Managing Financial Risk
Managing Financial Risk代写 The end goal is to measure next week’s tail risk by calculate the VaR and ES five days into the future. To do that
1 Instructions Managing Financial Risk代写
- The end goal is to measure next week’s tail risk by calculate the VaR and ES five days into the future. To do that, we need to construct the return distribution into the future. The methods of constructing the distributioninclude
(a)Historical Simulation(HS)
(b)GARCH + Monte Carlo Simulation (MCS) based on conditional normality assumptionsManaging Financial Risk代写
(c)GARCH + Filtered Historical Simulation (FHS)
We are first going to compare the three methods by looking at their in-sample daily VaR performances. Based on that, we are going the conduct (b) and (c) for the 5-day cumulative VaR and ES into the future.
Besides practicing the above mentioned risk management concepts,Managing Financial Risk代写
this assignment is also designed to prepare you with several Excel “best practices” and “tricks” as we will ecounter below.
- To alleviate your burden with managing the live data, let us pretend today is 4/11/2019. We are in the afternoon and market has closed. All data up to today is available. Let us pretendwe don’t know any information beyond today. So that you don’t need to worry about updating the data, which we already practiced in PSet 1. The end goal is to measure the risk 5 (business) days after today.Managing Financial Risk代写
- Also, we are not going to worry about OOS validation this time (the concept should be familiar after PSet 1). As we will see, some methods show problems IS So “sample” inthis assignment means the full sample from 1/4/2000 – 4/11/2019. Validation is done IS, but leaving out the first 200 days (since we need to wait 200 days to do a HS with m = 200.) So the validation sample is from 10/18/2000 to today.
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Tosave you some time designing your own Excel sheets,
you may start from the Excel template I prepared for you “Assignment2 Template.xlsx”. This file is based on the PSet 1 solution, where I have already estimated the GARCH model in the full sample. Please take those estimates as given. You may follow the template and filling the blanks step by step, or you may design your own which could well be better than mine.Managing Financial Risk代写
- Again, this is an individual (not group) assignment. Please finish the assignment indepen- Students are allowed to discuss with each other about the knowledge, skills, and the general strategy required to finish the problem set. Here, discussion is limited to talking,phonecalls, etc. It is not allowed to discuss the results. Especially, it is not allowed to trans- mit in any form the electronic documents of the assignment before due. You are required toreport all the peers with whom they have discussed the assignment to allow for cross-checking. It is encouraged to search the Internet for technicalities.
- This document looks very long. Don’t get scared. There is not much work for you. The document is long because I write lots of hints to help you. Read this document thoroughly. Many of the questions I got regarding PSet 1 could be solved if one reads the document carefully.Managing Financial Risk代写
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DUEDATES:
Some of you suggested splitting the homework into smaller portions and spreadevenly over the weeks on the Here is my new rule addressing your suggestions:Instead of due at week 6, I now extend the due date to the week 7 class (5/3 for section 81, 5/6 for sections 51/52). The cutoff time, as always, is the start time of the class, depending on your section. But I will award 5 bonus points if you submit one week earlier (before week 6 classes) according to the original plan. You may email Eric for the solution if submitted early. Do not circulate the solution document whatsoever. NO late submission after due on week 7.Managing Financial Risk代写
The new rule is not meant to make you procrastinate on the homework. As always, start working on it as early as possible.
- Please upload your responses in two files to Blackboard under “HW2” submission folder in “Assignments” before the deadline. Please include your name in the file
–An Excel spreadsheet with all the intermediate steps and quantitative results. Please, be concise and precise. Use proper color coding, number formatting etc., so that the grader’s burden is minimized. Think you are presenting to your
–Asummary report (pdf file) of responses to each problem, including figures and tables where You should think hard about and address every question mark. I always believe these conceptual questions are more interesting and useful than the executions in Excel. But, be concise in answering each question.Managing Financial Risk代写
- The solution will be released after due. You may email Eric for the solution if submitted The grades are expected to be released in oneweek.
2 ProblemsManaging Financial Risk代写
- Listthe names of the students that you have discussed with when finishing this problem set, if any.Managing Financial Risk代写
1.Draw QQ-plotsof Managing Financial Risk代写
(a)Samplereturns against a normal distribution with the same mean and standard deviation as the the sample returns. (This was done in the Excel Hands-on in Week 1 )
Looking at the QQ-plot, can we conclude that the (unconditional? conditional?) distri- bution of return (is? is not?) normal. If not, in what ways is it different from normal (left?right? tail too long?short?fat?)Managing Financial Risk代写
(b)Sample zt against a standard normal
(zt as defined in “step 1” in the slides. Use GARCH implied σt for conditional stan- dard deviation. Again, the “step 1” equation looks very simple, but you have to truly understand it to answer the questions.)Managing Financial Risk代写
Looking at the QQ-plot, we conclude that the (unconditional? conditional?) distribution of return (is? is not?) normal. If not, in what ways it is different from normal? (left?right? tail too long?short?fat?)
Excel Hints:Managing Financial Risk代写
-Maintain an Excel sheet that automatically turns a column of numbers into a QQ-plot against some Normal distribution. So that you just need to make different copies of the sheet, and only change the column of numbers, and the Normal parameters. This idea of maintaining a general purpose Excel/code/function is very useful to save time, while keeping things clear and manageable. You should always follow this idea whenever possible for any work. That is, when constructing a new thing, make it general and flexible, so that it can be easily adopted for similar situations.
