Journal

Construction & optimization of a portfolio from Dhaka Stock Exchange

(Using Sharpe’s Single Index Model)

Abstract:

The paper aims at constructing an optimal portfolio by applying Sharpe’s Single Index Model of Capital Asset Pricing. Taking DSI all share price index as market index and considering daily indices for the march’05-december’ 09 period, the proposed method formulates a unique cut off point (Cut off rate of return) and selects stocks having excess of their expected return over risk-free rate of return surpassing this cut-off point. Percentage of investment in each of the selected stocks is then decided on the basis of respective weights assigned to each stock depending on respective ‘b’ value, stock movement variance representing unsystematic risk, return on stock and risk free return vis-a-vis the cut off rate of return. Interestingly, most of the stocks selected turned out to be bank stocks.

Keywords: Sharpe’s single index model, Sharpe ratio, optimal portfolio, cut-off rate.

Literature review:

Debasish Dutt in an article published in “The Management Accountant”- November 1998, found that all the stocks selected are bank stocks .He used Sharpe single index model in order to optimize a portfolio of 31 firms from BSE for the period  October 1, 2001 to April 30, 2003 and used BSE 100 as market index.

Asmita Chitnis optimized two portfolios using single index model and compared them and he found Portfolios tend to spread risk over many securities and thus help to reduce the overall risk involved. “The greater the portfolio’s Sharpe’s ratio, the better is it’s performance”.

“This method of construction of optimal portfolio and further evaluation of its performance is very effective and convenient as revision of the optimal portfolio can be an ongoing exercise. The existence of a cutoff rate is also extremely useful because, most new securities that have an excess return-to beta ratio above the cutoff rate can be included in the optimal portfolio”.

Introduction

Modern portfolio theory (MPT) or portfolio theory was first introduced by Harry Markowitz with his paper popularly known as “Portfolio Selection”. Explaining the concept of diversification, Markowitz proposed that investors are to focus on selecting portfolios based on their overall risk-reward characteristics .In other words; investors should select portfolios and not individual securities.

Sharpe’s Single Index Model

Markowitz’s efficient Portfolio combines securities with a correlation of negative one in order to reduce risk in the portfolio to gain optimum return. In order to study a N-security portfolio using Markowitz model, the inputs required are:

• Expected returns

• Variances of return

• (N²-N)/2 covariance’s

As a result, Markowitz’s model requires [N (N + 3)]/2 separate pieces of information for identification of efficient portfolio. Hence the model is complex in nature. William Sharpe added with Markowitz’s work and found out a more simplified model; where he considered the fact that relationship between securities occur only through their individual relationships with some index or indices.

As a result of which the covariance data requirement reduced from (N²-N)/2 under Markowitz model to only N measures of each security as it relates to the index. Overall, the Sharpe model requires [3*N + 2] separate pieces of information as against [N (N + 3)]/2 for Markowitz.

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