PORTFOLIO MANAGEMENT

Portfolio Management

Name of Writer

Name of Institution

Table of Contents

SECTION 1Introduction3

SECTION 2Discussion3

2.1.1Method 1 - First principles4

2.1.2Method 2 - Historical beta estimated using a single-index market model5

2.1.3Method 3 - Adjusted beta5

Equally-weighted portfolio for comparison6

SECTION 3Theoretical Framework7

3.1.1Beta7

3.1.2Sharpe Ratio7

3.1.3Coefficient of Determination8

3.1.4Treynor Ratio9

3.1.5Systematic Risk9

3.1.6Unsystematic Risk10

3.1.7Probability and Expected Value10

3.1.8SML and CML:11

SECTION 4Conclusion12

4.1.1Choice of the Market Portfolio is Important12

4.1.2Beta is Probably Dynamic and Possibly Unstable in Short Run12

4.1.3Minimum-variance Portfolio Outperforms During Times of Crisis12

4.1.4Computing Efficiency is Higher Using Methods 2 and 313

References14

Appendix15

SECTION 5Working15

5.1.1Asset Weekly & Monthly Returns with AM, SD, GM15

5.1.2Benchmark's Weekly & Monthly Returns with AM, SD, GM16

5.1.3Asset & Benchmark's Variables17

Portfolio Management

Introduction

To make an the best possible financial commitment portfolio, traders not only have to incorporate several exclusive personal investments that have suitable risk-return features but also must consider the connection among these investment strategies that will help fulfil their financial commitment goals. The chance of a financial commitment can be calculated by determining the difference, or conventional difference of predicted profits. The bigger the difference or conventional difference, the higher the dispersal and higher the concern of upcoming profits of a financial commitment are likely to be. The connection coefficient standardizes and gives significance to the number found in the covariance. The traders can evaluate the connection between the return sequences of different investment strategies. By learning different portfolio opportunities and quantifying the risk varying for a chosen portfolio, traders can comprehend the reason why they need to broaden their investment stock portfolios and also what weightings of different investment strategies they should use to broaden.

The stock that has been used for this assignment is sony corp from the period of 12 March to 11 May 2012 a total of 9 weeks. The stock was benchmarked with the MSCI World index for the same period of time. Given below is a complete analysis of the stock and the index together , and all the working has been included in the appendix.

Discussion

According to Markowitz Portfolio Theory, a portfolio of assets is characterised solely by its return and risk:

Portfolio Expected Return:

E(Rp) = WTR

where W is an (n x 1) matrix of weights of individual assets

and R is an (n x 1) matrix of expected return of the individual assets

Portfolio Risk:

s(Rp) = {Wt COV W}½

where W is an (n x 1) matrix of weights of individual assets

and COV is the (n x n) covariance matrix of the individual stocks.

In order to obtain the minimum variance portfolio, we optimize the asset allocation such that the ex post portfolio risk is a minimum. To do that, use the optimization function of Excel to derive a minimum s(Rp) by adjusting W.

In our case, the covariance matrix COV is a 10 x 10 matrix with the diagonal elements the variance of the ten assets and the other elements the covariance between individual terms. We have use three different methods to calculate COV.

Method 1 - First principles

In method 1, we use the following formulae to calculate the elements in COV:

Var (Ri) = si2 = E(Ri)2 - E (Ri2)

Cov (Ri, Rj) = ?ij si sj

where ...