Department of Economics  Financial Economics

  1. 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?