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- 2. Normal distribution and standardization
- 3. Obs (CP) Mean Obs - Mean (Obs – Mean)/SD 355 515.5 -160.5 -0.65748 385 515.5 -130.5 -0.53458 410 515.5 -105.5 -0.43217 510 515.5 -5.5 -0.02253 84 515.5 -431.5 -1.7676 304 515.5 -211.5 -0.86639 853 515.5 337.5 1.382541 770 515.5 254.5 1.042539 864 515.5 348.5 1.427602 620 515.5 104.5 0.428076 Mean value = = 515.5 Mean value=0 SD = = 244.11 SD= 1
- 4. If X is a random variable and has a normal distribution with mean µ and standard deviation σ, then the Empirical Rule says the following: About 68% of the x values lie between –1σ and +1σ of the mean µ (within one standard deviation of the mean). About 95% of the x values lie between –2σ and +2σ of the mean µ (within two standard deviations of the mean). About 99.7% of the x values lie between –3σ and +3σ of the mean µ(within three standard deviations of the mean). The z-scores for +1σ and –1σ are +1 and –1, respectively. The z-scores for +2σ and –2σ are +2 and –2, respectively. The z-scores for +3σ and –3σ are +3 and –3 respectively.
- 5. If a stock has a mean return of 8% and a Std. Dev of 10%. Find its max and min value upto 3 std dev assuming that the data points are distributed normally Mean = μ = 0.08 Std dev = σ = 0.1 Formula for min and max value μ ± zσ Min and max values for 1 std dev μ ± zσ = μ ± 1σ = 0.08 ± 1*0.1 = -0.02 to 0.18 (About 68% of the x values lie Between -0.02 and 0.18) Min and max values for 2 std dev μ ± zσ = μ ± 2σ = 0.08 ± 2*0.1 = -0.12 to 0.28 (About 95% of the x values lie Between -0.02 and 0.18) Min and max values for 3 std dev μ ± zσ = μ ± 3σ = 0.08 ± 3*0.1 = -0.22 to 0.38 (About 99.7% of the x values lie Between -0.02 and 0.18)
- 6. What is the probability that a stock with mean return of 8% and standard deviation of 10% would yield a return of 6% or less. The probability that return is less than 6% [P(x<6)=0.4207]
- 7. What is the probability that a stock with mean return of 8% and standard deviation of 10% would yield a return of 15% or less. The probability that return is less than 15% [P(x<15)=0.7580]
- 8. What is the probability that a stock with mean return of 8% and standard deviation of 10% would yield a return between 12% and 18% [P(x<12)=0.6554] [P(x<18)=0.8413] [P(12<x<18) = 0.8413 – 0.6554 = 0.1859]
- 9. Covariance and correlation • Covariance: Co-movement between two assets • Correlation: Standardized version of covariance
- 10. Covariance (Historical data) Given below are the closing stock prices of two companies. Find out the covariance between them. Year Raincoat comp Sunglass comp 2017 100 300 2018 90 330 2019 80 350 2020 75 360
- 11. Covariance (Probabilistic data) You bought a share of Raincoat company for Rs 120 and one share of Sunglass company for Rs 280. Under the current scenario, three probabilities of share price movements for the companies are likely Prob RC SC 0.3 100 300 0.2 90 330 0.5 80 350
- 12. Beta
- 13. Beta (Sensitivity) Systematic risk Historical data
- 14. Beta (Sensitivity) Systematic risk Probabilistic data