Real World Analytics: Analysis of National Australian Bank Limited Share Prices

Real World Analytics 1
REAL WORLD ANALYTICS
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Real World Analytics 2
Question 1
In the stochastic process, σ t is defined as the variance per unit time. Actually, σ t is measure of
order of a random noise
μt is also known as drift measures expected return per unit time.
σ t and μt are time variant thus not constant
Assumptions
a) No transaction cost and taxes involved
b) All stock prices must satisfy the condition ds= μSdt +σ SdW.
c) No short selling
d) Trading is continuous
e) Securities are infinitely divisible
f) No dividends to shareholders at the end of trading periods
Question 2
7/19/2018 8/8/2018 8/28/2018 9/17/2018 10/7/2018 10/27/2018 11/16/2018
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A time series plot for Closing prices(p(t)) for National Australian
Bank Limited (NAB.AX) share price
Date
share price

Real World Analytics 3
A time series plot for the share prices for National Australian bank Limited shows a decreasing
trend in share price from August 1st, 2018 to 31st, October 2018. Historical share prices for
National Australian Bank limited (NAB.AX) are attached in excel sheet 1. The share prices used
in this question were downloaded from www.yahoofinance.com.
Question 3
The condition “S(t) = S0 eW t” must be satisfied by a share price in order to be considered a
Geometric Brownian Motion.
Suppose that S(t) = S0 eW t
Where W t = W 0 + σ Bt + μt
It is worth noting that S(t) follows a lognormal distribution with : W 0 + σ Bt and Variance= σ 2 t
Thus rewriting returns( r(t) inform of S(t) yields;
r(t) = S (t )−S (t−1)
S (t−1) ~ N( μ,σ )
Where:
S ( t ) = closing share price of a stock at time, t
S ¿) = closing share price of a stock at time , t-1
simplifying r(t) further gives :
r(t) = S (t )−S (t−1)
S (t−1) ~ μδt +σ ∅ √ δ t
δt = 1 day ⇒ δ t= 1
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μ =drift or mean
∅ ~ N(0,1) (normally distributed with a mean of 0 and standard deviation of 1)
σ = annualized volatility