InterDisciplinarian |

By Dhruv Sharma

**Abstract**

This
article aims to propose the creation of a marketplace mechanism that can create
significant wealth for the poor and low income citizens of a nation. The
innovative approach described here is to create legislation that allows for the
creation of a new product for investment targeted to low-income families. The distinguishing feature of this product
is that it creates wealth without imposing negative externalities on the
wealthy or future generations as traditional policy tools like taxes do.

**Introduction**

Recent
research on ‘Encouraging Retirement Savings by Low-Income Families’,
by Haisley and Lowenstein, shows that although low income families save disproportionately
less and discusses novel approaches to increase low income savings ( 2009).

Haisley
and Lowenstein’s behavioral research shows that behavioral finance can be
applied to increase savings via innovative techniques such as creating lottery
like mechanisms for savings which appeal to low income families.

This
finding is important as “lotteries that offer a small chance of a high
reward may be particularly useful for increasing motivation in low income
populations” (Haisley, 2008).

If
this is true then it can be further posited that low income families will find
the chance of accumulating large wealth to be even more appealing gambles.

**Problem
of Savings Disparity for Low Income Families**

Low
income families are not able to save for various reasons such as lack of free
cash flows of savings due to debt aka less money to save, along with “no
tax incentive for asset accumulation” (Haisley, 2009). From my personal experience low income
families tend to save via homeownership which has been a traditional source of
wealth creation as opposed to stock market or 401k plans. In general “Wealth accumulation
for low-income and minority households, although low, experiences a major
increase through home ownership (Boehm, Schlottman, 2005). Despite this as income and home prices
are correlated there is greater risk in recessionary periods of time for families
to lose income and face a decling home vale (Caplin, Chan, Tracey, and Freeman,
1997). This creates the scenario
that when local job markets experience shock the value of the savings of home
owners may dissipate just when they may need them to smooth out economic
crisis. Low income families also have
low savings due to high debt (Warren, Sullivan, Westbrook, 2000). If income is the primary source of
savings then the 3 decades of real income stagnation for low income Americans
is a growing societal problem (Lie, 2009). Given this problem, it is no
surprise that wealthy humanitarians like Bill Gates Sr. and Warren Buffet are
calling for higher taxes on the wealthy (Krangel, 2009).

**Alternative
Solutions to Taxation: Log Optimal System**

While the Huey Long approach of taxing the
Rockefellers of the world is not un-appealing other options which might also be
optimal should be examined. In this
regard we can view the problem of low savings due to income and wealth
disparity and also the underlying issue of “real income growth”
disparity (Gordon, 2007). This disparity might contribute to the reason why
lotteries are appealing to low income individuals along with behavioral
biases. If we reframe the
partiality of low income households to gambling like systems as desire for
rapid wealth accumulation then it would seem sensible to proscribe log-utility
to low income households. This is
the utility for people who “want to become millionaires” (Thorp,
1971). Recent research has shown
that people who consume compounding debt, which grows exponentially, also fail
to see benefits of compounding savings due to exponential bias (Stango &
Zinman, 2007).

If lack of capital, no real wealth growth through
income, desire for rapid capital accumulation evidenced by lotto fever and tendency
of falling victim to exponential growth bias are symptoms of the problem, then what
is the optimal “financial medicine”,
as Zinman would say, to address this issue?

One promising solution is to offer low income
households a log optimal investment vehicle which will grow capital faster than
any other competing investment approach and will accumulate wealth in minimal
time (compared to other approaches) (Breiman, 1961).

**Background of Log-Utility and Its Properties**

The Log optimal portfolio or growth optimal
investment has its root in information theory in the work of J.R. Kelly who
pioneered the Kelly Criterion (Kelly, 1956). Kelly’s formula allowed one
to compute the fraction of one’s wealth one should wager in a favorable
gambling scenario. Breiman in the
1960’s proved mathematically desirable properties of the Kelly rule or
log optimal investment (Sewell, 2009).
Thorp popularized the use of Kelly criterion for portfolio management in
various articles and by application in real life (Poundstone, 2005). If the optimal fraction f is
wagered according to the maximization of the expected value of the Logarithm of
X (aka E(LogX)where X is the capital invested then the investor never over
invests. By using fractional,
smaller wager than optimal f, an investor can assure that financial ruin will
not occur as not all of the investors money is invested in risky assets.

