The thesis proposes a framework for risk-averse investors to choose the best asset by balancing investment returns and the amount of risk they are willing to take, using the Mean-Variance Model and the Capital Asset Pricing Model (CAPM). The study investigates whether beta is constant over time and analyzes the stability of beta in some Indian market stocks using the rolling window approach. The study period is from 2010 to 2020, covering the American and Indian markets. The empirical findings show that the Indian market beta exhibits excessive volatility, which could significantly affect risk estimation accuracy, and the study emphasizes the importance of considering the impact of portfolio constraints on achievable portfolio characteristics when designing investment strategies. The study confirms the high volatility of the market during the observed period, as demonstrated by the significant volatility of the market beta. The Bartlett test and the Kolmogorov-Smirnov test confirm that daily returns are randomly distributed and conform to a Gaussian (normal) distribution. The findings support previous research by Blume (1975), emphasizing the varying risk levels of the market, suggesting that investors may need to adjust their investment strategies by increasing or decreasing their exposure to specific stocks with higher levels of volatility.