Solving Africa's Problems--PERMANENTLY

Roben Farzad's (BusinessWeek columnist) article titled Can Greed Save Africa?, reignited debate on the 'Aid to Africa' imbroglio, and, intensified discourse on the topic of aid-effectiveness.

He quoted the following interesting statistics (from a study conducted by William R. Easterly, an economics professor at New York University):

• Between 1960 and 2007 (a period of 47 yrs), Africa received a 'total of USD625 billion in foreign aid'. This translates to an aid disbursement of approximately USD247 million per country per year.
• Between 1976 to 2000 (a period of 24 years), 'Africa's share of global trade dropped to 1%, from an already negligible 3%'. This shows that Africa is becoming more of a net importer of commodities: a sign of African countries' declining (production) comparative advantage.
  
• 'The U.N.'s scale of human development, which considers health, education, and economic well-being, ranks 34 African nations among the world's 40 lowest'. This means that Africans generally have the lowest welfare in the world!

The statistics clearly imply that Africa has a negative aid-growth elasticity i.e foreign aid has worsened the welfare of African people. This could mean either or both, of the following:

• Aid doesn't influence economic growth: Foreign aid may have a neutral/negligible effect on economic growth in recipient countries. Hristos Doucouliagos and Martin Paldam's working paper titled Aid effectiveness on Growth: A Meta-Study, suggests that foreign aid has an insignificant effect on economic growth in recipient countries. Therefore, this implies that Africa's declining comparative advantage, could be driven by other factors that have no connection to foreign aid; e.g civil strife, corruption, e.t.c
  
• There are flaws in the conception, design and execution of foreign aid programmes: I suspect that foreign aid fails to stimulate economic growth & enhance social welfare in Africa because of inaccurate diagnosis of Africa's problems, and, because the programmes are poorly designed. J. Orlin Grabbe, in his speech titled In Praise of Chaos (presented to the Eris Society on 12 August 1993), stated that 'handing out free food in "refugee" camps in Somalia leads to a greater number of starving refugees, because the existence of free food attracts a greater number of nomads to the camps, who then become dependent on free food, and starve when they are not fed'. This example illustrates the adverse effects of 'poorly designed' aid programmes.
  

...Solutions to Africa's problems (according to me)

Problem 1) Learned helplessness

Decades of racially oppressive colonial rule, civil strife and state failure have had a toll on African Infrastructure, and African people.

Most aid programmes target infrastructure, education and nutrition. Some address health care issues, especially those related to HIV/AIDS... But it seems that there are no initiatives that focus on improving the mental health of African people.

People who go through oppressive colonial rule, civil strife and state failure; are bound to have mental and emotional scars that need healing. These 'scars', if unattended to, may have adverse effects on the well-being of individuals and society as a whole.

New age authors like James Ray, believe that a person's situation in life is a reflection of their mental state. Similarly, a society's collective 'situation' is a reflection of the society's collective mental state. Hence, a contracting economy, increasing HIV/AIDS infections and a galloping crime rate, may be reflections of a society's unhealed mental and emotional scars.

I believe that Africa's problems can easily be solved by average African Joes and Janes, without any external assistance. Why don't they solve their society's problems? Answer; Learned helplessness--a psychological condition in which a person has learned to act or behave powerless in a particular situation, even when he/she has the ability to change his/her unconfortable or even dangerous circumstance.

So, whats the solution for the learned helplessness problem?: Aid programmes should focus the majority of their efforts and resources, on identifying and addressing the underlying psychological causes of Africa's problems i.e heal the mental and emotional scars of African people.

Problem 2) Lack of Access to Capital

My travels across the African continent have given me a valuable insight: Africa's most recent generation, born between 1978 and 2008, is; relatively well-educated, tech-savvy, ambitious, entrepreneurial, smart, passionate and it also has an awareness of global trends and events. I call it Africa's Star Generation, because it has the potential to change Africa for the better through its entrepreneurial drive.

