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