During FHA’s 2014 fiscal year, the following events occurred: Home prices increased about 5% nationwide. FHA’s Home Equity Conversion Mortgage (“HECM”) reverse mortgage program shifted from production of predominantly fixed rate loans to predominantly adjustable rate loans. Thousands of seasoned loans paid off and were replaced by a FY 2014 vintage with lower Principal Limit Factors, i.e. Loan-to-Value (“LTV”) ratios, and higher Mortgage Insurance Premiums (“MIPs”). Each new HECM loan now pays a colossal 2.5% MIP at closing, or else is restricted for one year to a 60% draw of the Initial Principal Limit. The result of all this good news, according to FHA’s newly released MMI Fund Report and Fiscal Year 2014 HECM Actuarial Study: the value of the HECM portion of its Mutual Mortgage Insurance (“MMI”) fund declined by $7.7 billion. How is that possible?

The MMI Fund Economic Net Worth estimates are “Present Values,” that is, a single number that quantifies the economic value in today’s dollars of the fund’s future cash flows. In both the MMI report and the accompanying Actuarial Review (see page i), the vast majority (67%) of this decline is attributed to a change in the “Discount Rate.” What does that mean?

The terms “discount rate” and “discount factor” are central components of present value. They describe two different numbers that are inversely related. The “discount factor” is a number from 0 to 1 which, when multiplied by an amount of future cash flow, equals that future cash flow’s equivalent present value. The “discount rate” is a number from 0 to 1, typically expressed as a percentage, which is a measure of how much value is discounted over a discrete period, typically a year or a month. The two terms are related to one another in the basic present value equation:

Discount Factor = 1 / (1 + Discount Rate)^{t}

Where t = time period

For example, if the annual discount rate is 10%, the discount factor for cash flow at the end of year 1 is approximately 0.9090909. It follows that at a 10% discount rate, $100 received one year from now is worth approximately $90.91 today, and that $90.91 compounded at 10% for one year equals approximately $100. The Actuarial report gives another example on page C-4. Now, bear these relationships in mind when reading the Actuarial Report’s explanation for the large decline in the MMI Fund value, under Section f, “Discount Factor Update” on page 19:

“This decomposition step shows the effect of the FY 2015 budget discount factors. The latest OMB published discount factors are higher than the values of the FY 2014 factors used in last year’s Review, as shown in Appendix C. The higher discount factors decrease the present values of both future positive and negative cash flows. The net impact of discount factors is a balance among these opposing cash flow items**. **As HECM recoveries occur at longer durations in the future than claims, the higher interest rate assumption in the long run has a larger negative impact on the cash inflows than outflows. As the result [sic], the FY 2014 HECM economic value decreased by $5,182 million and the FY 2020 HECM economic value decreased by $13,763 million. This is the largest factor leading to the much lower economic value this year than last year.”

Let’s apply some decomposition steps of our own, and decompose this paragraph one sentence at a time.

**“***The latest OMB published discount factors are higher than the values of the FY 2014 factors used in last year’s Review, as shown in Appendix C.***”**

But wait a minute; at the bottom of page C-4, the same report states:

*“The discount factors used in this Review are lower than the corresponding discount factors in last year’s Review.”*

This contradicts the statement on page 19. Which one did they mean? Let’s read on and look for clues.

*“The higher discount factors decrease the present values of both future positive and negative cash flows.”*

This statement is doubly wrong. First, higher discount factors *increase* the present value of future positive cash flows. Second, the effect on positive and negative cash flows cannot be the same. Higher discount *factors* mean lower discount *rates*. Therefore, higher discount factors *increase* the present values of *positiv*e future cash flows, but *decrease* the present value of *negative *cash flows. This is because the higher the discount factor (in other words, the lower the discount rate), the higher the absolute present value of the future amount. That means a *higher* value for *positive* cash flows and *lower* value (that is, more negative) for negative cash flows. So no clues there.

*“The net impact of discount factors is a balance among these opposing cash flow items. As HECM recoveries occur at longer durations in the future than claims, the higher interest rate assumption in the long run has a larger negative impact on the cash inflows than outflows.”*

* *We assume that the reference to “higher interest rate assumption” means “higher discount rate assumption,” given the context. The federal government tends to use interest rates approximating the Treasury yield curve as the discount rates for calculating present values, as the Actuarial Report explains on page C-4. The discount factors shown in Appendix C, when translated into the corresponding rates, do indeed result in a reasonable set of discount rates which approximate the Treasury yield curve a few months back. In the attached **spreadsheet**, we translate the present value factors into discount rates.

Given the conclusions of this year’s report, we have to conclude that the report really does mean *higher *discount *rates*, which means they meant to say *lower* discount *factors* on page 19 as well as in the Appendix.