Unfortunately, the transformative effect of this generation may fail to be realized, because it lacks access to risk based capital and specialized business expertise--critical elements for the success of the Star Generation's new ventures. Africa's banking and micro finance industry is highly conservative and lacks innovation: the sector prefers to confine its services to 'blue-chips' that invariably; have collateral (asset rich balance sheets), have a proven track record of success and operate in traditional lines of business e.g mining, agriculture and the manufacture of fast moving consumer goods. This denies the Star Generation access to capital and their right to participate in the economy. Dejected, the entrepreneurial generation relocates to developed countries, where it joins the growing ranks of middle-class immigrants of African origin--that remit hard currency to Africa. This limits the economic development of Africa and restricts Africa from participating in the 'tech-age' economy.

So, how do we solve the capital access problem?: The Democratization of access to capital through legislative instruments and financial technology!

Don't you think I should become the secretary general of the United Nations? :-)

Oil, The US Dollar, Gold, The Vietnamese Dong

Two topics I've been thinking about:

Disclaimer: The following post is not intended as investment advice. Your capital is at risk when you invest in anything – you can lose some or all of your money, so never risk more than you can safely afford to lose. This post is solely for purposes of discussion. Always seek personal advice from your investment adviser, if you are unsure about the suitability of any investment.

1) Oil, The US Dollar

In his article titled US-Dollar Is The Best Looking Horse In The Glue Factory, Steven Syre (Globe Columnist) states a common perception among financial-market-players: 'The value of the dollar and the price of oil move in opposite directions on a dependable daily basis'. This perception is validated continually by empirical evidence -- it can almost be viewed as a law!

According to an article summary on KurzweilAI.net, General Motors is currently collaborating with thirty utilities in 37 states, and, with The Electric Power Research Institute to develop a charging infrastructure for electric cars. After reading that, one thing is certain: fossil fuel powered vehicles will not be a part of our future. This got me wondering: What will happen to the US dollar and the global price of crude oil, when electric cars (or cars with engines that are powered by a non-fossil fuel) become ubiquitous?

The demand of crude oil would be curtailed by wide-spread-global-adoption of non-fossil fuel powered vehicles. Obviously, this would have an adverse effect on the price of crude oil. But does this imply that the US-Dollar is set to appreciate rapidly (ceteris paribus), when electric cars become widely adopted (since 'The value of the dollar and the price of oil move in opposite directions on a dependable daily basis') ? Also, how will this affect Gulf economies, that solely depend on oil as a revenue source? Will their Sovereign Wealth funds have the ability to insulate them from the effects of falling oil prices?

One thing is certain: One can never go wrong by investing (with a long-term focus) in electricity generating ventures and in ventures that develop safe durable technology for electric car charging stations.

2) The Vietnamese Dong, Gold

According to an article on Bullion Vault, Vietnam is 'the second largest market for gold exports in the world, Vietnam has already imported 60 tonnes of gold valued at $1.8 billion so far in 2008, an increase of 100% over the same period last year'

Recently, the Vietnamese government temporarily banned gold imports to contain the country's ballooning trade deficit (which tripped this year).

Will this move help to shore-up the Vietnamese Dong? How will the Vietnamese property market respond to this ban? How will speculators trade the Dong when the ban is lifted?

I'm confident about one thing: the value of the Dong will plummet when the ban is lifted.

Why?

Gold is a US-dollar denominated asset, so when the ban is lifted, Vietnamese market players will scramble to trade in their Dong, for US dollars to purchase gold with. This will cause the price of US dollars to appreciate in terms of the Dong. By what margin? It's hard to tell.

I also believe that the price of gold will appreciate sharply when the ban is lifted; the majority of the price spike will be driven by speculators.

Note: I don't have a position, long or short, on oil futures or the Vietnamese Dong. I may have a combination of positions on Gold and the US-dollar. This post reflects my opinions and NOT the opinions of companies and charities I'm affiliated with.

