of return. This is the return provided by insured CDs and Treasuries. The return behavior is not only positive but it is guaranteed. If the guaranteed return is sufficient to discharge all future income, gifting, and bequest objectives, this is the return series for you. Unfortunately, such is generally the case only for individuals with initial wealth sufficient to overcome the drags of taxation and inflation (loss of purchasing power over time). Usually, the process of retirement income planning requires tradeoffs between the probability of financial success given only a finite amount of capital, and the risks required to generate returns greater than those available from risk-free investments. Furthermore, the guarantees of risk-free investments and the absence of volatility make the deterministic time series a poor model for the larger market return-generating process.

The third series [‘random walk’] exhibits some interesting behaviors. It crosses the zero line on the y-axis; but, unlike the white-noise series, does so much less frequently. In the meantime, the time series of returns can wander far above (profit) or far below (loss) the zero mark. However, as the time axis extends towards infinity, the random walk process offers an expected return of zero. You may be profitable for a long period; or, you may be in a financial hole for a long period. Eventually, however, you expect to end up where you started. Thus, unlike the helter-skelter white-noise process, the random walk process exhibits long-term mean reversionary behavior. If you had a highly refined ability to time financial markets (which, by definition, cannot exist in a market that is random), then this is the return series for you. For all others, this market model will seem implausible because it lacks positive long term expected return.

Finally, take a look at the fourth time series of returns [‘drift & diffusion’]. If we decompose the behavior of this series, it appears to exhibit a long-term trend (“drift”) coupled with a purely random element (“diffusion”). There is certainly risk in this return series and the downside periods can be severe. However, the slope of long-term growth is positive. It would not be too much of an exaggeration to advance the proposition that the drift and diffusion process is a combination of the deterministic and the random walk processes. This is not entirely correct. If you could get the CD rate of return without risk, why would you ever want to combine the deterministic return series with a zero expected return random walk series? In order to induce investors to put their money at risk, the financial markets must offer something more than a CD return over the long run—they must offer the CD rate of return plus a risk premium. Such a premium is time varying (both in its realization and in its expectation), but it must be there or no investor would ever risk their capital. Thus, for a drift & diffusion process, the slope of long-term growth is steeper than that obtainable in a purely deterministic time series process. Without periodic downside volatility, however, this would not be the case.

As a final observation, we note that the expected risk premium available to investors tends to increase the lower a market’s price level and decrease the higher the price level. Such a discussion, however, requires an equilibrium pricing theory which quickly gets us into some advanced econometrics. Let’s just simply say that, if you are sufficiently diversified, it is better to buy low and sell high. Thus, in a drift & diffusion process, portfolio risk is controlled by combining equity investments with deterministic investments (government guaranteed bonds), diversification across various capital markets, and, in some respects, by implementing rebalancing (buy low / sell high) strategies. In the absence of cash flows, the greater the volatility you choose to accept, the steeper the slope of expected growth, all else equal. More importantly, the drift & diffusion process seems to be a more realistic model for financial markets.

Are you comfortable with this type of wealth generating process? Have you calibrated the risk of your specific portfolio to your personal risk tolerance? What do you do if your aversion to risk prevents achieving the long-term return required to discharge your financial objectives? These are difficult questions and should not be decided by seat-of-the-pants reactions to current events. Nevertheless, it is crucial that all investors answer them satisfactorily. If you need all of your money over the short term, it is obvious that the deterministic process is the only rational alternative. If you have a longer term time horizon (you need some money short term, some medium term and some long term) then it may be appropriate for you to embrace a drift & diffusion process as long as it has a sufficiently well-thought-out mechanism for risk control. However, if you elect to participate in this type of wealth generating process, you must recognize the inevitability and necessity for periods of substantial price declines.

We have found that it is more productive to match the return generating process to investor needs and preferences than it is to make tactical investment recommendations based on short-term market prognostications. Investors want to know what we intend to do when markets decline. The answer is that we intend to provide information that will allow you (not us) to make intelligent decisions. The forthcoming Investment Quarterly discusses this issue further by providing additional insights based primarily on an empirical examination of past recessionary periods. It will employ a “frequentist” probability approach that differs considerably from the econometric approach of this letter. The point is that there is not a unique or universally correct approach; and, if anyone claims that they have found one, they are either dangerous or nuts (or both).

If you avoid market risk you also avoid market return; and, may inadvertently create a portfolio wholly incapable of meeting your required return objectives. Again, our job is to facilitate your preferences once we have established to our satisfaction that you have undertaken an informed decision making process.

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