Minimising Investment Risk in Sainsbury and Halfords

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In the modern world, companies and share holders aim is to gain maximum profit at minimum risk. Risk can be controlled, if thorough understanding of market is done. Risk also plays an important role in corporate finance both for company and investors. Companies face inconsistency in project cash flow, on the other hand investors faces unpredictability in capital gains and dividends (Watson and Head 2010). A Portfolio can be defined as a combination of securities. Portfolio analysis is a method for selecting the finest range that gives maximum return at minimal risk at various uncertain environments (Huang 2010). For the purpose of the assignment the author had selected one of the well performing retailer M/s Sainsbury and leading Automobile accessories retailer M/s Halfords. In this part of assignment share prices of Sainsbury and Halfords are taken on monthly basis for five years (December 2005-November 2010) and analysis is made [Refer Table-1 in Appendixes].

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Mean,Variance and Covariance

Based on the above table, the mean of Halford’s equity is 0.002400 and that of Sainsbury is 0.002046. Variance measures the volatility from an average. Volatility is a measure of risk, it helps determine the risk an investor might take on when purchasing a specific security ( No Date). The variance of Sainsbury (0.004600) is higher compared to that of Halford (0.004293). “Covariance is basically a number that reflects the degree to which two variables vary together” (Howell 2008, p.180) Positive covariance indicates that asset returns move together. A negative covariance means returnsA move inversely ( No Date). Covariance between Sainsbury and Halford gives a positive value of 0.001572.

Descriptive Statistics

Risk on investment is measured by standard deviation (AÆ’) of the return on share (Watson and Head 2010). The standard deviation for Sainsbury is 0.0678218, which is higher compared to that of Halford 0.0655209, clearly stating that higher level of risk on Sainsbury equity. A measure of the degree to which a distribution is asymmetrical (Howell 2008, p.49). Measure of symmetry is defined as skewness. Positive skewness indicates that there is a greater probability of getting higher return. Negative skewness indicates that there is a substantial probability of a big negative return. ( No Date). The Skewness of Halford is 0.065 and that of Sainsbury is -0.840. Kurtosis refers to the scale to which the curve is peak or flat (Rubin 2010). Halford and Sainsbury have positive Kurtosis of 0.713 and 2.339 respectively. Positive kurtosis indicates a “peaked” distribution ( No Date). The correlation between Halfords and Sainsbury is 0.01(Refer Correlation Table in Appendixes).

Risk Free Rate

Risk free rate of return can be defined as the return that investors acquire without any risk of losing money (Scott[online] 2010). For the purpose of finding out the monthly risk free rate, we had taken the yearly interest rate for 3 A¼ % Treasury Gilt Maturing on 07/12/2011 (United Kingdom Debt Management Office [Online] 2010)

Efficient Frontier

Efficient frontier can be defined as situation of maximum return from minimum risk ( No Date). Different combination of securities creates different level of return. The efficient frontier details the best of these security combinations ( No Date). The risk free rate for investing on the UK guilt is 0.00051573 which gives maximum return with minimum risk. Minimum risk is observed at the ratio 55:45 that of Halford and Sainsbury. Curve above this point can be termed as efficient frontier.

Investment Suggestion

Risk and return plays an important role for investment in a company. Diversification of risk can be done by investing in different portfolio. As explained earlier efficient frontier details the efficient combinations of risk and return. Based on the analysis of above data the best combination of investment is 65 % on Halfords and 35 % on Sainsbury. As per Markowitz theory the best method of investment is to diversify the portfolio.


Company Overview

Sainsbury PLC is one of the biggest retailers operating a total of 890 stores comprising 547 supermarkets and 343 convenience store. It equally owns Sainsbury Bank with Lloyds banking group. Sainsbury are also into property business having joint venture with Land Securities Group PLC and The British Land Company PLC ( 2010). Halfords is the UK’s leading retailer in Automobile maintenance and accessories. Halford portfolio comprised of 469 stores in UK and Republic of Ireland. Halfords differentiate itself from other competitors by having broad product range, strong brand recommendation, competitive pricing (achieved through scale of purchasing power) and better customer relation ( 2010).

Diversification of Risk

Modern portfolio theory explains the ability of investors to diversify the risk. It also suggest that investment on any of the portfolio’s that lies in the efficient frontier gives maximum return at minimum level of risk. Risk can be classified into systematic risk and unsystematic risk. Systematic risk details how the returns on the share are affected by factors such as business cycles, government policies and change in interest rates. Systematic risk is unavoidable or can be specified as market risk. Unsystematic risk is a specific risk for a particular share or risk of the individual company. Unsystematic risk occurs when the company is performing badly or going into liquidation (Watson and Head 2010).