...Lets see what happens!

Regional Integration Increases correlation of regional stock prices

The Free Online Dictionary (by Farlex) defines a stock market as 'The market in which shares are issued and traded either through exchanges or over-the-counter markets. Also known as the equity market, it is one of the most vital areas of a market economy as it provides companies with access to capital and investors with a slice of ownership in the company and the potential of gains based on the company's future performance.'

*****************

Stock markets, when viewed in abstraction, are essentially non-deterministic dynamical systems (stochastic systems). When these stochastic systems operate, current market prices are iterated from complex mathematical formulas that incorporate, among other things; preceding market prices and events.

Each stock market is a distinct stochastic system, that has its own 'unique formula' for pricing stocks. This 'unique formula' evolves constantly in response to:

• Political events in the country, and, in the wider global environment.
  
• Social trends in the country, and, in the wider global community.
  
• Technological trends in the country, and, in the broader 'global village'.
  
• Economic trends precipitating at a national and global level.

As regional political integration (and economic) progresses, nations within the respective integrated bloc increasingly resemble each other; politically, economically, technologically and socially (i.e countries within an integrated bloc converge towards a common order). Otherwise stated: regional integration 'homogenizes' countries with different traits. This has the effect of standardizing the underlying factors (or the 'unique formula for setting stock prices') that influence share prices within the region.

...What are the effects of this 'standardization'?

As regional integration increases, stock markets (within the respective integrated region) begin to behave in more or less, the same way: they increasingly become positively correlated.

(I suspect that) If you picked any two random shares, on any two random exchanges (within an integrated regional bloc) and studied them over a period of time; you'd find that the correlation of their prices increasingly approaches 1 (the number one).

Mathematically this can be expressed as:

Which reads As time approaches positive infinity, the correlation between two randomly picked share-prices (each from a different stock exchange within an integrated regional bloc) approaches one i.e they increasingly approach perfect positive correlation.

Note: the general assumption of the mathematical expression above, is that regional integration increases with time.

Where:

t represents time.
The 'lazy eight' represents positive infinity.
x1 Represents the price of the first randomly picked share at a specific point in time.
μ1 Represents the arithmetic mean of of x1 during a defined time period.
x2 Represents the price of the second randomly picked share at a specific point in time.
μ2 Represents the arithmetic mean of of x2 during a defined time period.
σ1 Represents the standard deviation of x1 during a defined time period.
σ2 Represents the standard deviation of x2 during a defined time period.

...And?

As stock markets (within an integrated region) approach perfect positive correlation, the (risk management) benefits of intra-regional diversification of share portfolios, diminish proportionately.

To put this into perspective: Intra-regional diversification of share portfolios, in an environment of increasing regional (political and economic) integration, is akin to loading different egg-filled baskets onto the same haulage truck.

Although your eggs are in different baskets, they still have a common environment...

What happens to your precious eggs, when another haulage truck crashes into your egg-carrying-truck?

Your attempt to limit risks by diversifying your eggs into different baskets, would have been an exercise in futility!

...Now think about mutual funds with a European Union listed-equity focus: What does this say about their risk management practices?

You have been warned! :-)

Mitigating the Global Food Crisis

There are 860 million people (~13% of the world's population) who are suffering from chronic hunger. 90% of these people, reside in developing countries i.e: mostly in Africa, Parts of Asia, South America and Eastern Europe.

****************

According to the agenda of the June 2008 HIGH-LEVEL CONFERENCE ON WORLD FOOD SECURITY (centered on THE CHALLENGES OF CLIMATE CHANGE AND BIO-ENERGY):

• 'During the first three months of 2008, international nominal prices of all major food commodities reached their highest levels in nearly 50 years, while prices in real terms were the highest in nearly 30 years!' Over the last year, the global mean price of food has risen by 56%, with wheat rising by 92% and the average price of rice rising by 96%.

