From Me to You
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This presentation reintroduces the discretionary wealth approach, why it is needed, and what can be done with it to improve financial planning and investment services.
It is an honor to be asked to speak to the Boston Economic Club. I particularly appreciate an invitation from Dan diBartolomeo. He has been a leader in supporting thoughtful discussion within the Boston financial community for many years.
My title: Financial Service: a Manifesto for Change, is not a typographical error – It refers to Service with a capital S. I believe in the power of financial service to help people. I also believe that we will have to do much more of it to prosper in tomorrow’s changed environment.
What we can do today is discuss a powerful tool for helping us deal proactively with financial service problems and turn them into opportunities. I call it the discretionary wealth approach. To pursue it further, you might start by reading the book I wrote with Frank Fabozzi titled Financial Advice and Investment Decisions: A Manifesto for Change.
I’ll set the stage, introduce discretionary wealth, pause for questions so that we all understand it, and then advocate its applications. The history of Boston suggests that we are in an excellent place to do fresh thinking about old problems.
Why here? John Winthrop, before embarking to establish the Massachusetts Bay colony, said it well: “For we must consider that we shall be as a City upon a Hill, the eyes of all people are upon us.”
Boston went on to instigate the first public schools in America, the American revolution, the prudent man rule for fiduciary duty, and the abolition of slavery. It became famous for its universities, hospitals and financial institutions.
Boston started the open-ended mutual fund industry in the US. Harvard and MIT helped create modern finance. And Boston still punches way above its weight as a financial center.
The eyes of the world are still upon us. If we get it right, others will follow.
We live in interesting times for our financial service industry.
Traditional financial skills have been displaced by low-margin commodity versions, and this trend is continuing.
Unfortunately, our attempts to preserve profitability have too often backfired. Government is responding, if not with pitchforks, with disruptive regulation.
At present, we are enjoying a revival in prosperity. But who here is confident we are not in the midst of the third major bubble in 15 years? And the collapse of each bubble threatens a still heavier regulatory burden.
Finally, growing machine intelligence is the shark swimming below us. If you scoff at robo-advisers now, you may repent later.
As we turn to “wealth management” as a solution our problems, will we prosper? The answer will depend on whether we are at the top of our service game.
We can offer better service through the discretionary wealth approach.
In the 1950’s, a rambunctious former pilot named John Kelly, who had turned to mathematics at Bell Labs, got to thinking about gambling with favorable odds. Kelly’s rule of maximizing the expected logarithmic return at each bet solved a problem Harry Markowitz did not tackle – how much risk to take. The main practical problem with Kelly’s rule is that to achieve best long-term results you might have to go through unendurable drawdowns.
We’re going to fix this, but let’s first understand Kelly’s contribution — using the kind of example he addressed – gambling. Consider flipping a fair coin, but with a very nice payoff structure. If the coin turns up heads, you double your bet, and if tails, you lose only half of your bet. This gives an expected return of 25%. You need to decide on the best policy for how much to bet at each coin flip.
What is most likely to happen? Let’s look at the median results – equal numbers of heads and tails. Since their order is irrelevant in this case, I have charted paths as alternate wins and losses. If you bet everything the median result is to end where you started.
We see in the chart that the best median result comes from betting half of your funds each turn, which results in a portfolio compound growth rate of about 6% a flip — far lower than the 25% one might think possible. I call this 6% the sustainable growth rate.
Can you see why maximizing the portfolio’s expected logarithmic return ln(1+r) maximizes the median result of a long sequence of bets? The floor is open.
This chart shows growth rate as a function of your policy for allocating capital to the bet versus holding cash as a reserve.
What happens if you bet even more than you have – that is, bet on margin?
Consider what happens to return if you get 10 heads in a row. What is the probability of this happening to you as an investor? What fraction of the probability distribution of outcomes of a long sequence of bets will lose money if you bet everything.
Is best median outcome a practical criterion of good strategy over time? Well, mathematically, it minimizes expected time to reach a goal and assures long-term competitive dominance over other policies of the same type if repeated long enough.
Could you use this model if a bet could result in its complete loss?
What return probability distributions are required for maximizing expected log return to give you the best long-run median outcome?
Let’s fix the Kelly rule’s practical problem of unendurable drawdowns from repeated losses.
