Risk and Uncertainty - Portfolio Theory

RISK AND UNCERTAINTY. PORTFOLIO THEORY.

1.0 Introduction

Examining the Naïve diversification, portfolio theory and capital market theory for selected securities from FT all share index during the period from January 2001 till December 2005 which include monthly returns for 60 months.

The analysis undertaken will illustrate the following:

Reducing risk exposure through selecting securities randomly (naïve diversification). A comparison between individual security risk and portfolio risk will demonstrate that even with naïve diversification the risk and uncertainty of equally weighted portfolio will reduce the risk exposure for the investors. This will be examined and presented in part A of this analysis.

The relation between the risk levels [SD(R)] of portfolios to the number of securities included in the portfolio. The analysis illustrates the risk reduction opportunities offered in large portfolios, As the number of securities in the portfolio increases, the risk will be reduced significantly. Portfolios of 1, 5, 10, 15 and 20 of equally weighted securities will be identified and the relation will be examined. The analysis is presented in part B.

2.0 Risk Estimates

2.1: Answer and Analysis for Question 4 part (a). i :

Five securities are chosen randomly from the FT all share Index (Annexure A.1) with the related monthly return for each company from January 2001 till December 2005 compromising 60 monthly returns. The securities chosen are CAIRN ENERGY, HANSON, MORRISON (WM)SPMKTS, REXAM and STANDARD CHARTERED

The average monthly returns are calculated with the variance and standard deviations which represent the risk associated with each security, results are shown in Table 2.1.

The basic calculations are based on the following equations:

VAR(Rj) = E(Rj-E(Rj))2

SD(Rj)= √(VAR (Rj))

Table 2.1: Risk estimates for five randomly selected securities.

CAIRN ENERGY HANSON MORRISON

(WM)SPMKTS REXAM STANDARD CHARTERED

AVERAGE MONTHLY RETURN 0.03724 0.00878 0.00221 0.01824 0.00801

VARIANCE 0.01547 0.00609 0.00575 0.00393 0.00654

STANDARD DEVIATION 0.12437 0.07802 0.07584 0.06269 0.08087

Table 2.1 illustrates that each security has its own risk value (SD) based on the dispersion of its outcomes during the period of 60 months, figure 2.2 shows the dispersion of the selected securities returns over the study period. The SD range for selected securities