Attractive
properties of the Kelly or Log Optimal portfolio summarized by Ziemba are as
follows:

- “Maximizing log
optimal growth maximizes the rate of rate growth asymptotically”
- “Time to reach
a pre-assigned investment goal is minimized with a strategy maximizing the
log of capital”
- “The log
optimal bettor never risks ruin.”
- “The E(LogX)
bettor has an optimal myopic policy”

(Ziemba
& Ziemba, 2007).

**Volatility
Pumping for excess Growth of Capital**

An
application of log optimal portfolios is volatility pumping. This is done by investing a fixed
fraction of one’s wealth in risky assets using optimal fractions based on
maximizing the log return. Thus log
optimal portfolios are involving maintaining constant proportions and can be
referred to as constant proportion investing or volatility pumping. Constant Proportion investing requires
an investor to determine what proportion of capital to allocate to each chosen
asset class. The investor then
rebalances the assets to the preset proportions as asset prices fluctuate. In addition to determining proportions
for each asset class in one’s portfolio the investor must also determine
how often to rebalance towards the proportions. Volatility pumping works by
reducing the magnitude of variance of returns which reduce returns over time
(Luenberger, 1998). As shown by
Luenberger, Volatility pumping does not add much value in a one asset portfolio
as this increases risk without much increase in return. For volatility pumping to be effective
at least 2 risky assets are needed.

One
concern regarding rebalancing frequency is transaction costs. Recently Luenberger and Kuhn have shown
that “ if the length of rebalancing interval is on the order of 1
year…[then] the loss incurred by infrequent rebalancing is surprisingly
small (Kuhn & Luenberger, 38).
Kuhn and Luenberger have shown that “continuous rebalancing only
slightly outperforms discrete rebalancing if there are no transaction costs and
if the rebalancing intervals are shorter than about one year (1)”

**Opportunity**** of Economic Crisis: uncertainty and excess
volatility**

Luenberger
points out to take advantage of volatility pumping one must have multiple assets
with large volatility. Given the
current economic crisis the use of a log optimal volatility based portfolio
takes advantage of the crisis to grow capital aggressively. Evstignev &
Schenk-Hoppe, in their appropriately called paper: “From Rags to Riches:
On Constant Proportions Investment Strategies” showed that if prices are
volatile and assuming small transaction costs, constant proportion strategies
yield a strictly positive exponential rate of growth (2001). Perold and Sharpe’s research on
dynamic asset allocation showed buy and hold to be superior to constant
proportion investing only in markets trending upward while constant proportion
referred to as constant mix tended to be better with greater fluctuations in
the market (Perold and Sharpe, 1998)
Volatility pumping is most advantageous when markets are in turmoil and
excess volatility exists such as in the current credit crisis. As noted in the last major economic
crisis,“stock return variability[is]...unusually high during
depression and is difficult to
explain” (Schwert, 1989).

**Universal
Portfolios for Low Income Families**

An
extension of log optimal portfolio concept is that of “Universal
portfolios” by Thomas Cover. Interestingly
Cover worked for California State Lottery from 1986 to 1994 (Levy, 2000). Prof. Cover’s Universal
Portfolios are based on data-compression algorithms to create the so-called
"universal portfolio." [where] each day the stock proportions in the
universal portfolio are readjusted to track the best performing constant
proportions. The universal
portfolio performs as well as the best strategies that keeping a constant proportion
of wealth in each stock would have performed in hindsight” (2000). Universal portfolios are not one
constant proportion strategy but instead consist of investing “uniformly
in all constant rebalanced portfolio strategies” (2000). Yale’s Andrew Barron and Wei
Qiu have recently developed algorithms that work on subsets of stocks making
the approach easier to implement (Barron and Qiu,2007).

