Yield and risk are the key terms for the share analysis. The knowledge of yield and risk is important for investors particularly as regards the diversification of portfolios. The division of overall investments into partial investments where the yields are independent to a maximum extent helps distribute the overall risk. The mutual dependence of yields is characterized by the correlation coefficient.
The risk, ratio of yield fluctuation, can be determined as a standard deviation of the rate of return µ during the selected period,
s(µ)2 = ∑i=1...n ( ( µi - E(µ) )2 ) / (n-1),
where E(µ) is the medium rate of return, average rate of return, for the selected period,
E(µ) = ∑i=1...n ( µi ) / n.
In this case, the risk level is determined in a different manner than in simple estimation, using the variation coefficient of the share quotations.
The correlation coefficient between the rate of return of two shares 1 and 2 can be determined as
ρ(µ1,µ2) = [ ∑i=1...n ( µ1,i - E(µ1) ) ( µ2,i - E(µ2) ) ] / [ ∑i=1...n ( µ1,i - E(µ1) )2 ∑i=1...n ( µ2,i - E(µ2) )2 ]1/2
The correlation coefficient characterizes the mutual dependence of the yields of the considered shares
The analysis focused on the average rate of return, risk and mutual correlation for the following shares traded on the Prague Stock Exchange in the SPAD system
in 2002‑2006. For the calculations, we opted for a sliding period of the previous year and used the rates of return determined on the basis of the market price model from the daily closing share quotations on the Prague Stock Exchange, and the dividends paid.
The average annual rate of return during the period concerned reached its minimum value in early June 2002, i.e. ‑29.2%. After this, the average rate of return continuously increased and reached the maximum value, 90.9%, by the end of 2005. During 2006 a drop up to the value of 76.4% occurred.
The development of the risk determined as standard deviation of the rate of return shows practically opposite development than the estimation using the variation coefficient of quotations. While the variation coefficient of quotations reaches the maximum value in May 2005, the risk determined as standard deviation of the rate of return reached maximum value of 32.4% in November 2002. This difference is understandable, because the maximum value of the variation coefficient of quotations in May 2005 reflects the decreasing quotation from September 2004, which relatively precisely defines the market price model. In this case, the different risk estimates, e.g. as of 31 May 2005 show that
Both statements are true but the second one is much more significant for investors’ decisions.
The initial significant direct proportion relation between the returns of ČEZ and ERSTE BANK, the value of the correlation coefficient was 0.85 in October 2004, continuously changed to indirect proportion; in June 2005, the correlation coefficient reached the minimum value during the period concerned, i.e. ‑0.85. At the end of period concerned, returns of CEZ and ERSTE BANK were significantly directly proportional again.
The mutual dependence of the returns of ČEZ and KOMERČNÍ BANKA, PHILIP MORRIS ČR and TELEFÓNICA O2 C.R. and UNIPETROL periodically changed during the period concerned. At the beginning of period concerned, correlation coefficient reached the maximum value of 0.94 for CEZ and KOMERCNI BANKA; in the half-year 2004 the value of correlation coefficient arrived at 0.94 also for CEZ and PHILIP MORRIS CR; at the end of period concerned, the value of correlation coefficient for CEZ and TELEFÓNICA O2 CR was 0.79; for CEZ and UNIPETROL attained 0.93. At the beginning of 2004, the minimum level of correlation coefficient (giving evidence of inverse proportion relation) of CEZ and KOMERCNI BANKA got to ‑0.62; at the beginning of period concerned, it attained ‑0.90 for CEZ and PHILIP MORRIS CR; at the beginning of June 2004 it was ‑0.80 for CEZ and TELEFÓNICA O2 CR; and at the end of June 2003 it was ‑0.79 for CEZ and UNIPETROL.
The issue has been traded on the Prague Stock Exchange since October 2002, the average annual rate of return has decreased from 57.6% to 15.0% since June 2004. The maximum value of risk, determined as standard deviation of the rate of return, was achieved in March 2005, i.e. 14%. Subsequently, the risk has been gradually decreasing, reaching the value of 2.6% in May 2006.
The correlation coefficients of the rate of return for ERSTE BANK and KOMERČNÍ BANKA and PHILIP MORRIS ČR from October 2004 to July 2005 show a significant direct proportion. In September 2005 and at the end of the period concerned the rates of return of ERSTE BANK and KOMERČNÍ BANKA have been independent. In September 2005, the rates of return of ERSTE BANK and PHILIP MORRIS ČR have been in indirect proportion and, by the end of the period concerned, the rates of return again show a significant direct proportion.
The rates of return of ERSTE BANK and TELEFÓNICA O2 C.R. have been indirectly correlated from October 2004 to December 2005, the maximum level of the correlation coefficient is ‑0,47 at the end of May 2005, the minimum is ‑0.83 in October 2005. As of 31 January 2006, the correlation coefficient equalled ‑0.04.
