Risk Management代写、VaR，ES留学生代写、代做R、R程序语言代做

日期：2019-04-05 10:22

Quantitative Risk Management

Coursework

The objective of the coursework is to allow you a first hand appreciation of some of

the key issues in measuring risk. There are two parts, one involving analysis of a

portfolio having a single risk factor, the other involving analysis of a portfolio having

two risk factors.

1. Select, and acquire historical data for, a traded financial asset. This might, for

instance, be a commodity, a security, or a stock market index. Suppose that

you had invested 1 million pounds in this asset at the date given by the earliest

date in your data.

(a) Explain your choice of sample size.

(b) Using the data up to, but not including, 20th February 2019, calculate

the simple daily returns for your asset [use simple returns throughout this

coursework]. Examine and describe the key statistical features of your sample

of returns.

(c) Calculate VaR and ES for 20th February 2019 using a one day holding period,

and a confidence level of 95%, using the following methods:

i. Basic Historical Simulation

ii. Age-weighted Historical Simulation

iii. Hull-White

iv. Parametric, using the Normal distribution, without volatility adjustment

v. Parametric, using the Normal distribution, with volatility adjustment

vi. Parametric, using an appropriate distribution, without volatility adjustment

vii. Parametric, using an appropriate distribution, with volatility adjustment

You should present your results in a single table, and briefly provide a commentary

on the similarities and differences.

(d) Explain why it would be problematic to have used log returns to calculate

VaR and ES for any of the parametric methods in the previous question.

2. Acquire data for another asset and suppose that at at the start of the time series

you invested 1 million pounds in this asset as well. You now have a portfolio

which at the start of the data series was worth 2 million pounds. Suppose initially

that your portfolio is not actively managed, so that your holdings of each asset

remain unchanged.

(a) Using the data up to, but not including, 20th February 2019, calculate the

simple daily returns for each of the individual assets which constitute your

portfolio. Examine and describe the key statistical features of your sample

of returns.

(b) Calculate VaR and ES for 20th February 2019 using a one day holding period,

and a confidence level of 95%, using each of the following methods

i. Basic Historical Simulation

ii. Age-weighted Historical Simulation

iii. Hull-White

iv. Parametric, using the Normal distribution, without volatility adjustment

v. Parametric, using the Normal distribution, with volatility adjustment

vi. Parametric, using an appropriate distribution, without volatility adjustment

vii. Parametric, using an appropriate distribution, with volatility adjustment

(c) Explain how you might have been able to reduce your risk exposure for 20th

February had you been able to adjust your portfolio on the 19th February.

The deadline for submission is as notified in the module outline. Please see Moodle

for further discussion of useful approaches to this topic, and hints about R code.