Arnold Kling

Mortgage Depreciation

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With Freddie Mac, a major mortgage lender (and once my employer) gripped by scandal, it might be useful to go over some basic economics of the mortgage business. In particular, I want so describe how mortgages are a depreciating asset.

To most of us, a mortgage is a liability. It is the money that we borrowed in order to buy a home.

On the other side of the transaction is the lender. On the lender's balance sheet, the mortgage is an asset.

From the borrower's standpoint, with respect to inflation, a 30-year fixed-rate mortgage is a "heads I win, tails you lose" proposition. If inflation and interest rates go up, you pay back your mortgage in cheapened dollars. If inflation and interest rates go down, your mortgage payments cost more in real terms--but only if you keep your mortgage. Instead, borrowers typically refinance.

Economists call this the prepayment option. We say the borrower is long the option and the lender is short the option.

The value of the option grows over time, because the more time passes, the greater the chance of an unanticipated change in interest rates. Since the lender is short the option, the fact that the value of the option increases over time means that the mortgage asset can be expected to depreciate over time.

Thus, mortgages depreciate as assets, and they do so in ways that depend on changes in inflation and interest rates. Accordingly, large lenders, such as Freddie Mac and Fannie Mae, engage in hedging. The most important hedge is for the lender, say, Fannie Mae, to fund the mortgage by issuing callable debt. Instead of funding the mortgage by issuing "straight debt" (borrowing money) for 10 years at 5 percent, Fannie will issue "callable debt" for 10 years at, say, 5.4 percent with an option to call the debt (to refinance, in effect) in, say, 3 years.

Because Freddie and Fannie have such large portfolios, and because callable debt does not perfectly address the depreciation of mortgage assets, the agencies also use more exotic financial instruments, known as derivatives, in their hedging. Freddie tends to do so more than Fannie.

While the mortgage assets are depreciating, the callable debt and financial derivatives are appreciating. If the hedging is done correctly, the appreciation matches the depreciation under a wide variety of market conditions and scenarios.

The accounting treatment of all of this is interesting. Generally Accepted Accounting Principles (GAAP) do *not* allow lenders to depreciate their mortgage assets (also known as marking assets to market). They also do not allow lenders to mark their callable debt to market. However, GAAP usually does call for derivatives to be marked to market. Freddie Mac tried to evade the GAAP treatment and treat their derivatives the same way that they would treat mortgages and callable debt. When Freddie Mac had to switch auditors from the Enron-tainted Arthur Andersen, the new auditor challenged Freddie Mac's stance, producing the scandal.

Being forced to use GAAP treatment for its derivatives means that Freddie Mac must recognize the appreciation of its hedges while not being able to depreciate its mortgages. The result is to create earnings that are front-loaded. In fact, Freddie Mac will soon re-state its earnings for the past several years to be higher than was reported. By the same token, reported earnings in future years will be lower than would have been reported under Freddie Mac's previous accounting treatment.

For Discussion. The pattern of earnings that Freddie Mac originally reported is close to the pattern that would have been reported if GAAP required all assets and liabilities (not just derivatives) to be marked to market. Economists favor mark-to-market accounting, but many banks complain that it makes earnings too volatile. What are other challenges with mark-to-market accounting?


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COMMENTS (12 to date)
JT writes:

I'll list a few of the obvious ones to kick off the discussion:

1) Many markets in derivatives are not particularly liquid and price quotes are few and may vary significantly according to the trading desk doing the quoting. Therefore, GAAP reporting of derivatives is particularly reliant on management estimates and, hence, management good faith.

2) Fluctuations in the markets can cause extreme shifts in the value of a portfolio of derivatives. This may create the illusion of insolvency when in fact a financial institution, such as Fannie Mae, can weather the storm and remain solvent. Understandably, management is extremely concerned about this problem.

3) As Arnold has pointed out, GAAP treatment of securities is not consistent. Bonds, shareholder's equity and preferred shares are not marked-to-market (and they shouldn't be, IMHO) yet derivatives are. The disconnect can present a false picture of a financial institution's actual economic status.

4) Investors in financial institutions are acutely concerned with large shocks to the institution's portfolio. Yet the exposure to such shocks is hard to gauge and difficult to conceptualize. "Value at risk" (VAR) is one of the typical terms applied to potential losses from shocks. VAR is difficult to calculate internally (by company management) and very difficult to estimate externally (by investors). GAAP does not elucidate the VAR for a financial institution. It is therefore in that common position of the accountant: "like a drunk looking for his keys under the light from the lamppost because that is where there is most light, not where he actually dropped the keys." That is, it puts a priority on the accuracy of information rather than its relevance.

Hope this helps.

Ted Harlan writes:

I'm quite surprised to learn that the "embedded put" grows in value over time. All things being equal, shouldn't the value decrease as the notional or principal of the option decreases?

And, for any quants out there, does this mean that the theta of a mortgage portfolio is negative?

Or have I misread the post?

Ted Harlan writes:

Err, call. Not put.

Adam Gehr writes:

The value of the call option will decrease over time (ceteris paribus--as long the interest rate on the mortgages doesn't change). It will decrease for two reasons:
1) The shorter the time to maturity the lower the value of an American call (or just about any call).
2) The mortgage is being repaid over time--part of your mortgage payment every month is a repayment of principal--so the call is a call on a smaller asset every month. Note that the exercise price is, likewise, decreasing but not enough to offset the decline in the value of the callable asset. It is similar to having an option on 100 shares of stock this month, 99 shares next month etc.

