Good day, in this lecture, we're going to talk about the assumptions behind the portfolio combinations. Let's start with the modern portfolio theory. Modern portfolio theory is an investing model in which investors invest with the motive of taking the minimum level of risk and earning the maximum amount of return for that level acquired risks. The modern portfolio theory is a helpful tool for investors as it helps them in choosing the different types of investments for the purpose of the diversification of the investment, and then making one portfolio by considering all the investments. According to modern portfolio theory, all the investments are combined together in a way that reduce the risk in the market through the means of diversification, and at the same time also generates a good return in the long-term to the investors. In this graph, on the y-axis, we have the expected return. On the x-axis, we have the risk. Then we have the risk-free rate. The assumptions of the modern portfolio theory are that returns from the asset are distributed normally. The investors making the investment is rational and will avoid the unnecessary risk associated, and investors will give their best in order to maximize return for all unique situation provided. The assumption behind modern portfolio theory is that investors are fully rational. Also, among the assumption, we have that all investors are having access to the same information set which we know is not always the case. This assumption is relatively strong. Also, the costs pertaining to the taxes in trading is not considered while making decisions. All the investors are having the same views on the rate of return expected. The single investor alone are not feasible and capable enough for influencing the prices prevailing in the market. Last assumption is that unlimited capital at risk-free rate of return can we borrowed. Let's see the capital asset pricing model which is a very popular model in finance. Capital asset pricing model is an equilibrium model that measure the relationship between risk and expected return of an asset based on the asset sensitivity to movements in the overall stock market. Capital asset pricing model is used to price the risk of an asset or a portfolio of assets. The model is based on the idea that there are two types of risks. One is systematic risk, and the other one is idiosyncratic risk. The investors should be compensated for both types of risks as well as the time value of money. Systematic risk refers to market risk whereas idiosyncratic risk refers to the risk of an individual asset. The time value of money refers to the difference between the present value of money and future value of money. The use of the model to measure the required rate of return for a capital budgeting projects, this can be done by using capital asset pricing model. The capital asset pricing model states that an asset expected return is equal to the risk-free rate plus the risk premium. The risk-free rate refers to the return on an investment without risk, for instance, can be investing in German bunds or US treasury bonds. The risk-free rate represents the time value and this is basically the time value of the money. On the other hand we have the risk premium. The risk premium represent the incremental return for investing in a risky asset. In capital asset pricing model, it is defined as the market premium or the overall stock market return less the risk-free rate multiplied by the beta of the asset. Beta is a factor that measure an asset sensitivity to movements in the overall stock market. According to capital asset pricing model, riskier assets should yield higher returns. The market reward to risk ratio is effectively the market risk premium and by rearranging the above equation and solving for expected return we obtain the capital asset pricing model. In this formula here, we have the capital asset pricing model where expected return is the ERi is the expected return on investment. Rf is the risk-free rate. The Bi, that's the beta of the investment and the difference between the ERm and risk-free rate is the market risk premium. The goal of the model is to evaluate if a stock is reasonable, is valued properly when the risk and the time value of money are compared to the expected return. A relevant element to consider in capital asset pricing model is the efficient frontier. The efficient frontier also known as a portfolio frontier is the set of ideal or optimal portfolios that are expected to give the highest return for a minimum level of risk. This frontier is formed by plotting the expected return on the y-axis, and the standard deviation as a measure of risk on the x-axis. The efficient frontier tell us that the risk and return trade off for certain portfolio. For building the frontier, there are three important factors that we have to take into consideration. They are the expected return, the variance or standard deviation as a measure of the variability of a return and then the covariance of one of the asset's return to that of another asset. The capital asset pricing model is a model established by Harry Markowitz in 1952. After that he spent a few years on research about the same which eventually led to him winning the Nobel Prize in 1990. The efficient frontier rate portfolios investment on the scale of return versus risk and compound annual growth rate of an investment is a commonly used asset return component while standard deviation depict a risk methods. The efficient frontier theory was introduced by Harry Markowitz. It is the starting point of modern portfolio theory.