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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).

mirliz says

Sir, so far i found VAR for 90%,95% and 99% in past papers. Will they ask for other than that percentage?

i know how to find the variance, but idk to estimate the +/- number between the variance in the table

John Moffat says

In theory they could ask for another %’age, but I would be astonished if he ever did because 90, 95, and 99 are the standard ones.

If you mean the apportioning between the table numbers for an extra decimal place, don’t worry about that. Just find the nearest one – that is sufficient 馃檪

mirliz says

Yes, that’s what i meant.

Oh i see. Got it sir. Thank you so much 馃榾

leonsa0808 says

Dear sir,

Noted the lectures are available from chapter 7 onwards. Any special reason please?

Many thanks

John Moffat says

I don’t know which page you are looking at but there are lectures on all of the chapters.

)Maybe you are looking at old P4 pages – P4 is now called AFM)

https://opentuition.com/acca/afm/acca-advanced-financial-management-afm-lectures/

dejoke says

Hello,

Please can you tell me if the material would be relevant for Sept 2018 exam or is it likely to change? Thanks

John Moffat says

The material is OK for September – there is no change to the syllabus.

leongacca says

Hi Sir,

I would like to know why the higher the confidence level, the value at risk would be increased as well.

ThankYou in advance

John Moffat says

At a 95% confidence level there is a 5% chance of being more than the VaR away from the average.

At the 99% confidence level there is only a 1% chance of being more than the VaR away from the average.

So for the chance of being further way from the average to be lower, we need to have a greater distance from the average.

leongacca says

Thankyou for that! appreciate it

John Moffat says

You are welcome 馃檪

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?

nice95 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).