Abstract This essay is about understanding the key issues related to portfolio analysis and investments. The scope of this essay will be limited to US stock markets only. This essay will build on existing portfolio theory and discuss the different types of risks investors might face and how they manage those risks. Topics such as the efficient frontier and optimal portfolios will be considered, as well as their relevance to investment theory, under the assumption of direct investment in the stock market. DETERMINING THE PURPOSE OF YOUR INVESTMENT One of the steps in building an investment portfolio is establishing objective investments. Investment goals are the financial goals you want to achieve by investing (Gitman and Joehnk, 2005). In other words, what do you want these investments to do for you or why you are investing in the first place. Some common investment goals include (Gitman, et al, 2005): 1) accumulate retirement funds, 2) increase current income, 3) save for major expenses, or 4) protect income from taxes. To get a stock valuation that fits certain risk tolerance levels and to maximize returns, investors should have an idea of ​​how much time and money they have to invest and the returns they are looking for (Investopedia.com, 2006).MODERN INVESTMENT THEORYModern investment theory, also known as modern portfolio theory (MPT), was introduced by Harry Markowitz with his article "Portfolio Selection", which appeared in the 1952 Journal of Finance (riskglossary.com, 2006). Before Markowitz's work, investors focused on evaluating the risks and returns of individual stocks that offered the best profit opportunities with the least risk and then built a portfolio from these (riskglossary.com, 2006). MPT is defined, according to investorwords. com (2005), as an overall investment strategy that seeks to construct an optimal portfolio by considering the relationship between risk and return, measured in particular by alpha, beta and R². MPT uses several basic statistical measures to develop a portfolio plan (Gitman, et al, 2005). Included are expected returns and standard deviations of returns for both stocks and portfolios, as well as the correlation between returns (Gitman, et al, 2005). Detailing the mathematics of diversification, Markowitz proposed that investors focus on selecting portfolios based on their overall risk-return characteristics instead of simply compiling portfolios from securities that individually have attractive risk-return characteristics (riskglossary.com, 2006). This theory proposes that the risk of a particular security should not be considered on a standalone basis, but rather in relation to how the price of that particular security varies in relation to the change in the price of the market portfolio (investorwords)..