ETF5952 Quantitative Methods for Risk Analysis Assignment 1

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ETF5952 Quantitative Methods for Risk Analysis

Assignment 1

May 2023

Question 1 (5+5+5+5+5+15+5+5=50 points)

The dataset Assign2Q1.csv contains the following variables:

rt: continuously compounded return of daily price pf ANZ stock;

volume: daily trading volume;

D1:  a dummy variable which is 1 if trading date is in Christmas period, and otherwise 0;

D2: a dummy variable which is 1 if trading date is in June, and otherwise 0;

(a) Check whether the continuously compounded return rt is predictable (no more than 30 words).

(b) Fit an AR(1) model and an AR(2) model to rt , comment on the results (no more than 30 words).

(c) ”Santa Claus rally” is a special term which describes a significant increase in the stock market (rt  > 0) that occurs in the last week of December through the first two trading days in January. Let consider the following model,

rt  = β0 + β1 rt − 1 + β2 rt −2 + γ1 D1,t + et ,                               (1)

Estimate the model and comment on the ”Santa Claus rally” effect (no more than 30 words).

(d) ”Tax loss selling” is a strategy that investors can leverage to minimise their net capital gains during a financial year for tax purposes. This often occurs in June each year. During this month, investors are willing to sell their stocks at a loss (rt  < 0) so that they can use capital loss to offset their capital gain. Let consider the following model,

rt  = β0 + β1 rt − 1 + β2 rt −2 + γ1 D1,t + γ2 D2,t + et ,                       (2)

Estimate the model and comment on the ”Tax loss selling” effect (no more than 30 words).

(e) Consider the following models,

rt      =   α + βrt − 1 + βrt −2 + volumet + et ,                        (3)

Estimate the model and comment on the volume effect.   (no more than 40 words).

(f) Discuss and compare all five models above, and find the best model (make sure you provide all the evidence needed, no more than 80 words).

Peter is seeking to invest $100,000 in the ANZ stock. However, he has limited knowledge of financial investment.  As a close friend of him, could you please provide some risk management advice in the following questions.

(g) Assume that rt  follows the normal distribution. What is the one-week VaR for the Peter’s holding of the stock at the 95% level of confidence?

(h) Assume that rt  follows the Student-t distribution with df = 6. What is the one-day conditional VaR for the Peter’s holding of the stock at the 99% level of confidence based on the RiskMetrics method?

Question 2 (12+12+14+12=50 points)

You are employed as a risk analyst in a commercial bank in Australia. Your daily job is to evaluate the risk of credit card customers in the bank. There are 30,000 credit card customers’ information recorded in the dataset Assign2Q2.csv. It contains the following variables:

EDUCATION: education level of a customer - graduate school; university; high school; others;

MARITAL: marital status of a customer - married; single; others; 

CREDIT LIMIT: amount of the credit given to a customer (measured in $); PAY AMT: amount of previous payment (measured in $);

AGE: age of a customer (measured in years);

DEFAULT: a dummy variable which is 1 if a customer default the credit card repayment, and otherwise 0;

GENDER: gender of a customer - male; female;

Based on dataset, you are required to evaluate customers’ default risk by completing the following tasks:

1.  Use different models/methods to evaluate customers’ default risk, sum- marise your results in the tables or graphs;

2.  Make prediction of probability of customers who may potential defaut the credit card repayment based on all models/methods you use. Use threshold q = 0.2 to evaluate the prediction performance (FPR, FNR and accuracy).

3. Compare and discuss the similarities and differences between these mod- els.  And find the best model/method for default risk analysis (no more than 140 words).

4. We have three new credit card applicants:

Eilish - a 21-year-old single woman with graduate degree who is applying for a credit card with $50,000 credit limit;

Sheeran - a 23-year-old single man who just graduated from university and apply for a credit card $5,000 credit limit;

Morrison - 55-year-old married man with university degree who is applying for credit card with $100,000 credit limit.

Please advise the bank whether to approve their credit card application with valid reasons.


2023-05-25