But the issue is still confused. That’s because the nature of FHA’s cash flows with regard to HECM are NOT as simple as “*HECM recoveries occur at longer durations in the future than claims, the higher interest rate assumption in the long run has a larger negative impact on the cash inflows than outflows.” *This implies that FHA’s cash flows are all back loaded, and its negative cash flows are all front loaded.** **In fact, this does not describe the lifecycle of any HECM loan. Consider the present value equation in Appendix C, paragraph C3 of the Actuarial Report, “Net Future Cash Flows” on page C-4:

** **“The portfolio cash flow for a HECM book of business can be computed by summing the individual components:

* **Net Cash Flow*_{t }*= Upfront Premiums*_{t} *+ Annual Premiums *_{t }*+ Recoveries *_{t }*– Claim Type 1s*_{t} *– Claim Type 2s*_{t} *– Note Holding Expenses *_{t}“

In other words, there is a lot more to HECM cash flow than recoveries and claims. What’s more, different loans have different patterns of cash flows, so one can’t make general statements about the impact of changing discount rates. Consider further four possible types of HECMs, categorized by four possible life cycles:

**HECM Loan Type 1**: This loan never defaults and pays off before reaching 98% of the Maximum Claim Amount (“MCA”) and before the loan balance exceeds the property value. FHA will simply collect premiums and never pay a claim. For these loans, a higher discount rate decreases present value but, as the cash flow is all positive, the present value to the MMI fund is positive regardless of the discount rate.

**HECM Loan Type 2:** This loan defaults and/or has a “crossover loss” before reaching the 98% Maximum Claim Amount. A crossover loss happens when the loan balance exceeds the property value at the time of payoff. For these loans, the MMI fund will earn premiums for months or years and then *may *pay a Type I claim when the loan pays off, *if* a loss occurs that is covered by FHA. For these loans, or any set of cash flows that is positive then negative, higher discount rates can *increase* present value, depending on the timing and magnitude of the cash flows.

**HECM Loan Type 3**: This loan never defaults and pays off after reaching 98% of the Maximum Claim Amount, but before the loan balance exceeds the property value. FHA collects premiums for several years, then buys the loan at the 98% Maximum Claim Amount (Type II claim), and then collects the accreted loan balance when the loan finally pays off. For these loans, FHA’s cash flow is positive, then negative, then positive again. The present value impact of higher discount rates also depends on the magnitude and timing of these cash flows.

Looking at the discount factors however, we notice that they are well below the interest rates that FHA would earn once it purchases a loan at 98% of the MCA. In other words, FHA pays a price of par to buy a loan earning premium interest, a fact much lamented by HMBS issuers. So even if these discount rates are higher than last year, they are not so high that FHA has a negative carrying cost. In the absence of losses, a loan in which FHA receives premium, then pays par, then collects premium interest, must generate positive present value for the MMI fund. Higher discount rates may or may not decrease the present value, but the present value cannot be negative. But of course, losses are not always absent, which brings us to:

**HECM Loan Type 4**: This loan defaults and/or has a crossover loss after reaching 98% of the Maximum Claim Amount. Premiums are collected, then FHA purchases the loan at 98% of the Maximum Claim Amount, then it eventually pays off. For these loans, cash flow is positive, then negative, then positive. At the time of payoff/liquidation, FHA suffers a loss, so the interest earned from buyout to payoff may not make up for losses (i.e. excess of Claims over Recoveries) and advances (i.e. the “Note Holding Expenses” in the equation above). FHA does not buy HECM loans that are in default, which means that these loans acquired under the Type II claim are clean loans that have been in compliance for years, including payment of taxes and insurance. HECM loans can default after FHA buys them, and these loans may become a larger problem for FHA, however, as the Actuarial report states on page D-4: “Default is a decreasing function of elapsed time from origination.” The likelihood of default diminishes with each passing year, so these loans are positively selected from FHA’s standpoint.

The report’s characterization of HECM cash flow describes at best *part* of the life cycle for *some* HECM loans. It could conceivably apply to the current MMI portfolio of HECM loans, which are all at different stages of their life cycle, but this seems unlikely, with so many new loans so far from the 98% assignment trigger. As a result, the report falls far short of explaining the results of its model.

The report also does not adequately account for the FHA’s conclusion “that the HECM portfolio is well over ten times more volatile than the Forwards” (MMI Report, page 41). Is this assertion supported by recent performance? The reports have very little empirical data on past performance. How many loans liquidated with losses last fiscal year? What were realized losses from claims on these loans? What was net cash flow? How much MIP was collected? Perhaps this data was in Exhibits II-10 and II-11, which seem to have gone missing from the MMI report.

A careful reading of these reports reveals a big difference between actual performance and projected performance. For example, Exhibit II-5 (MMI Report, page 37) shows the experience of the Fund during FY 2014. The Capital Resources of the forward loan portfolio declined 4.6%, the Capital Resources of the reverse portfolio declined 3.3%. That doesn’t sound like ten times more volatility.

How does this volatility break down by each variable, for example, home prices? The average LTV ratio of a new HECM barely exceeds 50%; many FHA loans have original LTVs as high as 97%. Yes, HECMs have negative amortization and future draws, but are HECMs really ten times more volatile when they start off with at least 30% more equity?

Finally, these Economic Net Worth numbers that cast HECM in such a relatively bad light are projections based on a set of assumptions. So which is really volatile: the loans or the assumptions? Are these assumptions more volatile in ways that favor forward mortgages versus reverse mortgages? With all of these problems and unanswered questions, we must question the model’s methodology and the validity of its conclusions.