• The global food crisis 'is provoking social unrest across the developing world'. For instance in Somalia, where thousands rioted during the first week of May 2008; protesting for food. Food riots have also occurred in Indonesia, Haiti, the Philippines and Ethiopia.

It is clear that the escalating prices (of food commodities) threaten to plunge millions into deep poverty. If unchecked, this crisis has the potential to trigger a chain of apocalyptic events: it may draw us closer to extinction...

That's how serious it is!

Below is a graphical illustration showing real and nominal average food prices between 1961 and 2008:

Source: HIGH-LEVEL CONFERENCE ON WORLD FOOD SECURITY: THE CHALLENGES OF CLIMATE CHANGE AND BIOENERGY AGENDA. For more information see conference materials

Explanation of the graphical illustration: The vertical axis shows prices and the horizontal axis shows time in years (between 1961-2008). The navy-blue trajectory shows nominal price movements (of food commodities) between 1961-2008 and the lime-green trajectory shows price movements (of food commodities) in real terms, between 1961 and 2008. From the illustration you can see that real prices and nominal prices of food are equal in 2003. Between 2003 and 2008, both real and nominal prices increase at a pace that was last witnessed in 1974! In 2008 the nominal price of food is at its highest and the real price of food is at the same level it was in 1978.

...What's causing food prices to soar?

World Bank Agricultural Economist, Don Mitchell believes that bio-fuels are the chief cause of the upsurge of food prices. According to Mitchell, the growing use of food crops as raw materials for bio-fuel generation, combined with falling grain stocks, speculation in commodity markets and food export bans; contributed to approximately 75 percent of the 140 percent rise in food prices between January 2002 and February 2008. He also attributes 65 percent of the 140 percent increase in food prices, to the depreciating U.S. dollar, increasing energy prices and associated increases in fertilizer costs. Another factor that's fueling the price escalation, is climate change (caused by global warming). Climate change generally has an adverse effect on agricultural yields.

The above-cited factors generally have a 'reducing-effect' on the global supply of food, which generally causes food prices to increase (assuming constant food demand).

Below is a supply and demand model that illustrates the effect of the aforementioned factors on global prices of food:

Explanation the Supply and Demand Model: The vertical axis represents the global averages of food prices. The horizontal axis represents quantity of food demanded globally and quantity of food supplied globally. The downwardly sloping lime-green line represents the global quantity of food demanded, at various prices. Global supply of food (at various prices) before the bio-fuel revolution is represented by the upwardly-slopping navy-blue line labeled S1. The global supply of food after the bio-fuel revolution has started, is illustrated by the upwardly-slopping navy blue line labeled S2. Point b (Q1;P1) is the point of equilibrium between demand and supply of food, before the bio-fuel revolution. Point a (Q2; P2) is the point of equilibrium between demand and supply of food, after the bio-fuel revolution has started. The bio-fuel revolution reduces the supply of food from S1 to S2 and the point of market equilibrium shifts from Point b to Point a. At point a the aggregate quantity of food supply is Q2 at an increased price denoted by P2.

...How do we mitigate the crisis?

Answer: By increasing food supply (which in turn reduces food prices) through any, or a combination of the following:

• Channeling an increasing proportion of bio-fuel feedstock to the food industry. However, this may undermine the productivity of bio-fuel projects, which would adversely impact Kyoto Protocol-sanctioned pollution-reduction initiatives. In the diagram below, the increase in food production from a reduction in bio-fuel production is illustrated by a movement from Point a to Point b.

• Development and wide-scale implementation of yield enhancing technologies. This would boost global food output. Effective yield enhancing technologies have the likelihood of emerging from the field of Biotechnology (specifically genomics and proteomics) in the form of; high yielding, nutrient-rich, pest resistant, 'all-weather' crops. In the diagram below the increase in food production that accrues from technological development is illustrated by a movement from Points a and b to either Point d or Point e.

