# Leverage and portfolio return

2010 past paper, question 9: Average client portfolio has an expected asset return of 7.4%, average portfolio leverage is 40% and we pay 4.25% in the repo market. Calculate average client portfolio return. My working is below: Gross profit on portfolio (assuming \$100) = 100 x 0.074 = 7.4 Cost of borrowed funds (assuming \$40) = 40 x 0.0425 = 1.7 Net profit on portfolio = 7.4 – 1.7 = 5.7 Return on average client portfolio = 5.7 / 60 = 9.5%

Can someone please tell me why I I’m not getting the model answer of 8.66%.

I don’t have the problem in front of me, but here is what I got:

7.4% + .4(7.4%-4.25%) = 8.66%

How I read the quesiton. The equity portfolio is targeting 7.4%, we’re leveraging that up by 40% that so 140% of the original equity will earn 7.4% and then you have to subtract the borrowing costs. So to modify your calculations:

\$140 * .074 = 10.36

\$40 * .0425 = 1.7

10.36 - 1.7 = 8.66

Also if you look at your answer as a dollar amount of \$5.7, it wouldn’t make sense to use the leverage because your unleveraged portfolio would make \$7.4.

The \$5.7 is still better though, the question was just unclear.

I see the confusion, and I agree the question isn’t clear. I focused on the “expected” perfomance of the portfolio would be 7.4% and then leverage is applied. Had it been that a leverage portfolio had returned 7.4% then I would go with \$5.7 as an answer.

If average portfolio leverage = 40%, doesn’t that mean your leverage ratio (B/E) = .67? For instance, your portfolio is \$100, your leverage is 40% so \$40. Therefore, your equity is \$60. \$40/\$60 = .67?

No @cook29. You have 100, you borrow 40, your gross assets are 140. Your levered 1.4 to 1

So when a question says “average portfolio leverage is 40%” how do we know which of the below to use cos i have seen both: 1. 100 equity, 40 leverage, 140 total assets 2. 60 equity, 40 leverage, 100 total assets

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So when a question says “average portfolio leverage is 40%” how do we know which of the below to use cos i have seen both: 1. 100 equity, 40 leverage, 140 total assets 2. 60 equity, 40 leverage, 100 total assets

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I feel like I’ve seen 2 as well, but 1 makes sense cause when you’re levering up, your equity would’ve been your 100% position before leverage. So when you borrow, it’s always going to be in excess of your equity position. What tripped me up is the way the question is worded. It says leverage is 40% of the average portfolio. To me that means your looking at the total portfolio including leverage and equity. I guess that’s not the case here. Really poorly worded in my opinion if that’s what it looks like from the source.