Criticism and Risks of Companies

Wecker [online] (2009) states that economist criticises modern portfolio theory for several problems. Firstly they argue that the forecast are inaccurate as it refers to historical data. Based on the historical data the future returns cannot be predicted. Error in estimation of future returns has enormous effects on the Mean-Variance optimization and asset allocation. Secondly the returns are not normally distributed in reality. Thirdly lot of efforts are required to evaluate the historical data. For example, for 10 securities one to need to find out 500 values and analyse about 10 equations. Additionally Watson and Head (2010) explain that practical application of portfolio theory is associated with problems. Practically it is difficult to assume that investors can borrow at risk free rate, since individuals and company are not risk free. Problem exists in identifying market portfolios as it require knowledge of the risk and return on risky investment and their corresponding correlation and coefficients. Due to higher transaction cost it will be expensive for smaller investors. Composition of market portfolio changes eventually, these changes shift the risk free return on the efficient frontier. The systematic and unsystematic risk of Sainsbury and Halfords are detailed below. Major incident or act of terrorism, impact of the economic and market risk, environment, sustainability, financial strategy and treasury risks, interest rate risk, foreign currency risk can be considered as systematic risk for both Sainsbury and Halfords. On the other hand new business strategy adopted by the board, reputation risk, potential fraud or dishonesty by employees, health and safety risk , IT and operational infrastructure risk, product safety risk and regulatory requirements particularly in relation to planning, competition, employment, pensions and tax lawsA  can be considered as unsystematic risks. Reliance on foreign manufacturer, responsiveness to changing customer preference, liquidity risk and capital management risk are also considered by Halfords as unsystematic risk (, 2010). Despite of better sales figure the share prices of Sainsbury fell by 2.5 p from 387.1 p, on October 2010 (Lowery [online] 2010). New non executive chairman had been appointed by Sainsbury on October 2010. This change in management strategy can make the sales and share prices rise or fall ( No Date).Based on the above facts the investors cannot rely on Markowitz theory. Portfolio theory does not comment about systematic risk. The systematic risk such as major events or act of terrorism can make the share prices falls across the world. E.g.: 9/11 terrorist attack made the share prices falls around the world (Kitzer [online] No Date). Portfolio theory relies on historical data and efficient frontier is drawn based on that. Smaller investors cannot rely on this type of analysis for decision making.


Briec et. al (2007) on his management science article recommends nonparametric measurement approach for selecting portfolios having problem in mean, variance and skewness space. Markowitz gave a theory of portfolio management in 1952. Modern portfolio theory balances the risk and return of the shares in a static context. This theory maintains strong dependency on probability distribution and utility function. Diagonal and CAPM models were developed by various economists in order to calculate the risk and returns. Despite of all these tools, Markowitz model is given more preference. Problem with the parametric approach is that, it depends on the mean and variance, of the random variable distribution. It is valid only when asset processes are normally distributed and investors have quadratic utility functions. Many ancient studies prove that generally portfolio returns are distributed normally. Preference is given to positive skewness by many investors. Third derivative of unity function is related to preference of the positive skewness. When decisions are made frequently and the distributions are compact, only then mean variance approach can be used. Due to the lack of accuracy in the quadratic approximation, limited portfolio decisions with finite time interval should use higher moments. In order to overcome the computational problem associated with the above approach the primal and dual approaches were developed. The primal approach determine MVS portfolio via a multi objective programming approach. The dual approach starts with the measurement of indirect MVS utility functions and determines the ideal portfolio using parameters of risk and skewness. Geometric interpretation of portfolio frontier is difficult to develop, as dimensionality of portfolio selection increases. This leads to difficulties in the selection of preferred portfolio in the boundary points. As there is less importance to represent MV portfolio and there is no way by which MVS portfolio frontier can be represented in three dimensions. Distance function can be employed in consumer theory for positioning of bundle of goods with respect to that of target utility level. Using production theory Luenberger (1995) introduced shortage function with respect to distance function. Distance function looks on reducing the input and expanding the output. Thus a distance function represents multidimensional choice set and also positions point closer to the boundary. Generally points beneath the frontier are inefficient. To project any portfolio on the three dimensional MVS frontier, a shortage function can be used. As suggested by management studies, shortage function can be used to project portfolios which show improvement with respect to risk, skewness and return. The following targets are achieved by economist, using shortage function in theory as well as in practice. Its rate portfolio performance by measuring distance between a portfolio and optimal bench mark projection onto the primal MVS efficient frontier. it provides a non parametric estimation of an inner bound of the true but unknown portfolio frontier, it judges simultaneously return and skewness expansion and risk contractions and it provides a new, dual interpretation of this portfolio efficiency distance. Primal approaches are capable of selecting a portfolio among many from Pareto efficient MVS frontier. It can be said that there will be some points on the MVS frontier which will not be favourable from the investor’s point of view. Recently dual approaches are affected by lack of knowledge, preference for risk and skewness. Global optimization algorithm can be used to solve MVS decision problem. Shortage function looks for investor’s preferences and can identify best portfolio. By opting a micro-economic tool, such as shortage function will give big advantage in integrating primal and dual approaches. As said by Prakash (2003) and Lai (1991), the MVS portfolio and MV portfolio are not the same. They differ from each other in the sense of return, risk and skewness. MVS portfolio will have higher risk with the extend of higher skewness compared to MV portfolio. Also as compared to MV portfolio, MVS portfolio has low returns at the extend of high skewness. The three dimensional MVS spaces shows us a way of portfolio selection approach with the help of tailor expansion. It can be concluded that non-linear programming approach act as a general frame work for any portfolio including traditional portfolio.

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Minimising investment risk in sainsbury and halfords. (2017, Jun 26). Retrieved November 26, 2022 , from

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