That said, the main point of the article, the inconsistent accounting treatment of derivatives is quite valid.

Bernard Yomtov writes:

I also was puzzled by Arnold's comments on the value of the call. Adam's analysis seems correct to me.

Arnold Kling writes:

"1) The shorter the time to maturity the lower the value of an American call (or just about any call).
2) The mortgage is being repaid over time"

Point (2) is correct, but a very small effect.

Point (1) is *not* correct as applied to this case. In fact, it is completely backwards. It is true that, other things equal, if I compare a short-dated option with a long-dated option, then of course the long-dated option is more valuable. But that is not the exercise.

The right exercise is this. Suppose that we have an at-the-money three-month option today with a strike price of $X. One month from now, would you rather have that option or buy a new two-month option at strike price $X for whatever option price prevails in the market at that time?

On average, an at-the-money option that has "aged" will be more valuable than a new at-the-money option of the same time to maturity. That is because the gains from options that have moved into the money exceed the losses from options that have moved out of the money.

Another way to put it is this. Other things equal, it would be better for the borrower to wait and get a mortgage a month from now, and thus have a later maturity date for the prepayment option. But that is not the exercise.

What is important is that a mortgage that has "aged" a couple of years (so that there has been time for interest rates to move) has a higher expected value of a the prepayment option than a mortgage that is issued today.

Ted Harlan writes:

So is the graphical representation of this call option's value over time shaped like a mountain on a prairie?

Any suggestions for additional reading?

Bernard Yomtov writes:

Thanks for the explanation, Arnold. I never thought about that.

After some calculation, it looks to me like the impact of interest rate movements reinforces this. That is, a downward movement increases the value of the asset more than an upward movement decreases it, so if the distribution of rate changes is symmetrical, the distribution of chnages in call value are not.

Is this correct?

Bernard Yomtov writes:

Getting back to mark-to-market. It does seem that improving the accuracy of financialstatements is no-brainer. That earnings become volatile is not much of an argument. If they're volatile they're volatile.

Of course it would be useful for banks to report profit and loss due to changes in the value of investment portfolios on a separate line. Why shouldn't investors get a picture of how good a job the bank is doing in this area?

Of course, there still remains the problem that not all assets can reasonably be marked to market. Real estate holdings, or ordinary commercial and personal loans, represent difficulties. Still, for loans, reserves for bad debts and reports on spreads give at least part of the picture.

ARnold Kling writes:

"That is, a downward movement increases the value of the asset more than an upward movement decreases it, so if the distribution of rate changes is symmetrical, the distribution of chnages in call value are not.

Is this correct?"

Yes. On Wall Street, the term for this is convexity. Since mortgage security owners are short the option (the opposite of borrowers, who are long the option), they use the term "negative convexity."

I agree with you that if earnings are volatile, then they are volatile. I think that the earlier commenter may have been assuming that the idea was to mark to market derivatives but leave the underlying mortgages at book. Such an approach would induce incorrect volatility, and in fact Freddie Mac was trying to prevent what they thought would be artificial volatility in earnings.

I also agree that some assets are hard to measure in terms of market value. A lot of the non-market-traded derivatives are "marked to model," about which Warren Buffett is quite contemptuous.

One approach would be to limit Freddie and Fannie to using market-traded instruments. That would reduce counterparty risk as well as model risk in their operations.

SANJEEV KL writes:

Pls comment : During Inflation, A Borrower Gains and Lender Looses

Hi, Sanjeev.

During unanticipated inflations, sometimes the borrower gains and the lender loses. This can happen if an inflation unexpectedly occurs after a fixed-interest-rate loan is contracted.

Here's how it works: Suppose you lend someone $1000 in January with an agreement that he will repay you $1050 in a year. (The interest rate is thus 5%.) With the extra $50 you will get the following January, you expect to be able to buy yourself four new CDs. Your friend knows that he'll have $50 less to spend on new CDs for himself the next January.

Now suppose that in September, an inflation suddenly occurs. That is, suppose that prices all suddenly increase, so that when you get your $50 in January, you will only be able to buy two new CDs. Suddenly you, the lender, are hurt by the unanticipated inflation! If you'd known about this price increase, maybe it wouldn't have been worth it to you to agree on only $50 in interest. Likely you would only have agreed to a higher interest rate--maybe 7% or 8%.

Similarly, your friend is unexpectedly benefited. The $50 he's agreed to pay you now only cost him the loss of two CDs instead of four.

Even the $1000 in principal now has a depreciated value for you, the lender, when you receive it, because with the dollars you will be able to buy less now that an inflation has occurred. It is similarly a less onerous matter for your friend, the borrower, who has to sacrifice less in terms of goods and services.

In most modern credit markets, lenders have an incentive to guess as well as they can about future inflation so that they don't get stuck with interest rates that are so low that they go out of business. (Borrowers also have an incentive to think about possible future inflation carefully! If there is an unanticipated deflation, or if inflation is lower than anticipated over the course of the loan, borrowers are hurt!)

Interest rates that automatically adjust (or are "indexed") for inflation often become the norm in countries which have experienced erratic, unexpected inflations. The adjustment may not be perfect, but it helps mitigate the unexpected harm that can happen to either party in a fixed-rate loan when inflation is not as anticipated.

I hope this helps you sort out the issues.

Lauren

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