From Me to You
This website is a personal outlet for information and opinions that don't fit into normal work routines. I hope you will find something useful here. I plan to contribute fresh material periodically, so please check back again if interested.
I wrote this draft article several years after the first one on “better risk management”, with a similar message. In a somewhat more polished form, it was published in The Journal of Portfolio Management Spring 2003, Vol. 29, No. 3: pp. 58-65.
Harry Markowitz & the Discretionary Wealth Hypothesis
By
Jarrod Wilcox
DRAFT
Draft Copyright 2000 Jarrod W. Wilcox
January 7, 2003
ABSTRACT
In his 1959 book, Harry Markowitz showed how return mean and variance combined to determine expected long-term growth rate of capital. But the maximization of that growth rate seemed to fit the risk preferences of only a narrow range of aggressive investors with no concern for shortfalls. This paper generalizes that goal to both conservative and aggressive investors by mapping the distribution of returns on total wealth to that of returns on discretionary wealth. It also broadens the definition of risk to include return skew and kurtosis where required, fully encompassing the concept of downside risk. The resulting change in frame of reference extends Markowitz’s criterion to many practical investment decisions involving maximizing long run wealth while controlling the probability of shortfalls along the way.
Harry Markowitz & the Discretionary Wealth Hypothesis
INTRODUCTION
We often wish to better understand the long-run impact of our short-term investment policies. One possible tool is Monte Carlo simulation, the random generation of many alternatives to discover the probability distribution of multi-period outcomes. Not many investors find this easy to implement. There is an unfilled need for practical guidance.
For single periods, we have the mean-variance criterion developed in the 1950’s by Harry Markowitz. He proposed that in each investment period investors should strive for portfolio returns having the greatest difference between their mean and the product of 1) the return’s variance, or expected squared difference from the mean, and 2) a risk aversion coefficient specific to each investor. This is a very useful yardstick, but it is inadequate for constructing policies that will lead to maximum long-term results with acceptable safety against shortfalls along the way.
In his 1959 book, Markowitz showed how return mean and variance combine to affect expected long-term growth rate of capital. But the maximization of expected portfolio growth rate seemed to fit the risk preferences of only a narrow range of aggressive investors. The purpose of the present paper is to show how to better use Markowitz’s ideas for achieving longer-run objectives. To do so, his criterion will be extended with optimal growth and shortfall avoidance concepts. This task has been attempted before with limited success, most notably by Hakansson [1971]; here we take a different approach, the discretionary wealth hypothesis, to overcome the remaining obstacles. By the end of the paper, we will have clarified not only the long-run impact of short-run policies, but also the perceived need to distinguish between variance and “downside variance,” referred to by Markowitz in his later writings as the semivariance.
This is a draft of an article published as “Better Risk Management”, Journal of Portfolio Management, Summer 2000, pp. 53-64. I thought to set the world on fire with better management of investment risk. A few listened then, and the approach has gained some high quality adherents since. There are still many opportunities for better risk management decsions, though! Note not only the working out of optimal return-risk tradeoffs depending on investor financial circumstance, but also the discussion of the impact of dynamic changes in risk exposure based on price changes.
BETTER RISK MANAGEMENT
By
Jarrod W. Wilcox
DRAFT: April 21, 2000
Draft Copyright 2000
Jarrod W. Wilcox
INTRODUCTION
For many years, quantitative investors trying to balance risk and return have been guided by academic finance. Harry Markowitz taught us to think about portfolios rather than individual securities. Most of his work focuses on static, or single-period, assessment of the tradeoff between the mean and variance of an expected portfolio return distribution. His 1950’s innovation was followed in the 1960’s by the Capital Asset Pricing Model (CAPM), articulated most convincingly by William F. Sharpe. CAPM taught us the value of index funds. These achievements richly deserved their respective Nobel prizes. However, what practice has done with their insights has been problematic. Passive investors are still at a loss to decide on proper risk aversion. Active investors are plagued with distortions in incentives and with strategies that look safe in the short run but turn out to be quite risky in the long run.
In recent years, two refinements to risk management have gained ground. First, we have begun to examine the downside tail of return distributions rather than being satisfied with mere statistical variance. This “Value At Risk”, or VAR, technique attempts to address the non-normal return patterns of complicated derivative securities. Second, we realize that the inputs used for Markowitz optimization are not certain. They are drawn from a distribution of possible inferences whose dispersion we can also estimate. This insight suggests ideas for improving the portfolio optimization. We can use more robust Bayes-Stein estimators, for example. Alternatively, we can repeatedly resample from the estimated distribution of possible mean, variance and correlation elements, and then average the results of many separate optimizations (Michaud, 1999).
However, these developments leave unanswered important issues in at least three broad areas. They are:
1. Sustainable investment policies over multiple periods. This involves deciding both optimal risk tolerance and the proper balance among single-period expected return, variance, skewness and kurtosis in constructing the portfolio.
2. Better risk performance policies. Risk performance measures based on ratios of return to variability, both total risk and tracking error, can fail to effectively discriminate good risk management performance. Further, active managers encouraged to manage only return and tracking error are motivated toward higher total risk rather than lower total risk.
3. Capturing the risk impact of dynamic policies. The impact of active price-sensitive investment policies on long-term risk is not captured by a snapshot of the risks in the portfolio. This is true with respect to not only absolute risk but also benchmark tracking error.
My purpose here is to answer each of these issues, in turn, within a single paradigm – maximum expected compound return of discretionary wealth.
