Correlation between Olympic Medals and GDP

I have been hit by the Olympic bug, stuck to the tv watching competitive events not normally televised. The Olympics seems to be a strange event where every 4 years we get behind our athletes to support them in events we rarely care about (how many times have you watched an IAAF meeting or a weightlifting competition outside of Olympic screening?)

As we see the USA and China in their familiar competitive environment, I looked at the medals tables over the previous 4 Olympics and began to wonder if I was just trying to reason random data, or if there is scientific proof regarding the economic prowess of a nation and its ability to achieve Olympic success. Stumbling on some academic work, I thought I should share... 

A June 2008 economic paper published by consultants PricewaterhouseCoopers found a strong historic link between money and medals: Countries with the bigger GDPs tend to be represented most often on Olympic podiums. It’s logical — nations with more resources can, if they choose, devote more money to investing in their athletes.

Similarly higher GDP per capita may also be associated with higher average nutrition and health levels could also boost performance in some sports.

Now for the stats...

In an article written by Xun Bian (2005) in The Park Place Economist, Volume XIII, the author attempted to quantify the relationship I mentioned above. The paper follows two studies on modeling national Olympic performance and using both a multiple linear regression model  and the ever popular Cobb-Douglas production function to estimate the influence of population size, economic resources, political and economic structure, and hosting advantage on nations’ Olympic performance.   

For the linear regression: Mt = C + α1 Nt + α2 (Yt / Nt) +α3 P +α4 Ht + ε. 

Mt denotes the medal number for a country at a particular Olympic Game.

Yt/Nt is therefore the per capita GDP of the country at the Olympic year. P and Ht are dummy variables for political and economic structure and hosting. P takes the value 1 if the country

has socialist background, which means the country is or was a socialist country, and it takes 0 if otherwise. Similarly, if the country is hosting the Olympics in that year, Ht takes the value of 1,

and 0 if otherwise. 

From the model we can note GDP per capita, population, socialism and hosting have positive coefficients noting the positive correlation between these variables, however we must not read too much into this model, with maximum adjusted R^2 of 50%, we would say that at least 50% of the variation in medal counts is unexplained by this model. Note however how statistically significant the variables are! 

Lets take a look at the second model, the Cobb Douglas Production Function: 

 As we have learnt in multivariable calculus, this is a function of 2 variables namely population (N), economic resources (Y):      Mt = At (Nt)^γ (Yt)^θ 

By taking natural log of both sides of the equation to make it linear in log form,  yields the following specification for Olympic medal counts: lnMt = lnAt + γ lnNt +θ lnYt + e. 

Since At captures other aspects that are influential on a country’s Olympic performance, we can

replace lnAt with the constant C, the communist dummy variable P, and the hosting dummy variable Ht. Therefore, the actual equation I used takes the

following form, in which α1 = γ and α2 = θ.

lnMt = C + α1 lnNt + α2 lnYt +α3 P +α4 Ht + e

The results are as follows: 

Notice we have not improved the adjusted R^2 and the coefficient ln Nt variable for population is now negative (but not statistically significant in this model), indicating a negative correlation between population size and Olympic performance. 

The author however says the above results are consistent with previous studies on national

Olympic performance (Johnson and Ali , 2000  & Bernard and Busse , 2000), this paper finds that socioeconomic variables, including population size, economic

resources, hosting advantage, and political structure have a significant impact on a country’s Olympic performance. 

In general, population size and economic resources are positively correlated with medal

counts. The larger the population size, the more likely a country is going to do better in the Olympics; the richer a country is, the more Olympic medals it will likely win. Being a hosting nation and having a communist background both have a favorable influence on a country’s Olympic performance.

The Young Economist

Risk - A Risky Businesss!

Model risk, business risk, trading risk, operating risk. The world of finance has some obscure risks, many of which are trying to be quantyified. Enter the magical mysteries of mathematics and statistics along with the German genius Carl Freferich Gauss, famous for the Gauss/normal distribution of probability.    

He noted many natural observations follow a 'normal' distribution with bell curve shapes such as the height of people.

As mentioned in my previous blog, key discriptions of distributions include the mean (the first moment) or average as well as standard deviations (how much the actual observations deviate from the mean) - the second moment.

Tchebysheff's theorem postulates that, for a normal distribution, 67% of all observations lie in 1 standard deviation of the mean, 95% within 2 standard deviations and 99% within 3 deviations.

Modern finance has become fixated on standard deviations as it describes the volatility or risk of a share. A share that moves by 2% is twice as risky as a share that has a standard ddeviation of 1%. The standard deviation is then scaled to a volaility index - 

1% per day * square root(250 business days a year)

= 15.81% annual volatility. 

