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- September 13, 2020
- By menge

Please upload an excel file that has the work on one or two pages and then the answers on a separate page.

FINC 460/560: Portfolio Analysis

Homework 3, due Oct. 20

40 points

Value at Risk (VaR)

Use any web data source to collect daily and weekly prices for PG (Procter & Gamble) and

GOOG (Google) from January 1, 2015 to December 31, 2015. I recommend the historical price

link at finance.yahoo.com, but you may use whatever source you prefer to gather these data. Use

Excel to complete the following analysis:

1. What are the mean and standard deviation of one-day logarithmic returns (not prices!) for

each stock? What is the correlation between the returns for the two stocks? Also, calculate

the mean and standard deviation for a portfolio consisting of 30% PG and 70% GOOG.

2. Using the parametric method, what are the 95% and 99% 1-day VaR for a $500,000 position

in each stock (so you are investing a total of $1 million, half in each)? Use this figure to

calculate the 5-day VaR for each stock for the same investment amount.

3. Use your answers from #1 for the individual stocks to calculate the 95% 1-day VaR for a $1

million portfolio that consists of 30% PG and 70% GOOG. (In other words, use naïve

inference, ignoring the portfolio statistics.)

4. Use the portfolio descriptive statistics from #1 to calculate the maximum possible 95% 1-day

VaR for a $1 million portfolio of 30% PG and 70% GOOG. (In other words, now use only

the portfolio statistic numbers from #1.) Is this number the same as your answer for #3?

Why or why not?

5. Use the weekly prices to calculate the 95% 5-day VaR for a $500,000 position in each stock

(assume 5 days is the same thing as one week). Do you get the same results as you did in #2?

Why or why not?

6. Using the historical simulation (nonparametric) method, calculate the 95% 1-day VaR for a

portfolio that consists of 30% PG and 70% GOOG, using the historical two years of returns.

Use the completely non-parametric method by reading off the 5% level using Excel?s

percentile function. Is your result the same as your figure from #4? Why or why not?

7. Conduct Monte Carlo analysis for the 95% 1-day VaR for a portfolio of 30% PG and 70%

GOOG. Assume that returns of the individual stocks are normally distributed with the

parameters from #1. Generate 1,000 replications; calculate descriptive statistics; and use the

parametric estimation method to generate the VaR.