This is an excerpt from the draft of an article I wrote in the late 1990′s which was published in The Journal of Portfolio Management, Jarrod W . Wilcox, “Investing at the Edge”, Spring 1998, Vol. 24, No. 3: pp. 9–21. The article described the advantages of investing in emerging markets because they were at that time rather independent of one another, and the advantages of diversification as a means of accelerating risky growth were not well understood. In the excerpt, I use a simpler example involving flipping coins to show that diversification is not just a means of reducing anxiety, but can actually lead to a faster growth rate of your funds.
A COIN FLIPPING ECONOMY
From elementary statistics, we know that the expected value of a product of two random, independent variables equals the product of their expected values. Then the ratio of expected terminal value to initial value of a multi-period, independently distributed, investment process is simply the product of the expected returns, plus one, of each step. Since diversification among investments of equal expected returns can not change the expected return of the portfolio for single periods, it also can not, therefore, change the mean terminal value after multiple periods.
However, mathematically, expected compound return is not generally equal to the “return” calculated from the expected terminal value.
Because of the multiplicative nature of successive returns, the distribution of possible multi-period outcomes will include some very high payoffs with very small probabilities. Under edge investment conditions, the median terminal value will be far below the mean terminal value. As we noted in reviewing Hakansson’s capital growth work, over many periods, the median terminal value is determined by mean compound return.
For most real-world investors, but especially professional investors, improving the odds of beating median returns will be an important consideration even if it does not result in improved mean terminal value or in the average return calculated from it.
We will use a coin-flipping example to see how dramatic the difference can be between these two concepts. Suppose you flip a fair coin once a year. If the first outcome is heads, your capital, which is initialized at 1, doubles. If tails, your capital is halved. The game continues for three years. The top half of Figure 1 shows the mean terminal value T after one, two and three periods.
From time to time, I’m asked for advice on how to get started in investing, or how to respond to a bad investing experience. Putting aside mistaken ideas about investing is a very good first step. You can get 80% of the results for 20% of the effort if you keep it simple.
ADVICE FOR NEW OR UNHAPPY INVESTORS
These suggestions do not replace in-depth self-education or objective, knowledgeable professional advice, but they should prove helpful as a good place to start.
| Common Mistakes | Things You Should Know | Pretty Good Answers | |
| 1. | Mistake price inflation for real investment returns. | Real returns are provided by economic growth. Price changes and taxes just affect who owns it. | Remember to subtract inflation and taxes from your returns. Think about whether the average investor can earn more than economic growth. |
| 2. | Think that it is easy to earn above-average returns. | If you want more, someone just as intelligent as you must give up the difference. | Invest in stock index funds or ETF’s. Add enough bonds and cash to fit your risk tolerance . |
| 3. | Buy stocks of only well-managed growth companies. | The stock is not the company. You need more diversification. | Buy broadly diversified stock index funds or ETF’s, or hold many different kinds of stocks. |
| 4. | Pay high fees for active management based on past performance. | Competition converts predictable economic events into nearly unpredictable stock price movements. | Allocate assets to stocks assuming you cannot time markets or pick managers. |
| 5. | Make decisions on isolated individual securities without thinking about diversification. Hold more than 10% of your portfolio in the stock of your employer. | The relationships among returns across different elements of your portfolio determine much of what you will experience. | Diversify holdings between stocks and bonds, and within stocks, among various industries, across big and small, growth and value, US and international. |
| 6. | Think fees, trading costs, and taxes are unimportant. | An extra 1% in fees, trading costs or taxes can dramatically affect compounding of wealth over a long period. | Keep turnover low and keep fees low. |
| 7. | Avoid the stock market entirely. | People will pay you to bear risk that is hard to diversify or hedge. Otherwise, your long-term real return is likely to be less than economic growth. | Keep a risk-appropriate fraction of your wealth invested in a broadly diversified stock portfolio. |
| 8. | React with emotion when the stock market rises or falls a lot. | Expected return for the market has only a small relationship with past performance. | Make modest adjustments in stock-bond proportions as your financial circumstance, not the apparent return of the market, changes. |
| 9. | Spend lots of time reading the financial press, financial TV, and Internet news sites. | Risk, tax and fee knowledge retains its value even if widely shared. Ideas for extra return do not. | Forget picking stocks or timing the market. |
| 10. | Rely on advisors who can do well only by getting you to churn your portfolio. Pay high fees for unproductive management. | Most financial service companies are structured in ways that produce conflicts of interest. | Consider fee-only financial planners, brokers who want lifetime relationships, or money managers with low costs who emphasize risk management and reduction of any tax impact. |
Long-Term, Non-Linear Investing
(Unpublished, unfinished short essay, by Jarrod Wilcox, written in 1996 for private use. Fifteen years later, it is clear that though some of the bets would not have worked, the overall batting average is surprisingly good. Today’s focus would of course be different. But the overall approach would be similar in any context.)
Active investors try to earn superior returns by investing differently from other market participants through one of several approaches. We can look at the same data and react to them the same way but more quickly, as when we immediately buy because of revisions in IBES consensus earnings estimates. Alternatively, we can try to make different decisions by reacting to the same data using the same concepts, but in a contrarian direction. This is what we do when we sell on good news.
However, there is yet a third and more radical alternative. We can try to avoid the decision inputs and concepts used by most market participants. This is easier said than done, because as social beings we get almost all of our ideas from others. However, we can harness three systematic approaches to step outside the market’s dominant conceptual framework.
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This article was based on work with my friend Jeffrey Horvitz, who taught me that the details are incredibly important in achieving better after-tax returns.
Better After-Tax Returns
Jarrod Wilcox, October 6, 2003
The best time of the year for thinking about taxes is here, and many investors still have opportunities in the unrealized losses they have left over from the bursting of the recent stock market bubble. Some of us don’t seem to enjoy tax time and have a hard time integrating it with our regular investment activities. Yet the US government is generous in its rewards to investors who pay attention to its encouragement of long-term investing through tax law.
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