The loan-to-value ratio (“LTV”) of a mortgage equals the loan amount divided by the property’s value. The LTV is a key indicator of mortgage quality. The lower the LTV, the more likely it is that the mortgage can be paid off even if there is a foreclosure and the property has to be sold, and the more motivation the homeowner has to stay current with his or her payments.

The weighted average LTV is a standard measure of the quality of a pool of mortgages. The weighted average LTV is calculated by weighting each LTV by the respective loan amount, and then dividing the sum of the weighted LTVs by the total loan amount.

Suppose we have a $6 million pool of mortgages with a weighted average LTV of 80%. We would expect the total property value to equal $7.5 million = $6 million/.8.

But the total property value is actually $9 million.

How is this possible?

**Other Posts on Puzzle #2:** Puzzle #2: Follow-up Questions, Puzzle #2: Answers to Follow-up Questions

**Other Puzzles:** Puzzle #1, Puzzle #3, Puzzle#4

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It is possible if the LTV distribution is barbell and skewed to the low LTV area.

The total property value is equal to $7.5 million = $6 million/.8, if each of the mortgages in the portfolio has a LTV of 0.8 which is equal to the average LTV of the portfolio.

If the total property value is actually $9 million, it means that some of the mortgages have LTV that is lower than the average 0.8. These low LTV mortgages are safe asset as their LTV is lower than the average LTV at 0.8. Since there are low LTV mortgages in the portfolio, there will also be high LTV mortgages in the portfolio so that the LTV of the portfolio is averaging at 0.8. These high LTV mortgages are risky mortgages and some would probably have LTV greater than 1 which will mean the borrower does not have equity interest in the mortgage anymore.

Cheers

Chun Lee

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Very good Chun Lee!

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I agree with Chun Lee and like his anaswer as it shows how deceptive weighted average can be. I advocate strongly for the simple average to become the standard measure as this is more transparent for the investor. The LTV is a measure of risk and not of performance. Weighted average is more useful tool when evaluating performance of a sample, such as returns in an index where there maybe multiple instances of the same result, within a range.

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