 It is a recognized fact in the field of investment that an optimal portfolio cannot be derived simply by adding numerous individual investments with the characteristics of merely risk and return. Rather to design an optimal portfolio, an investor must consider the relationship between the investments so that an investment objective can be met effectively and efficiently. Now how to design an optimal portfolio is the subject of portfolio theory. There are certain background assumptions of this theory, these say that an investor wants to maximize his return from all of the investments he holds. For a certain level of risk, the portfolio of an investor includes all types of liabilities and assets. The relation between the returns of all of the assets in the investment portfolio is very much important because it is the returns of the investment in the portfolio and the underlying investment's risk that determined trade-off for the investor. So we can say that a good portfolio is not merely the collection of individually good securities. There is a concept of risk aversion which says that given a choice between two assets with equal return, most of the investors will go for the investment having least riskiness. It is said that investors are risk averse and we have certain evidence. Let me include insurance plan where someone pays a little amount at present in order to avoid a larger amount of cash outflow in future. Similarly, different grades of bonds with varying yields of varying degree of credit risk are offered to the investors of varying likings for the riskiness. But everybody is a risk averse similarly neither the investors are fully risk averse. So this means that risk preference and risk aversion are basically the attitudes towards the risk which is also subject to the amount involved. We can conclude this discussion here while saying that recognizing the attitude of the risk preference and the risk aversion we can derive an assumption that most of the investors with the large investment portfolio are risk averse and a positive relationship therefore can be expected between the expected return on the investment and the risk associated with these investments. Now let me talk about Markowitz portfolio theory. In the early 60s the term risk was talked without using an appropriate risk mirror. It was the Markowitz who at first developed basic portfolio model. His portfolio theory basically quantified the riskiness of investment into an appropriate risk mirror. The Markowitz portfolio theory derives expected return of a portfolio for a portfolio of assets and the associated expected riskiness of these assets in the portfolio. This theory shows that variance of the return on the assets is a meaningful measure to determine the portfolio riskiness. This portfolio theory derives the formula for computing the variance of a portfolio showing that how to effectively diversify a portfolio. So Markowitz was the first person that determined a riskiness formula to measure the riskiness of a portfolio. There are certain assumptions of the Markowitz portfolio theory. The first is that investors consider each investment alternative as being represented by a probability distribution of the expected rate of returns over some holding period and this holding period may be of one week, of one day, one month, one year and so on. Investors maximize one period expected utility and their utility curve show diminishing marginal utility of wealth. This means that as they move towards higher riskiness of an investment their expected rate of return goes on decreasing. Investors estimate risk of the portfolio on the basis of variability of the expected rate of returns. So higher is the variation in the returns, larger is the riskiness associated with these returns. Investors base their decisions solely on the expected returns and the risk. So their utility curves are the function of expected return and the expected variance of the returns only. So risk and return determine the trade-off for the investor as per this particular theory. For a given level of riskiness the investors prefer higher returns. This means that for a given level of expected return the investor will go for the investment that carries least riskiness. This means that to be an efficient single asset or portfolio of assets it must offer higher expected return with the lesser risk or lesser risk with the expected rate of return at the higher level. So what are the expected rate of returns and how to determine these expected rate of returns? For an individual asset, expected rate of returns are the sum of the potential returns multiplied with the corresponding probability of each return. And for a portfolio of assets weighted average of the expected returns are for the individual investments in the portfolio. So for the portfolio returns we need to determine weighted averages in the investment baskets of the portfolio. Now how to determine these weighted averages? Basically these weights are proportion of the total value of individual investment in the portfolio. To determine expected rate of return for individual assets let's take an example. We have four probabilities four chances having assigned certain probability level and for each probability we have a corresponding rate of return. When we multiply this possible rate of return with the probability we have expected rate of return. The sum of these rate of return is then termed as the expected rate of return for individual risky asset. To determine the expected rate of return for portfolio of an investment. We have in the example four types of investments with their values in terms of absolute amount. The weights of these values are described here as 20%, 30%, 30% and 20%. Then we have the expected rate of return for each security. The multiplication of these two columns give us the expected return of individual security and summing up these weighted returns we have an expected portfolio return which is 11.5% in the example. Like expected rate of returns we have also some the measures to measure the riskiness of individual asset and the portfolio of assets. Here we have a measure called as variance or standard deviation of expected return. It is a statistical measure of the dispersion of returns around the expected value. This means that more dispersion in the expected returns greater is the uncertainty about the rate of returns. Another measure is the range of returns. This is basically the difference between the highest value and the lowest value in the series of returns. There is an advice for the investors as how to use the expected returns. This advice says that consider returns below the expectations. This means that advice can be termed as semi variance and semi variance we means it is a measure that counts deviations below the mean. How can variance or standard deviation of return can be measured for individual investment? We can see a formula of variance on the screen then we have a model to determine the standard deviation. We have four possibilities or the four probabilities of returns. We have four expected returns of a security. We have a deviation which is actual returns minus the average of these four returns. Then we have scare of these individual deviations. We have probability of each return when we multiply this probability value with these deviation squared. We have the sum of these probabilities of deviation squared and that is 0.000451. This is basically the variance. Now to standardize this we have another variance that is the standard deviation. When we remove the scare we have a standard deviation of 2.1237 and this is basically the riskiness of an individual asset.