We have selected the followings stocks: Barclays
We have selected the followerss stocks: Barclays ( BARC ) , Allied Domecq ( ALLD ) , Mark & A ; Spencer Group ( MKS ) , GloxoSmithKline ( GSK ) . The information we are analyzing correspond to the interval clip get downing on the 10/15/1994 and stoping on the 4/15/1997.
Our statistical description of these four series will hold two aims: the first 1 is to give a step of the cardinal inclination ; and the 2nd one to give a step of the statistical variableness. The step of the cardinal inclination will largely rest upon the calculation of the arithmetic mean and supplemented by the calculation of the lopsidedness, while the step of the statistical variableness will rest upon the calculation of the discrepancy or equivalently the standard divergence. We have used excel to execute the calculations. The expression used for the arithmetic mean is average.
The expression used for the standard divergence is
The expression used for the lopsidedness is
The Barclays’ serie has a meanand a standard divergence. Its lopsidedness ofindicates that its distribution has an asymmetric tail widening toward values greater than its mean. Besides, this going of the lopsidedness from nothing may bespeak that in this peculiar instance the mean is non the best step of the mean monetary value. An alternate step of the mean monetary value is given by the average with peers to. Its standard divergence indicates that the values comparatively dispersed from the mean.
1.2 ALLIED DOMECQ
The Allied Domeccq’s serie has a meanand a standard divergence. Its lopsidedness ofindicates that its distribution has an about symmetric tail, proposing that the sample may come from a usually distributed population. However this is non confirmed by its kurtosis, which is equalled to, and indicates a distribution comparatively flatter than the
normal distribution. Besides, this lopsidedness about equals to zero makes the arithmetic mean a good step of the mean stock monetary value, which in this instance is near to the average peers to. Its comparatively low standard divergence comparison to its mean indicates that the values reasonably dispersed around the mean.
1.3 MARK AND SPENCER GROUP
The Mark & A ; Spencer Group’s serie has a meanand a standard divergence. Here once more a lopsidedness ofindicates a distribution that has an about symmetric tail, proposing that the sample may come from a usually distributed population, though non confirmed by its kurtosis peers towhich indicates a distribution flatter than the normal distribution. Besides, this lopsidedness near to zero makes the arithmetic mean a good step of the mean stock monetary value, which in this instance is near to the median, peers to. Here once more the standard divergence is rather little comparison to its mean and shows that the values are dispersed around the mean.
The GlaxoSmithKline’s serie has a meanand a standard divergence. Here the lopsidedness peers, the kurtosis peers, and both indicate a distribution that can be justly approximative by a normal distribution, . Besides, with a lopsidedness near to zero, the arithmetic mean here is a really good step of the mean stock monetary value, and is about equalled to the median. The size of the standard divergence is rather large, nevertheless it besides matches the size of the monetary values. The form of the distribution of this serie is approximated by the undermentioned graph:
This graph has been obtained utilizing Excel. We have first calculate the chance to hold each monetary value, presuming that the serie comes from a usually distributed population, and so plotted the graph.
Finally, a secret plan of the point of each of the above series is given by the undermentioned chart:
We one time once more make usage of Excel to calculate the correlativity coefficients between our two series. The expression used by Excel for these computations is the followers:
With this expression, we have obtained the undermentioned consequences:
- The correlativity between Barclays and Allied Domecq
- The correlativity between Barclays and Mark & A ; Spencer Group is
- The correlativity between Barclays and GlaxoSmithKline:
- The correlativity between Allied Domecq and Mark & A ; Spencer Group:
- The correlativity between Allied Domecq and GlaxoSmithKline
- The correlativity between Mark & A ; Spencer Group and GlaxoSmithKline:
The correlativity coefficient represents the additive relationship between two variables ; normally it determines the extent to which values of the two series are “ relative ” to each other. However, in this instance, the correlativity coefficients between our series give us an indicant of how the monetary value motions are being made. A negative correlativity between two series indicates that the one the monetary value of first stock goes up, the monetary value of the 2nd stock goes down.
Since,, and, the monetary value of the Barclays, the Mark & A ; Spencer Group, and the GlaxoSmithKline stock will all travel up, when the monetary value of the Allied Domecq stock will be given to travel down. Furthermore, these correlativity coefficients are about equal and close tobespeaking that the degree by with the stock monetary value of Barclays, Mark & A ; Spencer Group, and GlaxoSmithKline go up will fit the degree by with the stock monetary value of Allied Domecq goes down.
We have,,, bespeaking that the stock monetary value of Barclays, Mark & A ; Spencer Group, and GlaxoSmithKline all move in the same way. These correlativity are close towhich shows that the degree of addition ( or lessening ) in any one of them will be similar to the degree of addition ( or lessening ) in the two others. This fact is peculiarly attempt in the instance of the Barclays’ stock and the GlaxoSmithKline’s stock with a correlativity coefficient peers to.
An investor in these stocks will be surely concerned by the degree of the return and the hazard associated with keeping each of these stocks every bit good as the overall degree of hazard of a portfolio dwelling of two or more of these stocks. It can be noticed that with the exclusion of Allied Domecq, all the stocks have performed good within the chosen clip interval, with an mean monetary value higher that their monetary value at the start of this clip interval, therefore we may be inclined to purchase them. However Barclays’ stock, Mark & A ; Spencer Group’s stock, and GlaxoSmithKline’s stock wholly have a positive correlativity between them ; it won’t hence be a safe attitude to keep a portfolio including all these stock as a public presentation of anyone of these stocks will connote a bad public presentation of the two others. Since the mean return for keeping the MKS stock is, much more lower than the mean return on BARC stock which isand the mean return on GSK stock which is, I will propose to sell the MKS stock and keep the two others. To fudge the potentially high volatility associated to the retention of GSK stock, it will be sensible to purchase the ALLD stock. The ground of this is because the two stocks have a negative correlativity so that a move of one stock monetary value in a way will connote the move of the other stock monetary value in the opposite way.
- James T. McClave, P. George Benson, Terry Sincich ; A first class in concern statistics, Prentice Hall, 1998
- Michelle Lawson, Stephanie Hubbard, Paul Pugh ; Mathematicss and statistics for concern, Harlow: Longman Scientific & A ; Technical, 1995
- Ronald M. Weiers ; Essentials of concern statistics, Belmont, Calif. : Thomson Brooks/Cole, 2005