The returns of ERSTE BANK and UNIPETROL were practically independent from October 2004 to January 2005, later negatively correlated (commencing in March 2005); the correlation coefficient fluctuates at around ‑0.7. By the end of the period concerned, the rates of return of ERSTE BANK and UNIPETROL are significant directly proportional. The dependence of the returns of ERSTE BANK and ČEZ was discussed in the previous text.
The maximum average annual rate of return during the period concerned, i.e. 58.5%, was achieved by the end of March 2003. Since then, the average rate of return has been decreasing, except for a flat local peak in September 2004; the closing value as of 30 June 2006 is 5.6%. The development of the risk determined as standard deviation of the rate of return does not differ significantly from the estimation using the variation coefficient of quotations. The maximum value of risk, determined as standard deviation of the rate of return, was achieved in late September 2002, i.e. 34.7%, while the variation coefficient of quotations reached its peak of 27.1% in June 2002. After that the risk decreased and during the last year of the period concerned, it has been fluctuating between 4.7% and 10.1%.
In March 2002, the correlation coefficients of the rate of return for KOMERČNÍ BANKA and PHILIP MORRIS ČR reached the minimum value of ‑0.66. For a considerable part of the period concerned, the returns reported direct proportion to a varying extent. By the end of the period concerned, the rates of return of KOMERČNÍ BANKA and PHILIP MORRIS ČR are practically independent.
The maximum value of return dependence for KOMERČNÍ BANKA and TELEFÓNICA O2 C.R. was 0.91 in September and October 2002, practically indirect proportion was reached in November 2003. By the end of the period concerned, the rates of return of KOMERČNÍ BANKA and TELEFÓNICA O2 C.R. are practically independent.
Correlation coefficient of return rate of KOMERČNÍ BANKA and UNIPETROL has a similar course. The maximum value of 0.75 was achieved in early March 2002, the minimum value of ‑0,96 in the half of 2004. The dependence of the returns of KOMERČNÍ BANKA and ČEZ and ERSTE BANK was discussed in the previous text.
The maximum average annual rate of return during the period concerned, i.e. 48.6%, was achieved in February 2003. Since then, the average rate of return has been decreasing, except two local peaks in late August 2004 and in March 2006; the closing value as of 30 June 2006 is 2.5%.
The volatility development as standard deviation of return rate has, except the first half-year 2003 minimum, as good as quite a reverse development than the estimation via variation coefficient of quotation. Whilst variation coefficient of quotation tends to arrive at the maximum value at the beginning of period concerned, in March 2005 the volatility as standard deviation of return rate reaches the maximum value of 24.2%.
By the end of the period concerned, the rates of return of PHILIP MORRIS ČR and TELEFÓNICA O2 C.R. show practically direct proportion. Practically indirect proportion was reached in June 2004.
The dependence of the rate of return of PHILIP MORRIS ČR and UNIPETROL gradually changed during the period concerned, from indirect proportion to relevant direct proportion. The minimum value of the correlation coefficient, ‑0.94, was achieved in late July and early August 2003, the maximum value of 0.78 proving the relevant direct proportion was achieved in late October and early November 2005. The dependence of the returns of PHILIP MORRIS ČR and ČEZ, ERSTE BANK and KOMERČNÍ BANKA was discussed in the previous text.
The average annual rate of return during the entire period concerned increased continuously from ‑69.2% in January 2002 to 34,6% in March 2006. The development of the risk determined as standard deviation of the rate of return differs from the estimation using the variation coefficient of quotations particularly in 2002 and 2003. While the variation coefficient of quotations reaches the maximum value by the beginning of the period concerned, the risk determined as standard deviation of the rate of return reaches a minimum value of 4.7% at the beginning of the period concerned, while the maximum value of 36.8% was achieved in late August 2002. This difference is understandable, because the variation coefficient of quotations reflects the decreasing quotation in 2001 from CZK 569.10 to CZK 184, which relatively precisely defines the market price model. For the last two years, the risk level development has been in both cases similar and the risk fluctuated by the end of the period concerned between 7.3 and 12.3%.
The minimum value the correlation coefficient of the returns of TELEFÓNICA O2 C.R. and UNIPETROL ‑0.76 was achieved in July 2002, while the maximum value of 0.90 was reported in early November 2003. The dependence of the returns of TELEFÓNICA O2 C.R. and ČEZ, ERSTE BANK, KOMERČNÍ BANKA and PHILIP MORRIS ČR was discussed in the previous text.
The average annual rate of return during the period concerned reached its minimum value in early June 2002, i.e. ‑47.6. After this, the average rate of return continuously increased, except a local peak in February 2005, the maximum value of 83.5% was reached in March 2006. The risk determined as standard deviation of the rate of return reached a maximum value of 39.6% in late September 2003, the minimum value of 6.4% was reported in May 2006.
The dependence of the rate of return of UNIPETROL and ČEZ, ERSTE BANK, KOMERČNÍ BANKA, PHILIP MORRIS ČR and TELEFÓNICA O2 C.R. was discussed in the previous text.
Roman Pospíšil, Karel Pliska, Michal Patka, 09-Jul-06