In1998, I read about Kelly’s rule and the work of growth optimizing academics like Hakansson and Latané. I saw that I could do what they had missed – represent any degree of conservatism by simply changing the zero point of the domain of the logarithmic utility curve. In crude terms, don’t bet more than you can afford to lose.
Visions of a Nobel prize danced like sugar plums in my head until I discovered that Mark Rubinstein had done the same thing in 1976. Although his paper was published in the Journal of Finance, it was discounted by a academic establishment reluctant to prescribe a specific utility function. (This seems like telling the three little pigs they can build their house of straw if they prefer.) Mark told me that “generalized logarithmic utility” made for a better market model, but he had not thought of adapting it as a practical tool for financial advice.
So let’s do it now! In the accompanying extended balance sheet, investments are on the left, and both liabilities and discretionary wealth on the right. You can think of discretionary wealth as a cousin to surplus or net worth, but one that includes the present value of plans for the future. The discretionary wealth approach is simply to apply the Kelly rule to managing discretionary wealth.
In the case shown in the chart, if we lose 10% on investments, we lose 25% of our discretionary wealth. That is, leverage L is 2.5 times. What are we managing? We seem to have gotten ourselves into a bigger picture than just managing investments.
The extended balance sheet including assets and liabilities based on plans for the future is a doorway to financial planning. It links goal-based advice to investment strategy, and does so much more transparently than through a dynamic programming approach.
We can add value by eliciting the client’s spending goals and commitment to them. Then the client can be helped to improve plans by seeing their likely consequences based on good investment policy. (By the way, this is just as relevant to institutional and corporate clients as it is to individuals.)
I believe this approach is how we can best move the financial service industry from commodities to high value added. Now let me show you more examples.
I promised to show you how to integrate sequential risk control with Markowitz diversification. If we remember enough calculus , we can express our criterion as a Taylor series whose first few terms closely approximate it. We discover that: [Read slide, noting the final Markowitz criterion].
In cases where using a Markowitz optimizer itself has the potential to give good answers, we can now use a risk aversion parameter based on the extended balance sheet rather than on today’s widely used questionnaires.
We can even do a quick rough assessment of stock allocation for an average person as (Es-Ec)/(LV), or even rougher as about, say, 1.3/L. Then we can customize that starting point for differences in tax rates and any active forecast we wish to make in E and V.
Further terms in the Taylor series give us insight into when we should pay attention to return skew and fat-tails (kurtosis), critical in the case of derivatives. The impact of these higher-order terms is very sensitive to leverage .
What should we think about the fact that the Taylor series may not converge for large values of leverage times investment return standard deviation?
This is one of many possible simulations that are generated to construct a distribution of outcomes. It can be made far more illuminating and realistic than usual today. Here, investment asset allocation is adaptive over time as leverage changes.
If you are old but your ample discretionary wealth keeps leverage low, you should invest heavily in stocks. Age-based target funds are problematic.
Given the extended balance sheet and investment return characteristics, an appropriate investment strategy can be constructed. But that is just solving a sub-problem that may already be suboptimal. To solve the real problem, you need repeated chances to reflect on whether, in light of the investment consequences, the assumed financial plan is the right one.
You could add even more value by making visible the impact of contingent flexibility in the financial plan. For example, show what happens if the client is willing to plan to cut spending by 5% if there are bad investment results.
At last! Taxes. We often assist clients to legally reduce their tax burden through estate planning, tax-loss harvesting, deferred realization of capital gains, locating highly-taxed investments in tax-advantaged accounts and trusts, and the like.
But not every financial advisor quantifies the important role of taxation in changing the balance between expected return and risk. Of course, relative risk reduction from taxation depends on the ability to offset realized losses with realized gains within a reasonable time period.
Since taxes reduce the average return linearly, but reduce risk through a squared term, higher tax rates appropriately shift highly-taxed individuals further toward risky investments.
Like low leverage, tax-based promotion of risk-taking is even more pronounced for returns with negative skew and high kurtosis. You may not be surprised to learn that highly-taxed individuals may be more comfortable with black swans than is a tax-exempt charity.
I believe leverage is a more accurate way to estimate appropriate risk aversion. But even so, uncertainties remain in future plans for saving and spending.
The chart on the slide was constructed from life-insurance tables for a 55 year old woman with a somewhat typical balance sheet. The resulting probability distribution for retirement spending needs translates longevity risk into risk in L.
