 # Historica Var / Monte Carlo Var Reading 39 CFAI Q 12

It is given MC but they have solved using historical Var Why?

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I think what it means is you are performing MC to come up with some returns out of which you calculate VAR using historical method. Check out pg.243. End of first paragraph for a better explaination. The check out the beginning of the last paragraph. Output from MC is being rank-ordered to calculate VAR.

You question is incomprehensible, please rephrase. 1) Historical VAR - based on actual observed returns, makes no assumption about normal distribution etc. 2) Monte Carlo VAR - is based on simulations, which are based on your assumed inputs regarding distributions, etc.

Thanks spart. Will check tonight and ask you if still don’t understand

artvandalay Wrote: ------------------------------------------------------- > You question is incomprehensible, please rephrase. > > > 1) Historical VAR - based on actual observed > returns, makes no assumption about normal > distribution etc. > > 2) Monte Carlo VAR - is based on simulations, > which are based on your assumed inputs regarding > distributions, etc. That question had monte carlo listed in it but answer is calculated via historical VAR which got me confused. I don’t have a book on me right now.

In other words, you use MC to generate bunch of returns. Then you look at the worst returns and rank order then. Then perform the historical method to figure out what the VAR would be. I think (correct me if I am wrong), historical VAR would actually make you look at ex-post returns from the range of period you are looking at then use that to forecast the VAR for the future. MC is more like inputting bunch of assumptions, then coming up with a range of output and then selecting the VAR in the same process as historical VAR does. The confusion may be because both use similar methodology in the end. I doubt think normality assumptions plays a role here. Isnt Analytical-variance method the only one that assumes normality in the output?

Sparty, You calculate VAR from Monte Carlo in a way similar to Analytical-variance method. In historical VAR, you select % of worst returns and select lowest among all worst returns. In this problem - They selected MC VAR and then used historical VAR to calculate it instead of using this formula = Notional Value [return - Z table value (std dev)]

sparty419 Wrote: ------------------------------------------------------- > I doubt think normality assumptions plays a role > here. Isnt Analytical-variance method the only one > that assumes normality in the output? I was saying with the historical method you don’t have to make an assumption about normality. With MC, you have to make an assumption about the distribution of returns (because you’re require to assume inputs). However, you can assume any distribution you want, it doesn’t have to be normal.

Dawg, I agree with your point. But in order to use the formula, you are using the expected return that you got from your MC simulations as the input. Whereas in this problem, you are actually looking at the whole range of returns (well, not really the whole range if there are a million simulations) and then rank ordering them to select the VAR just like you would in the usual historical method. So, I guess you could do both. @ ART… you are right. In the question, it actually mentions the returns were normally distributed.

if we do both then answers are not matching.

Sorry, I don’t have the book in front of me, but was there an expected return given in the question?

yes expected return, standard deviation and 1.65 (value from Z table) are given and that is why it got confusing

hmm…that sucks then…i’ll try and check it out later…

Dawg, I just quickly read to MC, ok so the reason the answers might different between both the methods is because (my understanding) 700 isnt enough to generate an outcome that would result in the expected return and standard deviation in the question. 700 is low enough that the distribution isnt entirely normal because its a small sample. You get close to normal distributions when simulations are done in hundreds of thousands or millions. Did that make sense?

Dawg, Are we ok with this problem? Wanted to know your thoughts.

if the sample for MC is large enough => it will follow normal distribution => we can calculate VAR from Monte Carlo in a way similar to Analytical-variance method. if the sample for MC is too small(700) => it may not follow normal distribution => we need to assembly return into a summary distribution to find the lowest 5% return, just like the usual historical method.

sparty419 Wrote: ------------------------------------------------------- > Dawg, > > Are we ok with this problem? Wanted to know your > thoughts. Not sure bud. Still not getting it. Is this covered in book? B_C - Where in the book it is being covereD?

Hey, check out one of my previous posts, with s the info. and page number. Its explained there, but its not to the point. Gotta interpret it. So, thats why i wanted to make sure I am on the right track.