代做FNCE 5321: Finanical Risk Modeling II Spring 2025代写Java编程

FNCE 5321: Finanical Risk Modeling II

Spring 2025

Group Project 1

Instructions:   You can work in groups of up to 5 students. Please email your project report to the TA by the deadline (one report per group), and indicate clearly the members of your group on the first page of your submitted report. The report should include your solutions/answers as well as the codes.

Question 1

For Question 1, use the data in Q1Data.csv, which contains daily closing prices on a stock market index for the period from July 2nd 1962 to December 30th 2016.

(A) Calcuate daily log returns Rt+1 ≡ ln(St+1) − ln(St), where St+1 is the closing price on day t + 1, St is the closing price on day t, and ln(·) is the natural logarithm. Plot the closing prices and returns over time.

(B) Calculate and report the mean and standard deviation of daily log returns.

(C) Calculate the first through 100th lag autocorrelations of daily log returns. Plot the autocorrelations against the lag order.

(D) Calculate the first through 100th lag autocorrelations of squared daily log returns. Plot the autocorrelations against the lag order. Do squared daily log returns have more or less autocorrelations compared with daily log returns?

(E) Suppose you own a portfolio which is 100% invested in this market index. Estimate the 1-day, 1% VaRs on each day assuming daily log returns are normally distributed and updating volatility estimates with the RiskMetrics model, i.e.

where Rt is the daily log return at day t, and σt+1 is the standard deviation of Rt+1. Plot the estimated VaRs. (Hint: Use the standard deviation from Part (B) as σ1 to start the iteration.)

(F) Estimate the 1-day, 1% VaRs on each day using Historical Simulation with a 250-day moving estimation window. Plot the estimated VaRs.

(G) What are the major differences between the two VaRs estimated in Part (E) and Part (F)?

(H) Estimate the 1-day, 5% VaRs on each day using Historical Simulation with a 250-day moving estimation window. Are the 5% VaRs smaller or larger than the 1% VaRs estimated in (F)? Explain why with intuition.

(I) Formally test whether the daily closing prices and the daily log returns are stationary using the augmented Dickey-Fuller tests.

Question 2

(A) Suppoese Xt follows an AR(1) model: Xt = 0.9Xt−1 + ∈t , where σ∈ = 0.5. Simulate an episode of Xt with 1 million observations (Hint: Use the R command arima.sim). Calculate the first through 10th lag autocorrelations of the simulated series. Compare the estimated autocorrelations with the theoretical counterparts (Hint: the theoretical autocorrelations for AR(1) is ρτ = φ τ 1 , in which τ is the lag.)

(B) Suppose Zt = Wt + Yt . Both Wt and Yt follow an AR(1) model:

Wt = 0.5Wt−1 + ∈w,t                          (1)

Yt = 0.5Yt−1 + ∈y,t                             (2)

in which σ∈w,t = σ∈y,t = 0.5. Is an AR(1) model appropriate to describe Zt?

Question 3

For Question 3, use the data in Shillerdata.csv, which contains the monthly closing price, dividends, earnings, and the PE ratio for S&P 500.

(A) Formally test whether the dividend series is stationary.

(B) Calculate the PD ratio on S&P 500 as follows:

Both PD and PE are valuation ratios. What is the unconditional correlation between the two series? Formally test whether the PD ratio is stationary.

(C) Redefine the PD ratio in logs:

PD = log(Price) − log(Dividends)

Formally test whether the PD ratio is stationary.