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hi John please can you explain to me what value at risk means and how its calculated. this is an example i copied from Kaplan text:
A bank has extimated that the expected value of its portfolio in two weeks time will be 50 million dollars with a standard deviation of 4.85 million dollars.
Using a 95% confidence level , identify the value at risk.
this is part of the solution. its says a 95% confidence level will identify the reduced value of the portfolio that has a 5% chance of occuring and from normal distribution table 1.65 is the normal distribution value for a one-tailed probability level. since the value is below the mean -1.65 will be need.
my main problems are where the 1.65 figure is from, what the 95% confidence level means, what does one-tailed probability means and why do we use -1.65 as the value for Z in the calculation
thank youI will try my best to explain in words (it is easier with a graph – when you have read this it might help if you look at the P4 Revision Notes. There is one page in there on VaR with a graph drawn on it!)
What we mean by 95% confidence level, is that we want to fix a ‘limit’ (a lowest value) where the probability of being above the limit is 95% (or the chances of it falling below that limit are 5%).
We assume that the graph of all possible values is symmetrical and so there is a 50% chance of falling below the average. So to find the limit we need to know how far below the average we can be before the chance of being further away is only 5%. So, we need to know how far from the average covers 50% – 5% = 45% (or 0.45)
We find it in number of standard deviations.The normal distribution tables tell you the probability of being any number of SD’s away from the average. We have to use them ‘backwards’ and see how many SD’s give an answer in the tables of 0.450.
If you look in the tables you will find the it is somewhere between 1.64 and 1.65 SD’s (if you want you can take half way between and use 1.645 🙂
We call it ‘one-tailed’ because we are only worried in one direction i.e. if the amount falls. We are not worried if the amount increases. (Although you do not need to mention the term ‘one-tailed’ in the exam).
Although we could repeat the above for any confidence level we want to, the only ones for the exam (and normally in real life as well) are 95% (where we work backwards in the tables for 0.45) and 99% (where using the same logic as above we work backwards in the tables looking for an answer of 49% (or 0.490)
I am not Mike :-))))
(Mike does not teach P4, and anyway he is not as good-looking as me! Grin!)Otherwise you are welcome!
Was looking on Google to find the answer to this query too and it took me approx. 1 hour of searching and not getting anywhere. Only 2 minutes into your answer and I can find the values depending on any confidence level now! Thanks John, you’re awesome.
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