• Development of 'food alternatives'. Recent advancements in the field of nanotechnology have given us the power to manipulate matter--at it's most basic level--with great precision. We could use this technology to create chemical substance equivalents of food, that mimic real food in terms of; taste, appearance, nutrition, texture and smell: I believe that in the near future, we'll be able to harness the power of light energy, carbon dioxide and synthetic chlorophyll; to create edible nutrient rich carbohydrate foods in labs (at a lower cost and at a faster speed than nature)... Also, currently, stem-cell technology is used to grow cartilage and skin (for medical patients who need replacements) in petri-dishes. We can use that technology to grow meat (parts of cows, fish, chicken etc) in labs. This will help conserve grain (and land), that would otherwise have been used as an input for animal husbandry projects (which are generally 'grain-intensive'). This would avail more grain for human consumption. (Side Note: Sounds like a florid, quixotic statement; embedded in deep romanticism? Wait and see! The passage of time will validate my assertion). In the diagram below this increase in food supply from food alternatives. is illustrated by a movement from Points a and b to either Point d or Point e.
  

Explanation of the graphical illustration: The illustration above is a Production Possibilities Frontier (transformation curve) model showing the maximal combinations of bio-diesel and food, that the global economy could efficiently produce during a specific time period, with the use of scarce resources. The vertical axis represents various quantities of bio-diesel and the horizontal axis represents various quantities of food. A northward movement from any point on the graph, means that more bio-diesel is being produced, whereas an eastward movement from any point on the graph, means that more food is being produced. The two concave slopes are called transformation curves. They show the various maximal combinations of food and bio-diesel that the global economy can produce efficiently. Each respective transformation curve represents a different level of technology utilization; with the navy-blue trajectory showing the maximal combination of bio-diesel and food that can be produced with the current level of technology. The green trajectory shows the maximal combinations of food and bio-diesel that can be produced if a technological advancement occurs. Point f lies lower than the navy blue trajectory; a movement from Point f to point either Point a or b, means that producers have scaled-up their operations--using the current level of technology--to (efficiently) produce maximal combinations of food and bio-diesel. A movement from Point a to b means that producers who are already producing maximal combinations of food and bio-diesel (using the current levels of technology), are increasing food production at the expense of bio-diesel production. A movement from Points a and b, to either Point d or e means that farmers are using new yield enhancing technology to (efficiently) produce greater quantities of food and bio-diesel.

...How do governments; channel an increasing proportion of bio-fuel feedstock to the food industry, facilitate development and wide-scale implementation of yield enhancing technologies, facilitate development of food alternatives?

I think that the Food and Agriculture Organization of the United Nations should encourage its membership to set voluntary, legally binding food production targets: a food production treaty. The treaty should be an adapted (to food security) 'reverse-engineered' model of the Kyoto Protocol, that among other things, sets specific targets and deadlines for food production. A treaty of this kind will provide the moral impetus for tackling the global food crisis.

A carrot and stick approach has to be implemented to encourage parties to the treaty to comply i.e reward compliance and punish non-compliance. Financial penalties should be set to punish signatories who don't meet targets, and, tradeable 'Food Production Credits' (similar to carbon credits) should be awarded to parties that increase food production beyond a set benchmark.

'Food production credits' have the added benefit of inspiring research into yield enhancing methodologies, and, will encourage producers to adopt yield enhancing technologies rapidly i.e 'food credits' will reduce the 'bottleneck' between (yield-enhancing) technology creation and (yield-enhancing) technology adoption.

And so on, and so on, etc, etc :-) . The academics can takeover from here.

Media Elasticity of Stock Prices

This article alleges that Bear Stearns' collapse was concocted by diabolical 'invisible forces'... It would be improper to comment on the Bear Stearns debacle before SEC investigations are concluded, so I reserve all comments (on this conspiracy theory) until then!

As I was reading that article, I experienced a flash of insight: Speculative negative media coverage adversely affects a firm's stock price, regardless of what the firm's fundamentals say. I knew that of course, but I now understand this from a Mathematical (and Economic) perspective. I term this 'mathematical frame' (negative) media elasticity of stock prices . The concept that underlies the paradigm is not new, it has been discussed extensively in academic circles.

