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SIT718 - Real World Analytics

Added on - 16 Dec 2021

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Performance of Share Prices1
THE BEHAVIOR AND PERFORMANCE OF SHARE PRICES
By (Name)
The Name of the Class (Course)
Professor (Tutor)
The Name of the School (University)
The City and State where it is located
The Date
Performance of Share Prices2
The Behavior and Performance of Share Prices
Question 1
Whereμtis called the drift at time t, andσtthe diffusion (volatility) at time t for a given stock.
No they are not constant since their respective values are dependent on time i.e. t=0, 1, 2. This
means that the values of drift and volatility change with variation in time. If they were constant
they would be represented in the formμt=μandσt=σ. The assumptions made are: the market is
stable and time is not considerably large[ CITATION Vla11 \l 1033 ].
Question 2
Closing stock prices for British Petroleum P.L.C. (BP) for the period between 1st of August 2018
and 31st of October 2018 were retrieved from Yahoo Finance. Other data columns (opening,
high, low, volume, and adjusted closing) were removed to remain with only the closing prices
(see table 1 in appendices).
Question 3
The dynamics for a given stock or share with diverse prices should be random and be easily
represented in the formS/Swhere there should be both a deterministic part and stochastic part
i.e.S/S=deterministicpart+Stochasticpart
This Stochastic Differential Equation can be further modified to
S/S=μt+σW
dSt
St
=μdt+σdWt
Rewriting the equation above we obtain the Geometric Brownian Motion
dSt=μStdt+σStdWt
We can prove this by testing whether the standard deviation of the share prices is considerably
small or equivalent to t. This will indicate that the market is stable because Geometric Brownian
Performance of Share Prices3
Motion models are only applicable in a stable market. Second we will evaluate the duration over
which the share prices were collect i.e. should be less than 2 years and preferably 3 to 6 months.
From the results below it is clear that our share prices satisfy the necessary Geometric Brownian
Motion conditions[ CITATION Abd06 \l 1033 ].
Standard
Deviation
1.579365
Duration in days65
Question 4
We first compute a new set of dataset (return on asset) from the share prices using the following
formula:

i=1
64Si+1Si
Si
Results are in Table 1 in Appendices
We will then find the mean and standard deviation of this new data set, and they will give us the
drift and diffusion respectively. The results are shown below
Drift-0.01515
Diffusio
n
0.120157
Question 5
Based on the information presented in the company annual report compare favorably with the
computed values of drift and diffusion indicating in our assessment the financial reports are for
the fiscal year 2017/2018. As such, they are also relevant to the share prices we have being using
the calculation of drift and volatility[ CITATION Dav18 \l 1033 ].
Question 6
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