The
power of Universal portfolios is shown by the following example from Barron

Looking
at the stock market in recent years, there are selections of stocks for which
if the portfolio is rebalanced monthly to a constant proportion then over about
a decade, e.g. from Jan 1992 through Dec 2002, one's wealth would have multiplied
5462 fold! Moreover, investing in
only 4 particular stocks in this way would have had a wealth factor of over
4000. That is, $1000 invested in
that selection of stocks would have become over $4 million. Other strategies with non-constant
portfolios would have had even higher return (Barron, 2003).

**Role
for Public Policy in the creation of Growth Optimal Portfolios for Low Income
Households**

Given
the powerful nature of log optimal portfolios and universal portfolios which
are resilient to volatility and catastrophic events, these techniques are an
appropriate tool to wealth creation for low income households. If governments can create incentives and
subsidies for the creation of such products to be sold to low income families
using behavioral engineered products such as the matched savings plans and
lottery based investment schemes then low income families will be willing to
participate in a gamble that is in their favor and has the potential to
aggressively grow capital for savings purposes.

**Subsidies
needed to make Universal Portfolios for Low Income Households a reality:**

- Transaction cost free
trading for investment plans for low income households
- This
could be implemented via tax credits to exchanges.
- Government could
provide a large enough starting capital base relative to which the
transaction costs would be small through aggressive initial matching
- Like the plans
discussed by Haisley and Lowenstein these investment schemes would be
matched savings plans where government would match savings with an
appropriate matching incentive.
- The owner of this
option own the terminal wealth generated by the investment scheme.

The
advantage of removing transaction costs for low income household investment
products will allow investment algorithms to convert a few thousand dollars of
savings into hundreds of thousands of dollars. An alternative version of this scheme
might be for the government to set aside money for each low income household
and put in the investment scheme for low income households and subtract the
initial capital from the terminal wealth after the investment scheme comes to
maturity (which could be based on retirement age). As the terminal wealth will be in excess
of initial investment the tax on the excessive return could be recovered from
the low income family wealth rather than by taxing other people.

**Role
for Private Enterprise**

Investment
banks and mutual funds or ETFs would provide the universal portfolio automated
strategy as a product line. For
this product to work it would need to highlight the important properties of the
product and market the product through appropriate distribution channels to low
income households and automate the trading strategy via software. This is important to shield the low
income households form cognitive burden of investment and also from behavior
biases shown to retard investment decision making. The product would be simple for the
purchaser as the low income investors are abstracted from the dealings of the
funds, trading strategy, or the assets contained within it.

**Regulations**

Governments
should create sufficient regulation and auditing of the log optimal universal portfolio
schemes to ensure that appropriate investment fractions are used and no fraud
is occurring. As significant wealth
will be created from the schemes it is important to sure the wealth makes it to
the low income investment holders and that investment management is not
charging excess fees. Also there
must be enough regulation to ensure too much leverage is not used in the
investment schemes.

**Conclusion**

Giving
low income families a subsidized engine for wealth creation will allow
substantial value and social welfare to be created without taxation. The aggressive growth of investment
capital would serve the needs of low income that are lagging severely in real
income growth, facing greater financial shocks, and are consequently unable to
save for the long term. Consistent
with recent behavioral finance research low income households would be willing
to invest in these lotteries like optimal gambling systems in a favorable game
of savings. Legislators in
government, experts from Academia from Information Systems Sciences and
Behavioral Finance experts in conjunction with private enterprise should work
to create this product a reality.
This product would benefit to all countries with active stock exchanges
and uses market volatility to help finance growth when and where it is most
needed. Once established log
optimal portfolios free of transaction costs could become a source of public
funds for various other public needs and are powerful alternative to taxes as
sources of social welfare.

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