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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).

sambathkun says

Dear John,

Could you explain ” how do we get the probability of 45% and 49%? ”

Best regards,

Sambath

John Moffat says

To be 95% confident, there has to be a 5% (100 – 95) chance of being wrong.

Since the curve is symmetrical about the mean/average, there is 50% chance of it being below the mean. To be in the 5% region means being more than 45% (50 – 5) below the mean.

ashifraj says

hi, there are 29 chapters in notes but only 19 chapters videos. So are the videos covering whole syllabus or we are missing videos for other chapters?

John Moffat says

The other chapters are for you to read yourself. Many of them (certainly the earlier chapters) are more a combination of background reading and revision of Paper P3.

ashifraj says

Thank you. So chapters 1 to 7 and 20 to 29 there are no videos? These chapters if I just study from this notes is enough or I should read text book as well?

Chi-chi says

Hi there. Why do the lecture videos start at Chapter 7?? What about the first 6 chapters??

John Moffat says

The first six chapters are a combination of just background reading and basic revision from Paper P3 – they are for you to read yourself.

Samphos says

Hi,

Is this topic (value at risk) one of the P4 syllabus?

John Moffat says

Yes, of course 馃檪

(that is why it is here!)

Samphos says

Thanks very much!

I just wonder why it is there at the beginning of other lectures. What chapter of the lecture note it is in, please?

Cheers!

John Moffat says

It is not in the notes – the note is actually with the lecture. It was added later because VaR did not used to be in the syllabus.

Amer says

Hey, John, I have understood the calculation part of the lecture, however, I have not been able to understand the relevance of VAR in the appraisal. Why are we doing in the first place and how can it affect an analysts decision?

John Moffat says

Here is a little example.

Suppose a bank had made loans to people totalling $20M. Obviously there is a possibility that some of the people would not repay the money and if the bank wanted to be 100% certain that they would not suffer, then they would have to make sure they had $20M kept to one side in case every one didn’t pay. However everyone not paying would be very unlikely, so they might decide that if they kept just $15M on one side then there would only be a 1% chance of losing more than $15M and take the risk of just keeping $15M (using VaR calculations).

Dhaval 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?

Miley 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.

Miley 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

Majestic says

Thanks John For these Great lectures : )

John Moffat says

Thank you for the comment 馃檪

Majestic 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.

Yasir 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!

Andrew says

Is it OK to just take (VAR for one year at 95% confidence) and multiply its results by 6? I would have thought that the 95% applies to one year, not six , as there are more ways things can go wrong over a period of six years …..

I can see how this simplification would work but am not sure the simplification is valid over a long term. I suppose that taking the p(tail) <= 0.05 for one year and 'multiplying up' would include the possibility that tail losses in, say, two years might be counteracted by gains above mean in other years, but I still feel this is not as accurate as it might be.

i.e., having a 95% confidence that returns are more than $1,166,250 for *one* year, is not the same as a 95% confidence that they will be more than $1,166,250 *every* year, for a large number of years.

Surely?

John Moffat says

Something has gone wrong with the typing – I will have it corrected (although the lecture itself explains it properly).

Over 6 years, the std devn = sq root (6 x (750,000^2)). (We add variances, which is the square of the std deviation)

The arithmetic from then on is correct and since the std devn over 6 years is a lot greater than that for 1 year, it does fit in with what you say.

jameschiniah says

Nicely explained as usual…Thanks

John Moffat says

You are welcome 馃檪

emad says

Great work, understood this first time after failing to understand from virtually everything… 馃檪

John Moffat says

I am pleased it helped you 馃檪

Tan says

Thank you. Your explanation helps me understand the questions and answer. 馃榾

John Moffat says

You are welcome – I am very pleased that it helped you 馃檪

suni6419 says

Thank you Sir for this lecture on VAR. I was struggling to understand VAR. Now I understood.. 馃檪 馃檪

John Moffat says

I am pleased that you found it useful 馃檪

Farouq says

Please, where are the lectures on Adjusted Present Value and Type I-III acquisitions and free cash flows.? i noticed the videos start from chapter 7. i really love the lectures.