Why sqrt(250)? (5days a week * 52 weeks) - 10 days public holidays. The square root is a statistical trick, known as the 'root mean square rule' based on Geometric Brownian Motion describing the random pattern a share price is 'expected' to follow (qualitative investors im sorry but this is one of the assumptions). 

The whole point of these calculations is to answer questions on a portfolio "with a 99% confidence, what is the maximum price change, what is the maximum I would loose".

When all of the posiitons are evaluated (daily), the chairman (or whoever is in charge) recieves a "4:15 Report" - a daily report summarising the risk, usually with a figure such as VAR - value at risk. 

A VAR figure of 50 million at a 99% 10 day means you have a 99% probability (1% probablity) that you wont(will) loose 50million in a 10 day period. 

Today VAR figures feature in banking regulations, and 'offers precision in a world of chaos'.

VAR and other risk management tools have come under considerable fire for failing under abnormal market conditions. In the words of Satyajit Das "what is often forgotten is that Gauss originally intended the normal distribution as a test of error, not accuracy"  

The Young Economist 

Principles of Quantitative Fund management

As the semester comes to an end and one is able to catch up on the reading sorely missed under the strain of coursework, I have found and put together a few gems (in my opinion anyway), regarding the underlying strategies or principles when looking at quantitatively managing money.

1. Diversification - the process, made popular by Harry Markowitz,  investing in multiple asset classes, seemingly to reduce risk. While this mitigates non-systematic risk, one is still always exposed to market risk (Beta).

2. Efficient Market Hypothesis - made popular by Eugene Fama at the university of Chicago, a share price is is said to be a reflection of information known about the share and the price can take 3 forms:
    i) Strong Form  Efficiency - where ALL info regarding the share is priced in.
   ii)Semi-Strong Form Efficiency - where all PUBLIC info regarding the share is priced in                                                                         iii)Weak form Efficiency - where the share price is just a reflection of previous prices. 

3. Mean/Variance - arguably the two most important descriptive statistics, managers always want to be able to calculate the expected return (mean), as well as how volatile the returns can be (variance). The more volatile the asset is, the higher risk it poses, which leads us to the final principle...

4. Risk/Return Trade Off - while this makes perfect sense and people have been trading these two variables off for years without officially naming it, The Capital Asset Pricing Model (CAPM) model was introduced by Jack Treynor, William Sharpe, John Lintner and Jan Mossin independently, building on the earlier work of Harry Markowitz on diversification and modern portfolio theory, introduced the CAPM to show returns should be compensated for a given level of risk. 


A Simple calculation ensues, 

where

•  is the expected return on the capital asset
•  is the risk-free rate of interest such as interest arising from US government bonds
•  (Beta - market risk)
•  is the expected return of the market
•  is also known as the risk premium

The Young Economist

SA Government - Useless Rich Pigs

You've got to love South Africa- the people, the vibe, the beauty and the diversity. We are in a stage where it seems people are motivated, optimistic and excited about the future prospects of this great country, however there is going to have to come a time where consumers need to be more protected.

The legislation passed concerning the Consumer Protection Act was a great leap forward, allowing us as consumers to be rightly protected from sharks trying to sell us everything from canned beans to high interest store cards.
But when are we going to be protected from the most powerful of sharks? The SA government has consumers by 'the short and curlies' if I may say so, controlling petrol prices, electricity, landlines, home affairs and everything relating to motor vehicle access.
The SA government literally controls our livelihood through energy, food, water and citizenship. From my experience they are not managing any of the above with any efficiency or effectiveness. Telkom is absolutely useless, in 2012, my internet and phone lines have been down more often than they have been working and we all know about Eskom's problems... having the data and forecasts for electricity demand, neglecting the population while top level management pockets huge bonuses for nothing (surely a 'bonus' is called a bonus for great work/achievement, an extra, not guaranteed?)

Similarly trying to get/renew licenses requires great patience. With the average level of intelligence at home affairs/traffic departments limited to that of a 6 year old, what are we all supposed to do?

We all know private businesses are far more efficient than those of government, private businesses have motivation to make profits, to be efficient and to use their resources more effectively resulting in businesses processes that work. Want proof? Compare our private business service with that of government, they realise   they have all the power.
We cannot do anything but wait, wait and get used to mediocre service.
With the constant call from Malema for nationalization, maybe we should heed his warning and do the direct opposite.
Privatization of all these major service providers will shake up the market, bring in competition and increase efficiency allowing all of us to not worry about the uselessness of service delivery but rather focus on the more important things, bringing this country out of the dark hole of poor delivery we so easily accept, to a country that can rival the 1st world powers we so often admire.

We have the people, we just need the opportunity to free ourselves from the shackles of government.

The Young Economist