Learning Statistics

Image via Wikipedia

Learning statistics is tough. How come we can be sure about population distribution by sample mean distribution? The answer is "not really", but statistics does provide us an unique measurement for unknown based on assumptions.

Sample mean distribution is normal distribution, which can be defined only by two variables: Mean and variance, and the mean of the distribution will be same as the constant value, population mean, provided the sample size is big enough. This is guaranteed by averaging out.

Once we know the sample mean distribution is normal, Z-value which is relative deviation from the population mean using SE (stand error, population variance divided by the number of sample) as the unit of the yardstick of measurement will explain the percentage of the probability, by what chance, the sample mean can fall within the reach of the Z-value yardstick. If the Z-value is +/-1.96, the chances are 95%. This could be fair, as any normal distributions are defined by mean and variance. Here come my questions:

Q1. How does the sample mean distribution guarantee the shape of the normal distribution by averaging out?
Q2. How come normal distribution can be defined only by two variables?
Q3. Where does the number 1.96 associated to 95% come from?
Q4. How can we state, “the sample is big enough” universally without knowing the real shape of the population distribution?

T-value (student’s T) is used when we do not know the population variance and replace it with a sample variance to construct the yardstick. For 95% chance, T-value can vary along with the degree of freedom (d.f.), which is the amount of information available based on sample numbers. For d.f. 120, T-value is 1.98, slightly bigger than the Z-value as we use less trustful yardstick of sample variance, rather than population variance. Again, here come my questions:

Q5. Where does the number 1.98 come from?
Q6. By what, it makes THE difference of THE NUMBER 0.02 for d.f.120
Q7. How come the divisor of sample variance is always “n–1“ to adjust the measure of spread? And how can we be assured –1 is always sufficient for any sample numbers.

Related articles by Zemanta

• Computing Sample Mean and Variance Online in One Pass (lingpipe-blog.com)
• Normal Distribution : View of a Back Bencher (analyticsbhups.blogspot.com)

Investment bank as wealth transfer vehicle from shareholders to traders

Image via Wikipedia

No matter how much traders make loss, their risk exposure is limited. For the worst case, they just get “fired”. No obligation to compensate for the loss. This position is so called ”owning put ” in a financial term, as their loss is floored but profit has no cap.

Therefore, it is reasonable for traders in an investment bank to leverage out the company’s capital to take more risks.

But, then who compensates their loss in this “zero sum game”? The answer is stakeholders of the investment banks.

If this business is lucrative, why they become public companies after a hundred years of their history? Not to continue to be partnership that allows partners to own their profits?

I think the reason is, the original investment banking businesses such as advisory on mergers, fund raise were indeed lucrative, so that it becomes extremely competitive. As a result, investment banks have become investing banks with high-risk exposure and it was a rational decision to let the companies go to be public to realize capital gain.

The hindsight is always fifty-fifty

Related articles by Zemanta

• Banc of America Securities-Merrill Lynch Research Names Sheryl King as Head of Canada Economics and Investment Strategy (newswire.ca)
• AGF Global Balanced High Income Fund To Be Terminated (newswire.ca)

A Vision for Bretton Woods Two - Removing systemic risks by reforming to the system based on debit settlement, not credit

Image via Wikipedia

The problem of the current economic system is the systemic risk embedded with credit settlement. To increase demand, each participant pay by credit, which means “I OWE YOU”(IOU). Others can use this IOU as asset, so that the owner of IOU could expand his/her credit further based on this IOU.

In this way, IOU is money and each time participant pay by credit, contributing to “money creation” and chaining one’s credit to another.

The worst comes when the last chain connects to the first. The credit of participant relies on the one of another interdependently, results in domino structure causing the systemic failure such as the current financial meltdown.

On the other hand, when people settle by debit, there is no space for IOU and each transaction is closed not to impact one another. There is no systemic failure to be triggered with debit.

With the economic system of debit settlement, we cannot stretch out our purchasing power by credit, which means less demand in the economy. The only way to increase the demand is to increase the velocity of money circulation. That is to increase the number of transactions with the given amount of money.

The profile of the new Bretton Woods Two is yet to be known, however, it is clear that the next bubble is inevitable as long as the demand relies on credit expansion. And the country in a position to expand credit will have the strongest economic power again in the global economy and the next ground zero of financial meltdown.

Reference:

http://www.boj.or.jp/type/exp/seisaku/expkess.htm

Note:

This article has been posted to newspapers, and no reply. Thereby posted to my blog here

Related articles by Zemanta

• Systemic risk (warintel.blogspot.com)
• Retail credit, debit transactions jumped in December (cbc.ca)