Question

a) It is commonly accepted that there are gains from adding securities to an investment portfolio. Explain what is meant by this statement. (Your answer should include a discussion and example regarding systematic and non‐systematic risk as well as an indication of the optimal number of assets to be included within a portfolio in theory and in practice.) ​​​​​

(b) The following table provides monthly percentage price changes for two well known market indexes.

Month	Russell 2000	Nikkei
1	0.04	0.04
2	0.10	‐0.02
3	‐0.04	0.07
4	0.03	0.02
5	0.11	0.02
6	‐0.08	0.06

Answer the following:   ​​

(i) What have you assumed about the distribution of data (that is, have you assumed the data is a sample or a population).

(ii) Calculate the expected monthly rate of return and standard deviation for each market index.

(iii) Calculate the correlation coefficient for Russell 2000 – Nikkei.

Answer 1

a) Gains from adding securitie to a portfolio

The benefits from diversification (that is, adding securities to a portfolio) increase as more and more securities with less than perfectly positively correlated returns are included in the portfolio. As the number of securities added to a portfolio increases, the standard deviation of the portfolio becomes smaller and smaller. Hence an investor can make the portfolio risk arbitrarily small by including a large number of securities with negative or zero correlation in the portfolio.

But, in reality no securities show negative or even zero correlation. Typically, securities show some positive correlation, that is above zero but less than the perfectly positive value (+1). As a result, diversification results in some reduction in total portfolio risk but not in complete elimination of risk. Moreover, the effects of diversification are exhausted fairly rapidly. That is, most of the reduction of portfolio standard deviation occures by the time the portfolio size increases to 25 to 30 securities. Adding securities beyond this size brings about only marginal reduction in portfolio standard deviation.

Adding securities to a portfolio reduses risk because securities are not perfectly positively correlated. But the effects of diversification are exhaused rapidly because the securities still positively correlated to each other though not perfectly correlated. Had they been negatively correlated, the portfolio risk would have contined to decline as portfolio size increased. Thus, in practice, the benefits of diversification are limited.

The risk of an individual security comprises two components, the market related risk called systematic risk and the unique risk of that particular security called unsystematic risk. By combining securities into a portfolio the unsystematic risk specific to different securities is cancelled out.

Systematic risk comprises factors that are external to a company and effect a large number of securities.

Examples: 1. Changes occur in the economic, political and social systems constantly.

2. Recession and wars they effect the entire market and cannot be avoided through diversification.

Unsystematic risk comprises of factors that internal to companies and only affect those particular companies.

examples: 1. Sudden strike by the employees of a company.

2. tecnological changes causes business risk etc.

b) i. I have assumed that the distribution of data is population

ii. Monthly rate of return for each market index is as follows