-You should put the empirical distribution on the vertical axis, and normal on the hori- zontal axis. To switch the axes (which I did not know how to do in week 1), right click the chart → Select Data → Legend Entries → Edit → Switch the contents in “Series X Values” and “Series Y Values”.Managing Financial Risk代写
-The QQ-plot benchmark is the 45-degree line. So we’d better make the X and Y axis
on the same scale, i.e. same interval lengths.
At Format Chart → Axis Options → That right-most button with three bars → Units: Major: set the same number for both the vertical and horizontal axes. Then drag on the chart so that the grid lines look square (of equal widths and heights). (I don’t know how to make this exactly square, feel free to Google and let me know.)
2.Computethe V aR0.05 and for every t from 10/18/2000 to today using the following methods:
(a)Historical Simulation with m=200
(b)GARCH model for the variance + Conditional Normal assumption ( z is standard nor- mal).Managing Financial Risk代写
(c)GARCH model for the variance + Filtered Historical Simulation withm=200 Hints:
-Write p = 0.05 in a cell and refer to that cell. Do not type 0.05 as a number within any formula, as we will change p later. Again, it is always a good practice to make things easily adaptable.
-10/18/2000 is the 201th day of the sample. So, on 10/17/2000, one could calculate the first HS and FHS VaR (V aR0.05 ). Although we don’t need to wait for 200 days to calculate the first GARCH-based VaR, let us keep it in the same sample for comparison.
-Use “Freeze Panes” under “View” menu, so that you don’t loose the column name row when looking at the 200th day below.Managing Financial Risk代写
3.Unconditionedperformances:
For the three methods respectively, construct the VaR breach indicator series. (that is, on each day t, 1 if breach happened, 0 if not.)
Calculate and report the VaR breach frequencies in the validation sample (from 10/18/2000 to today). What is the theoretical value of the frequency? Are the three methods close to the theoretical value? If a sample frequency is higher than the theoretical value, then do you think the VaR is too high or too low in general?Managing Financial Risk代写
4.ConditionalPerformances:
Bar chart (called “column” in Excel) the three breach indicator series against calendar days.
Hints:
-Since the values are either zero or one, the end result should look very similar to bar codes.
-Again, the best practice: First make one chart, adjust its label, axis etc. all perfectly. Then make two more copies and “Select Data” to the two other series. It saves a lot of time going back and force, and the charts are standardized in terms of formats.Managing Financial Risk代写
Eyeballing the charts, are the bars roughly “randomly” evenly spaced? Is there VaR breach clustering (meaning periods of very frequent breaches in between periods or very few breaches)? Which method has more severe clustering? Should there be such clustering if VaR were cal- culated perfectly in theory? Why or why not?
Can you recognize the periods with the most clustered breaches? Is the VaR too low or too high in that period? Is this a good time to over- or under-estimate risk?
5.Change p = 0.05 to 0. (Supposedly, you only need to change one cell, and everything including the charts should updateautomatically.)Managing Financial Risk代写
Report breach frequencies.
Do you see that the sample breach frequency for GARCH + Normal is off the most at
p = 0.01? Does that reflect an over- or under-estimation of VaR?
This implies what problem of the distributional assumption of this method? In what ways are the empirical distributions better than the normal distribution in avoiding this problem (given the evidences from the QQ-plots)
How come the problem was not so severe when p = 0.05? (think which p is about more extreme scenarios.) Let’s say keep p = 0.05, do you think the problem could emerge again or still be hidden when we are talking about one-day ES or multi-day cumulative VaR?Managing Financial Risk代写
6.At the end of the today compute and report V aR0.05 ,V aR0.05 , …,VaR0.05 and the same
t,t+1 t,t+2 t,t+5
for 5 ES’s using:
(b)GARCH model for the variance + MCS under conditional normality ( z is standard normal)
Simulate 1000 paths.
(c)GARCH model for the variance + Filtered HistoricalSimulationManaging Financial Risk代写
Simulate 1000 paths. Draw historical simulation of z from the full sample.
Change to p = 0.01, and report the 10 numbers again.
Hints: Managing Financial Risk代写
-The two methods should be all the same, except for the simulated z part. So do one perfectly, then make a copy and changes z’s to get the second one.
-Every simulated path should be the same, except for the random number generated. So make one path perfectly, then drag every column down 1000 rows. (Some times the shortcut “Ctrl + D” is very helpful.)
-For every path, the starting point should be the same. We know today’s R and σ, which give tomorrow’s σ, according to the GARCH recursive formula just like last PSet. So that σt+1 (already known at t) is the common starting point. Next step, simulate tomorrow’s z, that gives tomorrow’s R. Then use GARCH recursive formula to the day after tomorrow, so on so forth.Managing Financial Risk代写
-Every z’s formula should be the same, just the random numbers drawn are different.
Every time when the random numbers change, do the results change? Do they change a lot? Where does the problem come from and how can you alleviate the problem?Managing Financial Risk代写
Is VaR or ES greater for every horizon? Why?
Is VaR and ES increasing or decreasing for longer horizon? Why?
Does MCS give larger or smaller VaR than FHS? How about ES? How about when change to p = 0.01? Why?
In the end, report two numbers V aR0.010.01t,t+5as your measure of next week’s risk.
Which method (MCS or FHS) do you prefer to use?
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