Question

Familiarity with random variables is essential to understand the basics of portfolio theory. Given that next assignment is about portfolio formation, you need to strengthen your skills in dealing with random variables. Please review and explain the significance of basic concepts about random variables, namely, the mean, the variance, the standard deviation, and the correlation?

Answer 1

Mean

The expected return is the return an investor best guesses as to the return on an asset. One uses mean of historical returns or uses the returns from possible outcomes and the probabilities of those outcomes, to arrive at an expected return. This mean is helpful in finding the average return of the portfolio.

Variance and Standard Deviation

Risk is the possibility that actual returns might differ, or vary, from expected returns. It is important for investor to estimate the magnitude and likelihood of the difference between actual and estimated returns. By using the concepts of variance and standard deviation, investors can judge not only how wrong their estimates might be, but also estimate the likelihood, or probability, of favorable or unfavorable outcomes.

Correlation

The concepts of correlation is used to measure how the returns on assets relate to each other and the market in general and how it can be used to reduce the overall risk to the investor. A high positive correlation between the assets means higher risk and negative correlation means lower risk.