*************

In his research paper titled: Market and Individual Investors Reactions to Corporate News in the Media, Philipp Schmitz states that:

• '...The incorporation of information in prices is fairly fast. The main price reaction occurs on the day of the arrival of the new information.This price jump is especially large if the news coverage in the media is accompanied by ad hoc announcements made by the corporation itself. While there is only a very short-term post-event drift after good news, prices tend to drift for several days after bad news. The post-event trading volume is significantly higher than before the news for several days for good as well as bad news'.

This implies that negative media coverage has a sharper effect (than positive media coverage) on a firm's share price.


...The media can break a firm... And it can do this easily

Sustained negative (and baseless) media coverage can have a catastrophic effect on a firm's share price. To illustrate how: Baseless negative media coverage 'discounts' a firm's share price; which attracts a greater degree of speculative negative media coverage; which in turn causes a firm's share price to 'dive deeper' and so on. This self-reinforcing chain of causation continues to feed and magnify itself until:

• the media speculation is disproved or invalidated by changing macro environmental trends or by widely publicized developments in the underlying firm, or,
  

• it is curtailed by government intervention, through the use of legislative instruments, or,
  

• the media's speculative perspective becomes deeply ingrained within a society's collective consciousness; i.e society begins to take the negative media speculation as FACT. At this point, the firm's fundamentals begin to increasingly validate (previously baseless) media speculations i.e there starts to be a convergence of baseless media speculation and reality. When this happens, the firm's brand capital is increasingly decimated; its goodwill falls exponentially and the firm's financial health deteriorates rapidly. I don't know whether or not a firm can survive past this point, or,
  

• it just runs out of momentum because of an incomprehensible factor! (Irrational markets)

...Negative media elasticity of a stock price

Negative media elasticity (NMESP) of a stock price is the responsiveness of a firm's stock price to negative media coverage (of the firm).

A share price's NMESP is never fixed, it varies in response to changes in a firm's:

• Micro environment: These are factors that a firm has influence over, including its culture; its capital structure; its brand capital; its human resource mix; its public relations policy and its level of efficiency in general (to name a few). To lower its NMESP, a firm would have to 'improve' (..for lack of a better word) its micro factors.
  
• Macro environment: These are factors that a firm has very little to no influence over, including market volatility; societal openness; the elite media's editorial policy; the level of media technology the average person utilizes; and the number, level of activity & size of stock market participants.

A firm's NMESP is a function of its micro and macro environmental factors. Mathematically this can be expressed as:

NMESP = f(Ma; Mi)

Where :

NMESP is the negative media elasticity of a firm's stock price
f means a function of
Ma represents a firm's macro environmental factors
Mi represents a firm's micro environmental factors

...How does a firm's share price relate to negative speculative media coverage (in general)?

A firm's share price is inversely related to negative speculative media coverage i.e as negative speculative media coverage increases, a firm's share price decreases.

Below is a graphical illustration that shows an inverse relationship between a firm's share price and negative media coverage.

Explanation of the illustration above: The vertical axis represents a firm's share price movements and the horizontal axis represents percentage increases of (speculative negative) media coverage a firm receives. The inwardly curving navy-blue line represents the inverse relationship between a firms share price and the % increase of speculative negative media coverage it receives. From point a to b, the firm's share price falls very rapidly, a small increase in speculative negative media coverage causes a large decrease of the firm's share price. Between points b and c, speculative negative media has a reduced influence on the firm's share price. From point c to d, the firm's share price is no longer responsive to an increase in speculative negative media coverage, evidenced by the flat gradient between point c and point d.

