# leveraged borrowing - Fixed income

Can somebody please clear this doubt

Ri + B/E ( Ri-Borrowed rate)

I have seen so many questions where they use either entire asset value or equity value in denominator . I use appropriate value and most time i am wrong.Looks like i am lagging behind …

Simplisticaly, Return on asset is equal to the net return (return - debt return) from liabilities (that is debt/leverage) and return from equity portfolio

I dont even use that formula when solving exercises

I think the next:

Suppose I have 20% leverage ok? so I have 120% invested in something

then my return is the following:

1.2 * Return of the portfolio - 0.2 Costs of funding.

you can change the formula as:

1*return on portfolio + .2* return on portfolio - .2* costs of funding

= return on portfolio +.2 * (return on portfolio - costs of funding)

you know you are leveraged 20% which is Borrowed / Equity invested (which is 100)

Jorge

It’s only the equity value in the denominator. In other words, not including the leveraged portion.

In CFA "Chung " topic tests , why did they use 500 in denominator as Equity ?

I do something similar.

1. compute the total dollar return on original capital plus borrowed funds. So if i had 70 and borrowed 30, and earned 10%, the dollar return would be 10.

2. subtract the dollar borrowing cost from total earnings. So if it cost me 5% to borrow 70, I subtract 3.5.

3. divide net gains (total dollar return - dollar borrowing cost) by the original investment. Leveraged return = (10-3.5) / 70 = 9.3%

Just easier for me to think in dollar terms vs. returns

They use 100 in denominator. Check the errata.

I don’t ever use that formula either, and I have been successful on that.

I think it is better to focus on what is actually happening. How much are you going to make on your total assets (liabilities + equity), and how much is your borrowing cost. If you know that, then you can calculate the return on equity or assets.

Jorge’s explanation is good.

(E) Re = (A) Ra + (D) Rd

Equity in the denominator appears in the calculation of the Duration of Equity… aren’t you mixing things up?

(E) De = (A) Da + (D) Dd

It’s really the same formula in both cases.