With the information you have given, I would say never.
Remember the banker is a salesman, and the line of credit is the product.
If you don't need to borrow the money for something specific, then you don't need the line of credit in the first place.
Even if you did need something I would tell you to save up and pay cash for it.
On the tax advantage:
There is none, in the US you can deduct your mortgage interest on your taxes but it's not a tax credit
it's a tax deductions.
Let me explain further:
You spend $10,000 on mortgage interest, and you're in the 25% tax bracket.
You send the bank $10,000 in return
you get at tax savings of $2500.
You are still in the hole $7500
You would have been better off not taking out the loan in the first place.
On the Emergency Fund : You should have 3 - 6 months of expenses in cash, like a money market account.
This money isn't for investing, it's like insurance, and you don't make money on insurance.
The last thing you want to do is have to go into debt right in the middle of an emergency.
Say you lost your job, the last thing you would want to do is borrow money, right at the time you have no income to pay it back.
The bank is under no obligation to maintain you credit limit and can without notice reduce it, they can in most cases call the loan balance due in full with little or no notice as well.
Both of those are likely scenarios if the bank were to become aware of the fact that you were unemployed.
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There are two basic types of lines of credit typically offered at a retail bank: Overdraft line of credit is essentially a revolving personal loan that you can draw upon as needed or automatically draw on when you overdraw on your checking account.
Typically with a commercial bank there is a fee to use the automatic overdraft in addition to interest.
Some credit unions don't charge a fee.
Interest is typically computed using average daily balance.
A Home equity line of credit is a revolving loan that is secured against your home.
Interest on home-improvement related expenses is deductible.
Since the bank gets a lien on your home, the rates are low.
Sometimes you can even get debit cards that will hit the line.
I think these are a good idea if: You are making substantial home improvements.
You are a 1099 worker or business owner who doesn't always get paid on time.
A home equity line of credit is a cheap way to borrow money for a short term.
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A line of credit is a poor substitute for an emergency fund.
Banks typically have a clause that allows them to stop further withdrawals from your line of credit if there is a change of vaguely defined type.
For example, if you lose your job they can stop you from making withdrawals from your line-of-credit.
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The only really good reason to open a line of credit is that you want to buy something that you don't have money for.
That's got its own risks - see plenty of other places to see warnings about not borrowing too much.
The only other reason is that you might want to use a line of credit as your emergency fund.
The usual way of doing this is to keep the money in an easily acccessible savings account - but such accounts usually pay rather now interest, and there is an argument for instead investing your emergency money in a higher-interest but less-accessible fund and using a line of credit to tide you over until you can extract the money.
I'm worried about the comment that you can "deduct my interest on my tax returns".
That is usually only possible if you are borrowing money to invest.
It sounds as if your banker is going to persuade you to not only open a line of credit, but then invest that money in something.
Be aware that this kind of 'leveraging' is much higher risk than investing money you already own.
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I have a line of credit that I have attached to my checking account in case of an overdraft.
Since I haven't over drafted my checking account in 4 years, I typically borrow the minimum $5 from the line of credit and then pay it back the next day.
This usually costs me a couple of cents
and I have to do it twice a year, but it keeps the account active
and they don't close it down.
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I'm new to the concept of "line-of-credit", and my banker says I should be able to open one based on the number of stocks I own.  I have no mortgage.  I'm told that I'm able to deduct my interest on my tax returns.  When is it wise or unwise to open a line of credit?
When should I open a "Line of credit" at my bank?
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You should only open a line of credit if you want to borrow money to buy something. The answer to this question will be subjective, however, some people would suggest that opening a line of credit is only a good idea if you need to buy something that you don't have the funds for.
The answer to this question will be subjective, however, some people would suggest that opening a line of credit is only a good idea if you need to buy something that you don't have the funds for.