## Var

saichitale1994
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### Var

Consider a stock portfolio consisting of two stocks with normally distributed returns. The joint distribution of daily returns is constant over time and there is no serial correlation. Stock Epsilon has a market value of \$100,000 with an annualized volatility of 22%. Stock Omega has a market value of \$175,000 with an annualized volatility of 27%.
Calculate the 95% confidence interval 1-day VaR of the portfolio. Assume a correlation coefficient of 0.3. Round to the nearest dollar assuming 252 business days in a year. The daily expected return is assumed to be zero.
a. 3641 Incorrect
b. 5023 Incorrect
c. \$ 6007 Correct
d. 7176 Incorrect
VAR(portfolio) = 1.65 x vol(portfolio) x value of portfolio. Use data to calculate standard deviation of portfolio

Could not understand the logic.

edupristine
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### Re: Var

Solution:
Value A= \$100,000
Value B= \$175,000
Total Value= \$100,000 + \$175,000= \$275,000
Weight of Value A= \$100,000 / \$275000= 0.363636
Weight of value B= \$175000 / \$275000= 0.636364
Standard Deviation of Value A= 22%
Standard Deviation of Value B= 27%
Correlation Coefficient= 0.3
Standard Deviation of Portfolio=
[(0.363)^2 * (22%)^2 + (0.636)^2 * (27%)^2 + 2*0.363*0.636*22%*27%*0.3)^(1/2)= 21.02%
Z score for 5% VaR= 1.65
VaR annual= Z score * SD of portfolio * Total value= 1.65 * 21.02% * 275,000= \$95,361.76
VaR daily= VaR annual / SQRT(252)
= \$95361.76 / SQRT(252)
= \$6007.226

saichitale1994
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### Re: Var

If the daily 95% VaR of a portfolio is calculated as USD 5000. How would one correctly interpret the above statement?
a. One out of 100 days, the portfolio will decline by USD 5000 or more. Incorrect
b. One out of 20 days, the portfolio will decline by USD 5000 exactly. Incorrect
c. One out of 95 days, the portfolio will decline by USD 5000 or less. Incorrect
d. One out of 20 days, the portfolio will decline by USD 5000 or more. Correct
If the daily, 95% confidence level VaR of a portfolio is correctly calculated to be USD 5000, one would expect that 95% of the time (19 out of 20), the portfolio will lose less than USD 5000; 5% of the time (1 out of 20), the portfolio will lose USD 5000 or more.

According to the explaination given I feel that the answer can also be C.

saichitale1994
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### Re: Var

Use the following information for answering Question 7 & 8.
Thomson is a risk manager for investment bank XYZ. He is considering buying a 6-month American Call option on a non dividend paying stock OPQ. The current stock price of OPQ is USD 100 and the strike price of the option is USD 95. The stock price can move up or down by 25% each period. Thomson’s view is that the stock price has a 75% probability of going up each period and a 25% probability of going down. In order to find the no-arbitrage price of the option, Thomson uses two-step binomial tree model using annual risk-free rate of 12% with continuous compounding.

Question: What is the risk neutral probability of the stock price going down?
a. 56% Incorrect
b. 54.5% Incorrect
c. 43.9% Correct
d. 45.6% Incorrect
U = 1.25, D = .75
Probability of up move = (e(r)t – D)/(U-D) = (e0.12x(3/12) – 0.75)/(1.25-0.75) = .5609
Probability of down move = 1-Pu = .4391
Incorrect
Marks for this submission: 0/1.
Question 8
Marks: 1
What is no arbitrage price of the Call option closest to:
a. 21.18 Correct
b. 37.66 Incorrect
c. 21.82 Incorrect
d. 39.26 Incorrect

How did you get U and D?

saichitale1994
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### Re: Var

At present the shares of Microsoft Corp. Trade at USD 50. The monthly risk neutral probability of the price increasing by USD 5 is 40% and the risk neutral probability of the price decreasing by USD 5 is 60%. You are required to find out the mean and Standard deviation of the price of Microsoft Corp. after 2 months if the change in price is independent for consecutive months?
a. Mean = 48, SD = 6.93
b. Mean = 48, SD = 6.12
c. Mean = 36, SD = 6.93
d. Mean = 36, SD = 6.12

edupristine
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### Re: Var

Question 1 solution:
Part C cannot be the answer because 1/95= 1.05% and we need answer for 95% and 5% i.e 19/20 or 1/20. So according to the options given Option D seems to be correct.

Question 2 solution:
In the question ‘the stock price can move up or down by 25% each period’ is given. So if we assume stock price to be 1, So
U= size of the up move factor=1+25%=1.25
D= size of the down move factor= 1-25%=0.75

For Question 3 can you tell me the source of this question please.

saichitale1994
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### Re: Var

You are asked to find the price of the US Treasury note. The following table gives the prices of two out of three US Treasury notes for settlement on August 30, 2012. All three notes will mature exactly one year later on August 30, 2013. Assume annual coupon payments and that all three bonds have the same coupon payment date.
COUPON PRICE
5% 97.5
7% ?
8% 103.2
Approximately what would be the price of the 4 1/2 US Treasury note?
a. 99.64 Incorrect
b. 98.20 Incorrect
c. 98.64 Correct
d. 100.20 Incorrect
Explanation: 5% x X + 8% x (1 – X) = 7%, Therefore X = 80%.

saichitale1994
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### Re: Var

For the Question where U and D is to be found out I also did not get how to find no arbitage price of call.
The source of 3rd question is Quiz on Var named Quiz 1 in resourses of edupristine.

saichitale1994
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### Re: Var

Matt is asked to check for arbitrage opportunity in the Treasury bond market by comparing the cash flows of selected bonds with the cash flows of combinations of other bonds. If a 1 year zero coupon bond is priced at USD 97.42 and a 1 year 12% bond paying coupons semi-annually is priced at 104.18. What should be the price of 1 year Treasury bond which pays 8% semi-annually?
a. 102.40 Incorrect
b. 101.93 Correct
c. 99.58 Incorrect
d. 101.42 Incorrect
The solution is to replicate the 1 year 8% bond using the other two treasury bonds. The cash flow from the portfolio of two Treasury bond should be equal to cash flow of 8% bond. Weight of each bond needs to be determined in the portfolio.
Replicating the cash flow at the end of 1 year 1st equation
(100 x B1) + (106 x B2) =104
Replicating the cash flow at the end of 6 months 2nd equation
6 x B2 = 4
After solving both the equations, B1 = 33.33% & B2 = 66.67%
Therefore the price of the 8% bond = 0.3333 x 97.42 + 0.6667 x 104.18 = 101.93

edupristine
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### Re: Var

Can you please specify the problems you are facing in these questions?