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### Question

James has estimated an annual standard deviation of $750,000 on one of its projects, based on a normal distribution of returns. The average annual return is $2,400,000.

**Estimate the value at risk (VAR) at a 95% confidence level for one year and over the project鈥檚 life of six years.**

#### Answer

For 95% confidence, VAR is 1.645 standard deviations from the mean.

i.e. for one year = 1.645 x $750,000 = $1,233,750

This means that James can be 95% certain that the returns will be $1,166,250聽or more every year ($2,400,000 – $1,233,750).

Over six years, the total standard deviation is square root of ( 6 x ($750,000 squared)) = $1,837,117

Therefore the VAR = 1.645 x 1,837,117 = $3,022,057

This means that James can be 95% certain that the returns will be $11,377,943 or more in total over the six year period ($14,400,000 – $3,022,057).

dhaval10 says

Hi,

Can you please confirm which chapter as per the notes does this fall under?

I am doing them in numerical order and I wanted to know when should I go through this particular lecture.

Thanks.

John Moffat says

This one is not a chapter in the notes – the lectures is self-contained 馃檪

kingojoe2000 says

great lecturer, God bless you

John Moffat says

Thank you 馃檪

rida says

i could not understand how to calculate value from normal distribution table. for example if confidence level is 99% and annual standard deviation is 800000 and average annual return is 2200000. how to calcultae value from normal distribution table ?

rida says

kindly please explain i am confused.

John Moffat says

This is explained in the lecture.

mansoor says

VAR is an area under the curve? if yes, is this the area from -infinity to 5% or 5% to +infinity?

mileyshanna says

Hi sir,

Are there any lectures before Chapter 7 available?

John Moffat says

No, because those chapters are more background reading and do not contain calculations.

mileyshanna says

I got it. Thanks.

John Moffat says

Great 馃檪

cyh says

hi Sir, just want to confirm value at risk is 1,166,250 or 1,233,750?

John Moffat says

$1,223,750

smooth says

Thanks John For these Great lectures : )

John Moffat says

Thank you for the comment 馃檪

smooth says

I just wish you could teach the entire ACCA papers!. Amazing Lecturer!!!

Thank you so much John : )

Arun says

Hi John,

In calculating the standard deviation of 6 years you say that it is equal to the square root of 6 times the square root of standard deviation for one year to the power of two and you go on to multiply ?6 by 750,000. Am I right in saying that the reason you did not multiply ?6 by ?750,000 was because that the powers of 1/2 and 2 cancelled out each other?

And secondly when you multiply the standard deviation by $750,000, isn’t the treatment very much similar to what we do with probabilities such as when we compute expected values.

Thanks.

John Moffat says

The answer to your first part is correct.

With regard to the second part – not really! It is because we can only add up variances (not standard deviations) and the variance is the square of the standard deviation.

dewan says

wow what a great lecture.Cant thank you enough for your brilliant lectures hope this continues for thousand more years.

John Moffat says

Thanks a lot for the comment 馃檪

oluwanisola says

Thank so much for the lecture but please i would appreciate if you confirm i understand:

The VAR is actually $1,233,750 right? which is also the limit at which the is a 95% confidence level? i dont really understand the part of the cut off return/cutoff.

The limit return is the VAR which is &1,233,750 and does this cutoff mean the excess above the limit(95% chance greater) or below(5%chance less). if so, i got lost at the second part(6years question) where you put the cutoff on the illustration as the limit.?

Also, when calculating the standard deviation square, why did we just square root 6 and not squareroot 6×750,000?

John Moffat says

It means that the chances of it falling below 1,233,750 is 5%.

You will know from my lectures on portfolio theory that the variance = std dev’n ^2

The variance per year is 750,000^2. The variance for 6 years is 6 x 750,000^2.

So the standard deviation is the square root of (6 x 750,000^2).

Which is the same as (square root of 6) x 750,000.

jkhina says

Looked difficult and confusing at first sight, but you make it look so simple and easy to understand. You’re indeed a TEACHER! Thank you so much for such a charismatic display of pedagogy.

John Moffat says

Thank you very much for your comment 馃檪

zee says

Dear Jhon,

I want to thank you for all the support given for P4 and finally I passed the exam with flying colours.. actually won the local prize and became a proud affiliate… You are one of the great teacher I have ever met… I’m talking from my heart…. God bless you!

John Moffat says

Thank you very much for the comment, and many congratulations on passing 馃檪

I wish you all the best for the future.

brain33 says

Hi

Could any body help how chapter 4 example 1 answer share price is 9.63 in year 1

Could anybody help which formula used and in y4 11.95

John Moffat says

Why on earth have you posted this under a lecture on Value at Risk? In future, post in the Ask the Tutor Forum.

Share price = PE ratio x profit after interest and tax / number of shares.

yasir3029 says

Hi sir,

I am going to appear in September 16 session, please confirm if these lectures will be enough to pass exam.

Best regards,

John Moffat says

Yes, provided that you also work through our free lecture notes, that you revise any bits of F9 that you find you have forgotten or are unsure about, and – most importantly – that you buy a Revision Kit from one of the ACCA approved publishers and attempt every question properly.

hk1986 says

Thank you Sir, it is really helpful

John Moffat says

Thank you for the comment 馃檪

pamela25 says

thank you, didn’t know VAR was this easy

John Moffat says

Thank you for the comment 馃檪

mansoor says

as usual, an extremely intuitive lecture that just lays out the concept of VAR!

John Moffat says

Thank you for the comment 馃檪

ozemoya36 says

How can I access the videos please

John Moffat says

Click on ‘P4’ on the bar near the top of the page.

You will then get a page listing all our P4 free resources including the lectures and lecture notes, together with links to them.

5678 says

Nice explanation…..thanx

John Moffat says

Thank you for the comment 馃檪

badoutaal says

Hi John I have attempted P4 twice and failed, now am going for the third time and I would like to honestly know whether depending on your class notes and videos would help in turning a fail to a pass?

John Moffat says

They can only help! However most important of all is practice – I assume you have a Revision Kit and have worked through every question? If not then you should. Also watching my lectures working through several question 1’s from recent exams may help you because I discuss the approach to the questions as well as working through the technical content.

(In future please ask any questions you have like this in the Ask the Tutor Forum rather than as a comment on a specific lecture 馃檪

grantcallaway says

Hi John. Thanks again for the lectures! Just wondering in what context a var question could be asked?

The reason I ask is that when you mentioned using std deviation squared over multiple year, and reference to variance, I link that back to risk and calculating beta factors.

They wouldn’t expect us to work backwards from a given value at risk to calculate the standard deviation and link in to business valuations would they?

John Moffat says

If VaR is wanted then it will be a specific part of a question 馃檪

I cannot imagine that they would ever expect you to work backwards!