(solution) I get stuck in the futures contract part, can you guide me?

(solution) I get stuck in the futures contract part, can you guide me?

I get stuck in the futures contract part, can you guide me?

Overview
The task you are given is to estimate the market risk for a hypothetical holding of 10,000 NAB shares,
held on August 1, 2016 (you are working out the risk position assuming that you own these shares at
the open of trading that day). You will do this by estimating the Value-at-Risk for the stock using
historical data. You will then analyse two hedging strategies using derivatives that will alter the risk
of holding these shares. Description
You will be asked to calculate the following;
– 10 day VaR for the portfolio of NAB shares at confidence levels of 99%. Note: This risk estimate applies to the 10 days from August 1, 2016 until August 12, 2016 (i.e. ? it
should be a forecast of risk).
Based on what you have learnt from EFB344, you realized that you have several options for how to
compute this risk measure. You are considering using a VaR based on a) the normal distribution
based on a 252 day rolling window, b) the normal distribution with a variance estimated by the
EWMA, or c) historical simulation based on a window of 252 days.
To aid in the decision of which to use, you are going to consider the recent historical performance of
the three models in calculating 1 day VaR at the confidence levels of 99%. You will do so by first
examining the frequency of instances when the VaR was exceeded by the observed return using the
last five years of data (e.g. ? from 1/08/2011 to 29/07/2016).
You will then evaluate the appropriateness of these frequencies over time relative to the Basel traffic
light levels discussed in lectures. Based on this performance, and any other factors you want to
discuss, select the best model and report the required VaR(10, 99%) for August 1, 2016. Next, you will look at the possibility of beta hedging the portfolio of NAB shares using S&P200 Index
futures contracts. To do this you will need to calculate the following
– The number of futures contracts required to eliminate beta from the portfolio. – The 10 day VaR for the joint holding of the NAB shares and the S&P 200 index futures at a
confidence level of 99%. To undertake this part of the task, you will use the historical data obtained for NAB as well as
historical data for the S&P 200 Index (ticker code AXJO). To calculate the historical beta for NAB, you
should use the formula1 1 This is valid under a basic CAPM model with a constant risk free rate. ? NAB = Cov ( Ret NAB , Ret S ?P 200 )
2
? S?P 200 To calculate the components of this beta, you should use the method you selected as the best for
calculating the VaR for NAB shares (i.e. ? rolling window/historical simulation or EWMA). Under the
assumption that returns for NAB shares and the S&P200 Index are jointly normally distributed, you
can then calculate the VaR. To simplify the analysis, you can make two further assumptions.
1. There is no margin requirement.
2. Changes in the futures price are perfectly correlated with the spot price for the S&P200
Index over short horizons (e.g. ? over 10 day windows). Finally, you will look at the possibility of hedging your risk over the next three months using an
American put option written on NAB shares that expires in exactly three months. The current stock price as of the close of trading is $26.54. Your portfolio consists of 10,000 shares.
The risk-free rate is currently 2% p.a. continuously compounding. The annual variance of NAB shares
can be estimated from historical data. a. Noting that each put option covers 100 shares, determine how many put options you would
need to buy to hedge your risk. Next, determine the appropriate price for each of these put
options when the strike price if $26. Use a six-step binomial tree for this task. b. Plot a profit diagram that shows the profit from the stock holding, option holding and the
combined portfolio (stocks and options) as a function of the share price at maturity (assume
that you didn?t exercise the options early and you were able to buy them at the price from part
a). Presenting your results
– You will then write a brief report of no more than twelve pages including graphs that present
your results. A rough outline of what your report could include is
o Present the final VaR(10, 99%) for August 1 based on your preferred model. You
must also include some explanation of how these final estimates should be
interpreted (what does this VaR number mean). o A brief description of the final/preferred VaR model you used. This includes the
length of any subsamples of data or selection of any fixed parameters. o Presentation of the main results in the back-testing study. The raw results should be
accompanied with an evaluation of the relative performance of the various models
and a clear justification of which model is superior. With this should be a brief eria description of data (start/end dates, number of observations and details of where
you got the data, what the data was (e.g. ? closing prices?), how the data was
cleaned (e.g. – non-trading days) and how you calculated returns. – o A section on the beta hedging strategy. Present the details of the hedge, how you
have formed your estimates, what risk is being removed and what risk remains. o A section on the option hedging strategy. Present the profit diagram representing
the hedge, how you priced the option, what risk is being removed and what risk
remains. You will also be asked to submit the excel file in which you conducted your analysis. It should
be formatted in a reasonably clear way, so that someone who was given the job after you
was able to understand and replicate what you had done.
o I would ask that you use multiple worksheet with the excel file. The first should
include the raw data (with dates) as given to you by your source. All working and
final results can be compiled on subsequent worksheets. Additional Notes and Instructions
– You will need to source the data yourself. I recommend using Yahoo Finance as was outlined
in lecture 2. – For the backtest, you need only start with five years of data when you begin your analysis.
This is does not mean that you will have five years of VaR numbers and exceedances to
compare (you will have less than this). This will make sense once you begin. – Your excel spreadsheet should contain the formulas that you have used for all calculates (i.e.
? don?t paste the values of the main calculations). This does not apply to the steps you
undertook to clean the data. Criteria and Standards Sheet for Assignment Part A (30 marks)
High Distinction Distinction Credit Pass Fail Demonstrates an
adequate understanding
of relevant finance and
risk management
concepts and
techniques. Insufficient or inaccurate
understanding of
relevant finance and risk
management concepts
and techniques. onstrate and apply integrated discipline (including technical) knowledge
Demonstrates
comprehensive
understanding of
relevant finance and risk
management concepts
and techniques. Demonstrates a
developed
understanding of
relevant finance and risk
management concepts
and techniques. Demonstrates a
developed
understanding of
relevant finance and risk
management concepts
and techniques but with
a few errors. y technical and technological skills appropriate and effective for real world business contexts eria High Distinction
Document prepared and
formatted according to
standards required by
the subject. Distinction
Document generally
prepared and formatted
according to standards
required by the subject,
but with a small number
of minor errors Credit
Document generally
prepared and formatted
according to standards
required by the subject,
but contains some errors Pass
Frequent errors, but
displays an ability to
prepare and format the
document according to
standards required by
the subject. Fail
Fails to format the
document to an
appropriate standard
required by the subject cise independent judgement and initiative in adapting and applying knowledge and skills for effective problem solving sis Provides a clear and
well-reasoned
justification for the
choice of superior risk
management model that
fully considers the
empirical findings. Provides a strong
justification for the
choice of superior risk
management model that
is supported by the
empirical findings. Provides a solid
justification for the
choice of superior risk
management model
which is generally
consistent with the
empirical findings. Provides only weak
justification for the
choice of superior risk
management model
which barely takes
account of the empirical
findings. Fails to provide a
justification for the
choice of superior risk
management model
and/or the arguments
are at odds with the
empirical findings. y teamwork knowledge and skills for effective collaboration ly in t Students will assess their team peers on how effectively they performed in the team and on their contribution to the team product via an
online survey. Each student will assess every member of their own team and themselves. Students? score out of 5 marks on this criterion
will reflect the average of the ratings received from their peers and their own rating. Overall Grade: HD, D, C, P, F
Overall Mark: ________
Comments: An overall mark is awarded to the group, but can be adjusted for individuals at
the discretion of the unit coordinator.