Ewha Womans University
Department of Economics
Financial Economics
Spring 2020
Homework
(Due: 6:00pm on May 14th)
Note: You also have to provide your R scripts.
1. [Lecture 3] See "KOSPI.SNP.csv." There are monthly data set for two
stock indices (i.e. KOSPI and S&P 500). There are index value and return
series for each stock.
Suppose that the total value of your portfolio is $1,000. The proportions
of KOSPI and S&P 500 indices within your portfolio are 0.6 and 0.4,
respectively. Letís call this portfolio "International portfolio." Compute
the following VaR measure for one-month holding period.
(a) Before considering "International" portfolio, consider the portfolio
with KOSPI alone. Compute 5% VaR using the delta-normal method.
(b) For the "KOSPI only" portfolio, compute 5% VaR using the historical
simulation method.
(c) Now we consider our "International" portfolio. Compute 5% VaR
using the delta-normal method.
(d) For "International" portfolio, compute 5% VaR using the historical
simulation.
(e) Is there any risk-reducing e§ect from constructing International portfolio?
Brieáy, discuss it.
2. [Lecture 3 & 5] Your portfolio is composed of Stock A, B, C, D, and E
(See Fama.French.R.csv for their historical data) with portfolio weight
w = (0:1; 0:2; 0:3; 0:3; 0:1).
(a) Compute 5% VaR using the historical simulation method.
(b) Compute 5% VaR using the delta-normal method (Hint: Lecture 5
provides a recipe for how to compute a mean and standard deviation
for multiple assetsíportfolio.).
1
3. [Lecture 5] Tabulate and draw the investment opportunity sets of the two
risky assets Stock and Bond funds with di§erent correlation coe¢ cients.
Use investment proportions for the stock fund of 0 to 100% in increments
of 10%. Input data is given as E(rS) = 20%, S = 20%; E(rB) = 5%,
B = 10%. Try di§erent correlations BS = 1;
0:5;
0; 0:5; and 1:
4. [Lecture 6] Consider the following four assets G, H, I, and J from "Fama.French.R.csv."
Answer the following questions.
(a) Provide an expected return and standard deviation for the portfolio
with w = (0:1; 0:2; 0:3; 0:4)0
:
(b) Provide the global minimum portfolio (i.e., portfolio weight, expected
return, and standard deviation).
(c) Provide the optimal risky portfolio, also known as the tangency portfolio
(i.e., portfolio weight, expected return, and standard deviation).
Assume that the riskfree rate is 3% per annum. Thus, on a monthly
basis, the riskfree rate is 3/12%.
5. [Lecture 9] Consider the following four assets G, H, I, and J from
"Fama.French.R.csv." Use "Mkt.RF" as a systematic risk factor. Use
"RF" as the risk-free rate. Estimate the CAPM model for each asset (i.e.,
provide alpha and beta for each asset.). Which stocks does a security
analyst who believes CAPM recommend to buy?