What impact will the interaction effect between longer than expected lifetime and worse than expected investment return have?
Combining risk in L with risk in return is not an additive process within our criterion for best median result. If it were, creating a fictional liability for retirement spending and applying Markowitz optimization might be sufficient. One way forward if we want to add more value is through Monte Carlo simulation as part of the optimization process. That sounds more difficult than it is. It may well be worth several minutes of computer time for a more reliable answer. [By the way, this critique also applies to human capital as a representation of savings plans and delayed retirement.]
The discretionary wealth approach can provide a useful paper trail (and ethical backbone) for suitability and fiduciary judgments. This goes beyond assessments of stock allocations and beta.
The higher moments of the Taylor series representation tell us the impact of leverage on sustainable median return in the context of optionality. The example burned into my brain by personal experience is not to sell an option income fund, with its negatively-skewed return distribution, to gain extra income for cash-strapped retirees.
Can we use this insight to better understand Warren Buffett’s investment style?
For my last illustration of the power of the discretionary wealth approach, let’s talk about managing the investment organization and the agency process. Performance measurement has not been much good for selecting managers, but it is extremely effective in motivating the bright people in our industry, sometimes in the wrong direction.
Pension plans are generally treated more similarly than their funding circumstances would justify. Why not have the client pick their spot on an efficient frontier using a joint assessment of leverage? This is a holistic exercise where a financial advisor could add enormous value.
Shouldn’t investment manager performance then be judged on a risk-adjusted basis, with the risk adjustment based on the client circumstance, not on a broad market index? And especially not be judged based on a tradeoff of return versus benchmark tracking error.
Does measuring risk as tracking error bias managers toward excessive risk in general?
Can we negotiate a leverage to be applied to performance evaluation for that client? We do it for allowed investment universes and for benchmarks. Why not do it for appropriate risk aversion?
Recall from our earlier mathematics that we made our criterion look like Markowitz risk aversion by dividing its Taylor series representation through by leverage. We can do the same thing by dividing L into our original criterion, and without losing skewness and fat-tails , to get an absolute risk-adjusted return.
If we want to compare to a benchmark, we don’t need to bias results by using tracking error as a measure of risk. We can just take the difference between the actual portfolio and the benchmark index in client-based risk-adjusted return.
How many observations do you need before you can calculate such a measure?
What would happen if the client and manager negotiated an incentive contract with this relative risk-adjusted return? What would hedge fund incentive pay look like? Would you still hire mainly first quartile managers or hedge funds ?
What would happen if you gave a new manager a contract incentivizing 5-year performance and specifying a hypothetical pre-history of four years of zero relative risk-adjusted returns?
How hard would it be for a trader to game this system?
It takes practice to get used to managing the sustainable growth of discretionary wealth.
The chart shows four quite risky wealth paths with the same final result of 7.3%. The client’s leverage is 3 times. The risk-adjusted return is only 3.9% for a return series generated from a normal distribution.
Adding negative skew or fat-tails to the pattern produced by a normal distribution further reduces the estimate of sustainable return on discretionary wealth – from 3.9% to 3.6%.
The shocker for even very intelligent professional investors is the impact of what seems to be just slightly higher volatility when volatility is already high and leverage is involved. In this case, it produces a much greater further reduction of sustainable return on leveraged discretionary wealth – from 3.9% down to 2.8%.
Ignorance of the impact of risk-taking is pervasive even among those who should know better. The discretionary wealth approach has the potential to inject the equivalent of many years of painful experience throughout an organization.
I began by talking about adding value through better service.
Those who understand the discretionary wealth approach can add value without the aid of computers, often with just a rule of thumb or a quick mental calculation .
But to take it to its logical extension, both in handling complexity and in managing an organization , computer assistance is invaluable.
As time goes on, the intelligence that resides within machines will incorporate more and more that is self-generated by analyzing data. What we have seen so far in “robo-advisers” are only the scouts of an advancing army of financial applications.
The discretionary wealth approach offers a refuge against commoditization. By adding more value it reduces government motivation for disruptive intrusion. It could even help us resist the emotions that aggravate bubbles. I believe it can also help us to partner with, rather than be replaced by, new technology.
Many financial organizations have already taken steps toward better service to clients. But there is much more to be done. The time window for effective action may be shorter than we think. Thank you.