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# Leveraging/Margin Investing Question

CalgaryPosts: 2 Associate

Hey everyone - brand new to the forums, but have used previous answers many times prepping for Level 1.

I have a question I can't find answered anywhere regarding Rate of Return on Leveraging. It's stumped me, my business partner and a couple colleagues.

This site does a great job explaining the main concept: https://analystprep.com/cfa-level-1-exam/equity/margin-transactions/

My example has to do with leveraging off a revolving credit facility like a Line of Credit. The issue is that you can invest with 0 equity (100% leverage).

Example:

A trader purchases \$100,000 of a stock at 100% leverage (100% borrowed capital, no equity) with an 8% interest cost. The trader has no commissions and receives no income. A year later, the trader sells the stock for \$125,000 (again, with no commission). The trader is charged 5% interest while the funds are borrowed.

Calculating the Profit:

1. Gross Sale Proceeds: \$125,000
2. Purchase Price = \$100,000
3. Realized Gain = \$25,000
4. Loan Interest = \$5,000
5. Return = \$25,000 - \$5,000 = \$20,000
6. Rate of Return = Return / Initial Investment

i.     This is where I can’t figure out how to calculate the rate of return, since you can’t divided \$20,000 by 0. With 100% leverage, what is your equity?

ii.     Logically to me, since my ‘equity’ exposure to this transaction was the cost of the interest, I would just divided \$20,000 by \$5,000, giving a return of 400%, but that doesn’t seem fully correct

Any insight would be appreciated!

Tagged:

• With 100% leverage, as you said your equity is 0. So if you follow the calculations for a margin transaction, the return on investment should be infinite ∞. However this metric ceases to be a useful one at this point, as the risk profile would be a much more significant consideration.

Is this a theoretical shower thought, or did you find a question by a provider that asked this? If it's the latter, I'd be interested in knowing which provider as I don't think the question would particularly useful as an exam question.

• CalgaryPosts: 2 Associate

This is actually sort of a combination of both shower thought and real world situation.

A client asked for assistance in calculating possible returns on a fully leveraged investment into markets given certain return profiles. The calculation of the FV is simple enough, but the actual ROI was what stumped me.

I agree that the risk profile is the more pertinent real-world issue, which we raised with the client. This is not an investment we would be handling for the client - he was asking for for assistance with the math.

• Charterholder London - UKPosts: 1,547 Sr Partner

100% borrowed capital is not 100% leverage, it is infinite. If your client is 100% leveraged they should be putting in \$1 equity for every \$1 borrowed.

In reality, banks will not lend that unsecured or without margin. Banks will take margin or the underlying securities as collateral. An infinite leverage situation is impractical, unless e.g. you're getting a risk-free loan from a relative.

Also revolving credit line is different, only given to companies with decent track record. Fees usually will be charged even before any drawdown.

Also not sure why interest rate can change from 8% to 5%, but that doesn't change the crux of the question (or the answer).

Hope that helps!