1. Calculating Expected Return for a Single Investment. Consider investment A, which has a 20% probability of producing a 15% return on investment, with a 50% probability of producing a 10% return, and 30% probability that it will produce a 5% loss. This is an example calculating a discrete distribution of probabilities for a potential outcome of a return. The probabilities of each potential return are derived from examination of historical data on the previous returns of the investment asset being evaluated evaluated. The specified probabilities, for this case, can be derived from examination of the asset's performance over the previous 10 years. We will assume that it has produced an investment return of 15% in two of of those 10 years, a 10% return in five of the 10 years, and a 5% loss in three of the 10 years In three of those 10 years. Calculating Expected Return of a Portfolio 2.A calculation of an expected return is not restricted to the calculation of a single investments. This can be performed on a portfolio too. Average expected return for of an investment portfolio is a balanced value of expected returns of each of its components. The components are weighted as a percentage of of the total value of the portfolio. Examining the weighted average of a portfolio's assets assets can also help investors evaluate the diversification of their investment portfolio. portfolio. To help illustrate the anticipated investment portfolio returns, suppose that the investment portfolio is composed of investments in three asset classes. A portfolio consists of investments in three assets, X, Y, and Z. $2,000. invested in X, $5,000 invested in Y, and $3,000 invested in Z. Assume that the expected returns for X, Y, and Z have been calculated to be 15%, 10%, and 20%, respectively. From the respective investments in each component asset, please calculate the The expected return on the portfolio. Analyzing Investment Risk 3.Investors also need to consider, in addition to calculating expected returns, the the risk characteristics of investment assets. Doing so helps determine whether the portfolio component(s) are consistent with the risk tolerance of the investor and the individual investor's investment goals. Assume in this example exercise that the two components of the portfolio showed the below returns returns, respectively, over the past 5 year period: Portfolio component A: 12%, 2%, 25%, -9%, 10%. Portfolio B component: 7%, 6%, 9%, 12%, 6%. Calculation of expected returns for both portfolio components gives the same figure: an expected return of 8%. figure: the expected return of 8%. When each component is considered, however for risk premised on the variation in the expected average yield from one year to the next, you find that one portfolio carries more risk than the other portfolio. Calculate the standard deviations of the respective portfolios and explain their risks.