In 1959 Markowitz did the groundwork for the capital asset pricing theory also known as CAPM. He introduced the notion of mean-variance efficient portfolio. According to him it is optimal for an investor to hold a mean-variance efficient portfolio. The mean-variance efficient portfolio is a portfolio for an investor where he minimizes the portfolio return, given the expected return and maximizes expected return, given the variance. Later Sharpe and Lintner further developed the work of Markowitz. In their work it has been showed that if the investors' expectations are homogeneous and when the hold the mean-variance efficient portfolio then in the nonexistence of market friction the market portfolio will be a mean-variance efficient portfolio.

Capital Asset Pricing Model is a general equilibrium model. It not only allows improved understanding of market behavior, but also practical benefits. However, there exists a risk-free asset in the assumption of the CAPM. Investors are able to borrow and lend freely at the rate may not be a valid representation of the working of the marketplace. Therefore, in this paper, it studies that the efficient frontier of portfolio in different borrowing and lending rate. The aim of this study is to develop the mean- variance analysis theory with regard to market portfolio and provide algorithmic tools for calculating the efficient market portfolio.

Capital market theory builds on Markowitz portfolio theory and develops a model for pricing all risky assets. It relates the required rate of return for any security with the market risk for the security as measured by beta. The concept of a risk-free asset is critical to the development of capital market theory. The expected return on a risk-free asset is entirely certain and the standard deviation is zero. Covariance of a risk-free asset with a risky asset is zero. Each investor is assumed to diversify his or her portfolio according to the Markowitz model, choosing a location on the efficient frontier that matches his or her return risk preferences.

Capital market theory assumes that is all investors are efficient investors; meaning investors follow Markowitz idea of effective leading edge investors choose to invest in portfolios along with the frontier. Next is investors borrow and/or lend money at the risk-free rate; meaning the rate remains fixed for any amount of money. Next is all assets are infinitely divisible; meaning partial shares can be purchased and the stocks can be “infinitely divisible”. Next is no taxes and transaction costs; meaning assuming that investors' results are not affected by taxes and transaction costs. Next is all investors have the same probability for outcomes, meaning when deciding the expected