Margin maths not right

Barry_Bear

A test yourself question which doesn’t appear to add up? 

Tony has a margin account and wants to invest $200 in a bond with a face value of $200 and trading at $23. The broker’s initial margin requirement is 10% of market value. 

Q1. How many bonds can Tony buy allowing for margin requirement? 

Q2. What is Tony’s total resulting exposure and actual margin requirement?

a. $2,000 for a margin of $200

b. $1,840 for a margin of $184

c. $1,600 for a margin of $160

Q1 how can Tony invest exactly $200? If he buys 7 he needs $177.10 ($23.00+$2.30=$25.30 x 7 = $177.10), or if he buys 8 $202.40 ($23.00+$2.30=$25.30 x 8 = $202.40). No?

Q2 he wants to invest $200 at 10% margin so how can his total exposure and margin requirement be any of these? 

Can any good folk here explain the correct answers where my figures are wrong, if they are?

maxsteam

Barry_Bear said:

A test yourself question which doesn’t appear to add up? 

Tony has a margin account and wants to invest $200 in a bond with a face value of $200 and trading at $23. The broker’s initial margin requirement is 10% of market value. 

Q1. How many bonds can Tony buy allowing for margin requirement? 

Q2. What is Tony’s total resulting exposure and actual margin requirement?

a. $2,000 for a margin of $200

b. $1,840 for a margin of $184

c. $1,600 for a margin of $160

Q1 how can Tony invest exactly $200? If he buys 7 he needs $177.10 ($23.00+$2.30=$25.30 x 7 = $177.10), or if he buys 8 $202.40 ($23.00+$2.30=$25.30 x 8 = $202.40). No?

Q2 he wants to invest $200 at 10% margin so how can his total exposure and margin requirement be any of these? 

Can any good folk here explain the correct answers where my figures are wrong, if they are?

When people talk about the face value of a bond, they usually mean the amount that is paid out when it matures. As interest rates change, it's normal for a bond to be trading at a little more or a little less than face value but it would be unusual for a a bond with a face value of $200 to be trading at $23.

There are also a few mistakes in your arithmetic. For example 23 + 2.30 does not equal 25.30 x 7.

underground99

Barry_Bear said:

A test yourself question which doesn’t appear to add up? 

Tony has a margin account and wants to invest $200 in a bond with a face value of $200 and trading at $23. The broker’s initial margin requirement is 10% of market value. 

Q1. How many bonds can Tony buy allowing for margin requirement? 

Q2. What is Tony’s total resulting exposure and actual margin requirement?

a. $2,000 for a margin of $200

b. $1,840 for a margin of $184

c. $1,600 for a margin of $160

The face value is a red herring of course - what it costs you to buy the bonds, and what you stand to lose if they default, is whatever they are trading for, when you buy them. If you use your cash to buy 8 bonds at market price $23 each, you will have initially spent $184 on the bonds. You can't afford another one because you don't have another spare $23. 

But if you use the market value of that small $184 pile of bonds as collateral to meet the 10% margin requirement on a bigger trade, you could get exposure to 80 bonds total (market value $1840) supported by your real holding of the 8 bonds which are worth $184. If all those bonds failed and became worth $0 each, you would be out the whole $1840 (the $184 you had already paid up front and another $1656 that you would owe the broker for, on the bonds that you hadn't actually given any cash for, when you did the trade on margin).

So from that it seems answer to Q1 is 80 bonds (or 8 'bought' in cash and 72 acquired by being able to meet the margin requirement of having covered 10% of the total position), and Q2 is (b) with those 80 bonds trading at $23 each which might drop to $0 each, you have $1840 exposure for your $184 of margin.

If it wasn't a multiple choice answer, the more intuitive thing to guess at would be: I'd like to buy 86 bonds trading at $23 each which would be a total $1978 exposure please, and my broker will make me post at least 10% margin which would be $197.80. I couldn't get 87 bonds because that would be an exposure of $2001 requiring margin of $200.10, and I can't afford as much as $200.10 because I've only got $200.00.  So that might cause you to guess at 86 bonds being purchased as long as you post a 10% cash margin.

However, that 'more obvious' answer isn't really going to work. If you did have 86 bonds trading at $23 each, worth $1978 at that point in time and had put $197.80 into your account sitting as cash (and not bought any bonds with it), you would get stuck if the bonds started to trade a bit higher, say $26 each.  Because those 86 bonds would now be worth $2236, which requires $223.60 margin, and we know you don't have any more than $200 of cash, so it's not enough collateral to maintain the position if the price rises.

This means the only way to be able to afford to stay in the game when the market price rises (without having to offload your holdings) is to use your cash to buy the 8 bonds for $184 to support the $1840 of total market value. If the bonds tick up in value a bit and are now trading at $26 each, the whole position is worth $26 x 80 = $2080, and the margin requirement on that is $208, but this is fine because you had bought 8 bonds which are now worth $208. The 8 bonds which you bought with your cash will always be sufficient collateral to meet a 10% margin requirement on a position of 80 bonds, even if the bonds start to trade at a value twice as high.

QED ? I don't know, as you were trying to do some maths around the concept of "$23.00+$2.30=$25.30" and I have no idea what you are doing there, so perhaps you don't understand the concept of margin and had been trying to follow a different lesson.  If this is a 'test yourself' question, presumably it comes after some sort of lesson or instructions in a book or website. So, go back to the book or training website and read it again to see what it was really saying. 

TheAble

I can't face trying to work that out. Looks dreadfully dull. Why not just buy the bond for cash already?

Barry_Bear

underground99
Big thanks for that reply. Much better explained than the material.

"I don't know, as you were trying to do some maths around the concept of "$23.00+$2.30=$25.30" and I have no idea what you are doing there"

I was thinking FRB Reg T so the math was 10% borrowed. Not 90%. Bonds are not equities but 90% for retail investors? I didn't think a broker would extend Tony that leverage as margin accounts normally require clients to maintain much lower LTV and was working on that basis.