Help with GARP Sample exam questions - Quantitative Analysis

[filip313]

Hi,
Could someone please explain the answers to these 3 questions in the second book af GARP official material (Quantitative Analysis)?

6. You simulate the price path of stock HHF using a geometric Brownian motion model with the fiollowing parameters:

• Drift = 0
• Volatility = 0.2
• Time step = 0.01

Assuming that St is the price of the stock at time t, if S0 =50 and the simulated standard normal random variables in the first two steps are e1 = -0.521 and e2 = 1.225, respectively, by what percent will the stock price change in the second step of the simulation?

Where is this explained in the Quantitative Analysis book? In which reading?


7. Which of the following statements about Monte Carlo simulation is incorrect?

• Monte Carlo simulations can handle time-varying volatility.
• Monte Carlo methods can be used to estimate VaR, but cannot be used to price options
• For estimating VaR, Monte Carlo methods generally require more computing power than histroical simulations

I can't find in the readings where these 3 are mentioned/explained


10. Based on 21 daily returns of an asset, a risk manager estimates the standard deviation of the asset's daily return to be 2%. Assuming that returns are normally distributed and that there are 260 trading days in a year, what is the appropriate chi-square test statistic if the risk manager wants to test the null hypotesis that the true annual volatility is 25% at a 5% significance level?

I do not understand why in the answers they say that: volatility = sqrt(260)*2%
Where does this come from?

 

[Alex_1]

Hi, with regard to your first 2 questions - I believe (but am not 100% sure, as I am also trying to grasp what has been added/deleted from 2013) that these two topics are not anymore relevant for 2014. Although, for what it is worth, the simulation of the stock price change should be similar (from the calculation procedure) to the volatility forecast from Hull Chapter 22 (pages 9 and 10 in the corresponding notes).
With regard to the last question: this should be the so-called square root rule: if the daily volatility is 2%, the returns are i.i.d. and there are 260 trading days in a year, then the annual volatility is sqrt(260) x 2%.
If something I have written above is not correct - anyone else please give a shout.
Thanks

 

[frm_risk]

Yes, agree with Alex_1 that Brownian motion and Monte Carlo were part of the reading on 'Monte Carlo Simulation' from Jorion which has now been removed for 2014.

 

[filip313]

Thank you for the clarification.

So what I am wondering is why GARP left the 2 questions in the official material of 2014. They give you only 10 sample questions for the entire Quantitative Analysis book and 2 out of these 10 are not relevant...

I understand the one with the square root rule now. Thanks