The Argo Hedge fund has the following portfolio of options of the XYZ stock

Type	Position	Delta of Option	Gamma of Option
Call	−1,000	0.50	0.2
Call	−500	0.80	0.6
Put	−2,000	−0.40	1.3
Call	−500	0.70	1

A new option becomes available with a delta of 0.6, a gamma of 0.5

What position in the new option and in XYZ stock would make the portfolio both gamma neutral and delta neutral?

Question 2

Suppose that the price of Trisco Corp at close of trading yesterday was $275 and its volatility was estimated as 2% per day. The price of Trisco at the close of trading today is $278. Suppose further that the price of Baldi Corp. at the close of trading yesterday was $100, its volatility was estimated as 1.5% per day, and its correlation with Trisco was estimated as 0.8. The price of Baldi at the close of trading today is $98. Update the volatility of Trisco and Baldi and the correlation between Trisco and Baldi using

(a) The EWMA model with l= 0.94

(b) The GARCH(1,1) model with w = 0.0000018, a= 0.03, and b= 0.96.

Question 3

You have a portfolio of options:

1. 200 long European calls on ABC corporation shares maturing in 9 months. The current price of ABC shares is $45 and its annual volatility is 30%. These options are “”at the money”.
2. 300 short European puts on VWX corporation shares maturing in 9 months. The current price of VWX shares is $50 and the strike price for your options is $51. The volatility of VWX is 20% per year.

The correlation coefficient between returns on ABC and VWX is 0.25

Both corporations don’t pay dividends. The risk free rate is expected to be at 2% per year. Use 10-day time horizon and 99% confidence level.

1. Calculate VaR of your portfolio using the delta linear model.
2. Calculate VaR of your portfolio using the delta-gamma quadratic model. Assume that each option’s price depends on only one risk factor (i.e. cross-gammas are 0)

Question 4

Consider the following data on three ETF funds A, B and C:

		s
A	0.1	0.1
B	0.08	0.09
C	0.15	0.2

The correlation matrix is given by:

	A	B	C
A	1
B	0.2	1
C	0.4	-0.5	1

1. What is the variance and the expected return on the equally weighted portfolio of A, B, and C.
2. Assuming that returns on A, B, and C are jointly normally distributed, calculate the 95% VaR for this portfolio
3. What are the benefits of diversification from the VaR perspective?
4. Calculated the 95% expected shortfall for this portfolio

Question 5

You have a portfolio of two assets with independently distributed returns. You invested $10M in Asset X and $20M in Asset Y. The distributions of returns on both assets are given below:

Probability	Return on Asset X	Probability	Returns on Asset Y
0.01	-25%	0.015	-20%
0.05	-5%	0.045	-5%
0.94	8%	0.95	10%

1. What is the 95% VaR of this portfolio?
2. What is the 95% expected shortfall of this portfolio?
3. Suppose that the lowest possible expected return on Asset X was reassessed to be instead of with the same 1% probability. Recalculate VaR and ES of this portfolio, taking this change into account.
4. Based on your calculations, what is your opinion about shortcomings of VaR?

Question 6

The value of the XYZ’s equity is $10 million and the volatility of its equity is 40%. The debt that will have to be repaid in three years is $10 million. The risk-free interest rate is 3% per annum.

1. Use Merton’s model to estimate the probability of default
2. Find the credit spread implied by Merton’s model

Transcribed Image Text:

-25% -25% -25% -25% -25% -25%

Answer rating: 100% (QA)

Question 1 In this case the delta of portfolio is given by Delta of portfolio 1000 050 500 080 2000 040 500 070 The Gamma of portfolio is given by Gam... View the full answer