Abstract
After selecting three (3) S&P 500 companies, quantitative models have been applied using price and return data from a website like Investing.com for a 5-yrs period, and the corresponding spreadsheet and SAS models have been built. Using graphs, tables and figures, the document presents the results of the analysis.
Extract
[...] Financial statistics Case of APPLE Inc. (AAPL) Min -12,86% =MIN(C3:C1260) VaR 99% HS =PERCENTILE(C3:C1260,0.01) VaR 99% DN =-NORMSINV(0.99)*F9 VaR 95% HS =PERCENTILE(C3:C1260,0.05) VaR 95% DN =-NORMSINV(0.95)*F9 Average 0,19% =AVERAGE(C3:C1260) Median 0,14% =MEDIAN(C3:C1260) Max 11,98% =MAX(C3:C1260) Daily SD 2,14% =STDEVP(C3:C1260) Annual SD 33,95% =F9*SQRT(252) Skewness -0,01 =SKEW(C3:C1260) Kurtosis 5,75 =KURT(C3:C1260) Min / Daily SD 6,02 =ABS(F1)/F9 Comment: The chart shows that Apple Inc's stock price trend is upward, with multiple bullish impulses over the 5-year period Financial statistics Case of Nvidia Corporation (NVDA) Min -18,45% VaR 99% HS VaR 99% DN VaR 95% HS VaR 95% DN =-NORMSINV(0.95)*F9 Average 0,28% =AVERAGE(C3:C1260) Median 0,30% =MEDIAN(C3:C1260) Max 17,16% =MAX(C3:C1260) Daily SD 3,11% =STDEVP(C3:C1260) Annual SD 49,34% =F9*SQRT(252) Skewness 0,04 =SKEW(C3:C1260) Kurtosis 3,51 =KURT(C3:C1260) Min / Daily SD 5,94 =ABS(F1)/F9 =MIN(C3:C1260) =PERCENTILE(C3:C1260,0.01) =-NORMSINV(0.99)*F9 =PERCENTILE(C3:C1260,0.05) Comment: The trend in Nvidia Corporation's share price has been on the rise since October 2022 and this increase has been drastic since January 2024 when it went from 475 to 942 in just three months. [...]
[...] Augmented Dickey-Fuller test show that NVDA is stationary. Autoregression Case of AAPL Comment: The probability Prob = 0;0000 less than 0,05 Thus, AAPL has a unit root. Augmented Dickey-Fuller test show that AAPL is stationary. Autoregression Vector Autoregression Estimates: Case of AAPL: We have Autoregression Vector Autoregression Estimates: Case of MDFT: We have Autoregression Vector Autoregression Estimates: Case of NVDA: We have Seasonal Case of AAPL: Comment: Over the 5-year period, we see that the average per season is highest in July for the AAPL company and lowest in September Seasonal Case of MDFT: Comment: Over the 5-year period, we see that the average per season is highest in november for the MDFT company and lowest in September. [...]
[...] Then we will study the dynamics of each of these three variables in relation to their values in the past by expressing for example the variable Yt as a function of Yt-1 and/or Yt-1 and Yt-2 Autoregression Case of MDFT Comment: The probability Prob = 0;0000 less than 0,05 Thus, MDFT has a unit root. Augmented Dickey-Fuller test show that MDFT is stationary. Autoregression Case of NVDA Comment: The probability Prob = 0;0000 less than 0,05 Thus, NVDA has a unit root. [...]
[...] Single-index model Case of AAPL We run a linear regression of past returns of AAPL's stock againts past returns of the market index. Comment: alpha = 0,029 is positive. Thus, the stock/porfolio of AAPL performs better than the market, Beta = 0,522 is less than the stock/porfolio of AAPL is less risky than the market. Single-index model Case of NVDA We run a linear regression of past returns of NVDA's stock againts past returns of the market index. Comment: alpha = 0,07 is positive. [...]
