Example of the Scatterplots:

6. Analyze the series of data in the plots and explain the main conclusion, which we can make in the base of this charts.

7. Create the tables for the calculation of the unbiased point estimators of the Net return over month R_t for each stock (two-sided deviations):

Unbiased point estimators of the Net return over month Rt for "________"
Sample Mean m R
Sample Variance D R
Sample Standard Deviation σ R;
Coefficient of variation CVR

8. Calculate unbiased point estimators and define them appropriate names.

9. Using the Histogram analysis tool (tab Data / group Analysis / Data Analysis) calculate absolute individual frequencies for a cell range of data of the Net return over month of each stock (specify in the dialog window of the Histogram only Input range and Output ranges).

10. Add the column "Probability density function of the Net return over month" and calculate the values of this column as a ratio of Frequency and sum of Frequency by column (Note: ).

Probability distribution for net return over month

ON "_________"

Bin	Frequency	Probability density function of the Net return over month p(Rt)
…	…	…
More

11. Define the names of this arrays.

12. Insert the scatterplot "Probability distribution for net return over month".

Example of the Scatterplot:

13. Analyze the plots and explain the conclusion about comparative amount of expected volatility by each stock, which we can make visually.

INTERMEDIATE CONCLUSION

14. Create the tables for the calculation of the semi-characteristics (we estimate earnings risk) for the Net return over month R_t.

Semi-characteristics (one-sided deviations)
Sample Semi-Variance SD Rt
Sample Semi-Standard Deviation Sσ Rt
Semi-Coefficient of variation SCVRt

For this purpose to add columns to the main tables for each stock:

Deviation of the net return from the mean	i – the indicator of the undesirable (risky) deviations
……	…….

15. Calculate:

• deviation of the Net return over month R_t from its expected value m_R

R _t – m _R

• _i –“ counters”, allows to include into the calculations only negative (risky) deviations:

• semi-Variance SD _R (only undesirable deviations):

 In the numerator of the formula use a function SUMPRODUCT.

• Semi-Standard deviation: SCV_R.

• Semi- Coefficient of variation: SCV_R = ( Sσ_R / m_R) · 100% .

16. Define them appropriate names.

17. Build the charts showing the dependence of the standard deviation from the expected profit rate for two-sided and one-sided deviations. Analyze the results.

For example:

18. Make the conclusion, if the net return over month distribution is symmetric or not and what outcome (positive or negative) is more probable.

 To automate the calculations use a function IF() using the following algorithm:

IF SCV_R = CV_R, then net return over month distribution is symmetric

IF SCV_R >CV_R, then net return over month distribution is not symmetric and more probable positive outcome

IF SCV_R < CV_R, then net return over month distribution is not symmetric and more probable negative outcome

19. In the base of the obtained results of quantitative risk analysis of stocks formulate the advice for decision maker, provides for possible automatically generate the answer for making a decision on the choice of type of stocks, that guarantee the best combination of the expected value of Net return over month and degree of risk.

ADVICE FOR DECISION MAKER

 To automate the calculations use a function IF() using the following algorithm:

IF m _R1=m _R2 and σ _R1 < σ _R2, then choose stocks of the 1^st type

IF m _R1=m _R2 and σ _R2 < σ _R1, then choose stocks of the 2^nd type

IF m _R1>m _R2 and σ _R1 < σ _Rx2, it is logical to choose stocks of the 1^st type

(comment semi-characteristics)

IF m _R2>m _R1 and σ _Rx2 < σ _R1, it is logical to choose stocks of the 2^nd type

(comment semi-characteristics)

IF m _R1>m _R2 and σ _R1 > σ _R2 and v _R1 < v _R2, it is logical to choose stocks of the 1^st type

(comment semi-characteristics)

IF m _R2>m _R1 and σ _Rx2 >σ _R1 and v _R2 < v _R1, it is logical to choose stocks of the 2^nd type

(comment semi-characteristics)

otherwise – the choice is determined by the decision maker, but it is desirable to comment on the expected results.