John Moffat says

There are lectures on Adjusted Present Values. There is no lecture on the types of acquisitions because the techniques involved are dealt with in earlier lectures.

Calculating free cash flows is the same as calculating the net cash flows for investment appraisal and there are lectures on this.

The first six chapters of the lecture notes do not involve calculations and are more background reading. The are for you to read yourself and do not warrant lectures.

Farouq says

Oh ok. Thank you very much. I’m very grateful.

nounrattanak says

Oh, I understand the logic behind now

John Moffat says

Great 馃檪

Boyd says

Perfectly explained. Spent hours trying to grasp from BPP. 20 minutes watching this and I get it!

John Moffat says

Great 馃檪

timmy100 says

Hi sir,

Excellent lecture. My question though is would the result be different if instead of calculating the VaR for one year you used two weeks for example?

John Moffat says

Yes it would because you would need to use the 2 week standard deviation.

timmy100 says

Thank you.

ds766 says

I am not sure if this is the right place to post- but I would like to thank Sir Moffat for his brilliant way of explaining things. I passed my P4 June 15 sitting in my first attempt and no base of F9 (as I got exemption for that) whatsoever. His lectures cover good base and this is what you need to pass – to really understand the core areas. Sir Moffat is always quick with his responses which surprisingly you won’t find with your paid classes sometimes. I did not take any other classes for this module and used LSBF book for self study. I would also like to give credit to my study buddy whom I found here in opentuition. Having a study buddy really helps. We did our revision over skype (it works). So good job Sir Moffat for this brilliant website and all your hard work.

Many thanks

Dee

ds766 says

P.S. In case you are wondering, my study buddy passed as well.

John Moffat says

Thanks a lot for your comments, and congratulations on passing 馃檪

Dthind says

The way you explain sir is really wonderful. You make the topic so easy.

tonia2010 says

No better explanation, Thanks John!

John Moffat says

Thank you 馃檪

supergaga says

Hello Sir!

Please tell me if the following statement is correct.

Given the average return of 2.4 M and the standard deviation of 0,75 M it means that 2.4/0,75 = 3.2 . looking for 3.2 in the standard normal distribution table we will find the probability to have a positive outcome. Is this correct ?

thank you!

your work is highly appreciated by all of us!

John Moffat says

Well….yes (if by positive you means greater than zero), but……

1 You would add 0.5 to the table figure because the table figure gives the probability of being less then the average – there is a 0.5 probability of being more than the average

2 No distribution like this will be perfectly normally distributed (which is one of the practical problems with VaR in practice). If it were truly normal then it could be negative but in reality that is probably impossible – in which case the probability of it being positive would be 100%

3 The tables you are given don’t go so far as 3.2 馃檪

4 This is not the way VaR is used in practice and so you would never be asked for the probability of it b being positive in the exam – you will only be asked the sort of thing I do in the lecture (e.g. 95% confidence)

supergaga says

Thank you, Sir!

I will come back to thank you once again when the results will be released.

braske77 says

I love you John 馃檪

gift2050 says

Thank you Sir Moffat ,i am enlightened,i hope this third sitting with OT i will be able to make it.

tfabienstef says

thank you for explaining this, did the past paper question and had no idea how they got the answer. much thanks.

Yuliya says

Very well explained. Thanks for teaching us!

rowetigere says

Great lecture.thanx John.so the VAR is1,166,250 for one year and 11,377,943 for six years.just seeking clarification

John Moffat says

Yes.

freddie25 says

great lecture

P4 says

Hi John,

Great video! Just one small thing, the value is $1,166,250 not $116,625 as mentioned in the description. (The Video has the right figures)

John Moffat says

Thanks 馃檪

P4 says

John, what if the examiner asks VaR for lets say 6.5 years so we’ll just do Square root of 6.5 * standard deviation?

John Moffat says

That’s correct 馃檪

(although I am certain he would ask for a while number of years!)

amirali92 says

This is a wonderful lecture explaining how to go about VaR. I’ve been having a lot of trouble being able to understand the concept. This lecture has simplified the VaR concept and I’m actually looking forward to having this question in the June 2015 examination.

Thanks OpenTuition!