To mathematically express the relationship between a firm's share price and the % increase of speculative negative media coverage it receives:

ShP = k/NSP

Where:

Shp is the firm's share price
k is a constant number
NSP is the % increase of speculative media coverage the firm receives

...To calculate a firm's Negative media elasticity of its stock price
(NMESP)

NMESP = % change of a share price divided by the corresponding percentage increase of negative media coverage the firm receives within a defined chronological period

Now I need to figure out how to use those equations to generate cash flows!

Carl Icahn's Battle Against Yahoo! Board

For the Open Letter to Yahoo! Shareholders click here
For the Definitive Proxy Statement click here

Lets see what happens....

How do you identify weak companies - Part 2 (stocks to short-sell)?

In the post titled How do you identify weak companies (stocks to short-sell)?, I stated that a corporation's fiscal stability can be ascertained through examining the relationship between its capital structure and its (micro and macro) environmental risks. If a corporation is 'fiscally stable', its risk in capital structure varies inversely with its (micro and macro) environmental risks.

In this post, I'm going to discuss how to use Multiple Discriminant Analysis (MDA modeling) to assess a firm's insolvency risk. The MDA indicator I'll discuss is a statistical harmonization of five weighted financial ratios--derived from a firm's balance sheet and income statement--called Altman's z-score.

So what is Altman's z-score?

It is a multivariate formula developed by Edward Altman to 'measure' a corporation's financial 'soundness'. Altman's z-score is a highly effective diagnostic tool, that helps to forecast a corporation's probability of entering bankruptcy within a two year period. This model has an accuracy rate ranging between 72%-80%, and studies show that it is universally applicable!

The five weighted inputs for Altman's model include:

1. Return on Assets ratio (ROA): which is equal to earnings before interest and taxation divided by total assets (EBIT/Total Assets). This ratio gauges how efficiently a corporation generates revenues from its assets.
2. Sales to Assets ratio: which is equal to sales divided by total assets (Sales/Total Assets). This ratio measures the efficiency of a corporation's sales and marketing function.
3. Equity to Debt ratio: which is equal to market value of equity divided by book of value debt. (Market Value of Equity/Book Value of Debt). This ratio measures a firm's level of leverage and is a general indicator of its capital structure. Note: The book value of debt gives an inflated picture of a firm's true leverage. For an accurate picture of a firm's leverage, use the market value of long term debt i.e the discounted present value of debt interest and principal payments.
   
4. Retained Earnings to Total Assets: which is equal to retained earnings divided by total assets (Retained Earnings/Total assets). This ratio shows the degree to which assets have been paid for by company profits.
5. Working Capital to Total Assets: which is equal to working capital divided by total assets (Working Capital/Total Assets). This ratio tests for financial distress.

Computing the z-score

Z= 3.3x1 + 0.999x2 + 0.6x3 + 1.4x4 +1.2x5

Where:

Z is the z-score
x1 is the Return on Assets ratio
x2 is the Sales to Assets ratio
x3 is the Equity to Debt ratio
x4 is the Retained Earnings to Total Assets
x5 is the Working Capital to Total Assets

From the equation you can see that the Return on Assets Ratio receives the highest weighting and that the equity to debt ratio receives the lowest weighting.

Interpretation of the z-score:

• If a firm has a z-score that is greater than 3, it is safe
• If a firm has a z-score that lies between 2.7 and 2.99, it is financially weak
• If a firm has a z-score that lies between 1.8 and 2.7, it has strong changes of entering into bankruptcy within a year
• if a firm has a z-score that is less than 1.8, it is in the danger zone
  

You've taken your sample of mis-financed firms [which have risk in capital structure doesn't vary inversely with the firms' respective (micro and macro) environmental risks] calculated their z-scores, then whats next?

I then take all the z-scores that are less than 2.7, categorize them into very narrow ranges and plot the normal distribution of the scores.

You'll have something that looks like this:

The normal distribution will ALWAYS be positively skewed. I suspect that this is because bankruptcy (for listed companies) is a rare occurrence. I then focus my attention on everything that lies to the left of the mean--the green zone on the graphical illustration. That's where the 'gold' is!