The risk levels associated with shares, currencies, commodities, bonds or markets are usually expressed via volatility. The term volatility is derived from the Latin "volare" - to fly, and its value defines the degree of yield fluctuation. The knowledge of the risk level, volatility or the historical development is important for investors particularly as regards the diversification of portfolio.
The easiest way to assess the volatility of shares is to use the variation coefficient of the share prices. The variation coefficient v(p), is defined by the following formula
v(p) = s(p) / E(p),
where s(p) is the share price standard deviation during the selected period,
s(p)2 = ∑i=1...n ( ( pi - E(p) )2 ) / (n-1)
and E(p) is the average value of the share price during the selected period,
E(p) = ∑i=1...n ( pi ) / n.
The comparison focused on the volatility in 2002-2006 for the following shares traded on the Prague Stock Exchange in the SPAD system
For the calculation of variation coefficients, we opted for a sliding period of the previous year and used daily closing prices on the Prague Stock Exchange.
At the beginning, the volatility during the studied period decreased from 16.8%, which reflects the decreasing quotation in 2001 from CZK 112.70 to CZK 57.80, reaching the minimum value of 4.4% in April 2003. After that, the volatility showed an increasing tendency until April 2005 as a consequence of the growing quotation, reaching the maximum of 31.4% within the studied period. Since April 2005 the volatility continued in downward trend.
The maximum volatility value, i.e. 18.8%, was achieved in early May 2004, as a consequence of the growing quotation, from CZK 1,670 in October 2002 to CZK 4,229 in June 2004. During the next period the volatility dropped until the minimum value of 4.5% has been reached in June 2006. The issue splitting in July 2004 did not influence the volatility trends in any manner.
Volatility sharply grew from the opening 6.9%, which reflects the growing quotation in the second half of 2001 and the first half of 2002, from CZK 806.70 to CZK 1920, reaching the maximum value of 27.1% in June 2002. Then during the monitored period the volatility has virtually been sinking except the local maximum 16.3% was reached by the end of April 2004 and arrived at the minimum value of 4.8% reached in June 2006.
At first, volatility increased from the opening 9.6% and practically doubled reaching 18.3% in early October 2002. The growing volatility reflects the growing quotation from April 2001 to October 2002, i.e. from CZK 5,326 to CZK 12,766. Subsequently, there was a decrease to 7% in May 2003, followed by growth to 15.8% in April 2004. Then the volatility dropped up to 5.6%. At the end of the studied period a sharp jump of the volatility occurred as a result of fall in the rate to CZK 10,276.
The maximum volatility of 24.4% was achieved at the beginning of the studied period. This value reflects the decreasing quotation in 2001, from CZK 569.10 to CZK 184. Volatility decreased until the end of 2004 to the value of 5.8%. The last maximum, i.e. 13.7%, was achieved in early July 2005, after the quotation increased from CZK 283.50 to CZK 465.70. The minimum volatility of 5.7% was achieved at the end of May 2006.
Until mid 2004, volatility had fluctuated between 9.6% and 23%. After that, the situation stabilized for several months and subsequently increased sharply to reach 30.8% in May 2005 which reflects the growing quotation in 2005. Since May 2005 decreasing volatility trends occurred.
The volatility decreased from the value of 19.3%, which reflects increasing quotation from CZK 481.10 to CZK 969, reaching the current value of 11.2%.
Roman Pospíšil, Karel Pliska, Michal Patka, 09-Jul-06