Arnold Kling  

Efficient Markets vs. Mortgage Leverage

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A Pacifist Syllogism... Men of Respect...

Patri and Mike want to argue that taking out a big mortgage to invest in the stock market is really clever. Here is the counter-argument.

Think of this transaction as two transactions:

1. First, you take out a 6 percent mortgage to buy taxable bonds yielding 5 percent.

2. Second, you trade the taxable bonds for stocks.

Step 1 is a loser. True, you can deduct the mortgage interest from your taxes. But you have to pay taxes on the interest on the bonds. So, whether we're talking pre-tax or post-tax dollars, you lose money.

Step 2 is a risk-return trade-off. In an efficient market, the "equity premium" is not an arbitrage opportunity. It is compensation for taking more nondiversifiable risk.

You can do step 2 without doing step 1. For example, you can buy exchange-traded index mutual funds on margin. Or you can buy futures contracts on the S&P 500. Or you can buy call options on S&P futures. You pick the mechanism that offers the lowest interest rate, and that would not be the mortgage rate.

This is one topic where I think that untrained people are really, really out of their league making comments. For example, anyone who says that efficient markets theory only holds when all investors are identical clearly has never worked through the proof of the portfolio separation theorem. And unless you understand that theorem, I am not going to be convinced by what you have to say.

One final point: in an efficient market, tax effects are clientele effects. If you are in a moderate income bracket, chances are you do not benefit from a tax-advantaged investment, such as municipal bonds. That is because investors who are in higher brackets than you will bid up the price of these bonds to the point where your after-tax returns on them are low.


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The author at EclectEcon in a related article titled Differences in Lending and Borrowing Rates writes:
    I've been following the conversation between Mike Moffat and [Tracked on December 14, 2007 7:51 AM]
COMMENTS (34 to date)
Patri Friedman writes:

You can do step 2 without doing step 1. For example, you can buy exchange-traded index mutual funds on margin. Or you can buy futures contracts on the S&P 500. Or you can buy call options on S&P futures. You pick the mechanism that offers the lowest interest rate, and that would not be the mortgage rate.

The key to the argument is that step 1 is at a 4% nominal interest rate (6% - 2% tax deduction). To trade on margin, I get a 9% interest rate. So those aren't comparable at all. Only if you can get leverage for 4% from one of those methods does this argument hold.

I have heard that there are ways of using long-term call options that have leverage that cheap, but note that options don't capture the dividend return of the S&P, so it isn't actually comparable to buying stocks on margin.

You seem to be implying that I have non-mortgage alternatives to do the same thing, but I don't. I have no other way of borrowing cash at 4%.

Step 2 is a risk-return trade-off. In an efficient market, the "equity premium" is not an arbitrage opportunity. It is compensation for taking more nondiversifiable risk.

Again, given the limited opportunity, I don't see why this is an argument against the strategy. Suppose that I am very risk-tolerant (perhaps because I am young and have high income potential - which is indeed the case). The value to me of investing in stocks is > than the value of investing in bonds. So even if the equity premium is only compensation for risk, there is nothing illogical about my being willing to take out a loan at 4% to buy index funds but not to buy bonds. The two investments have different risk/return characteristics, so for my purposes they are not equivalent.

This also implies that I have a 100% equity portfolio, but I don't see why it is an unreasonable strategy.

One final point: in an efficient market, tax effects are clientele effects. If you are in a moderate income bracket, chances are you do not benefit from a tax-advantaged investment, such as municipal bonds. That is because investors who are in higher brackets than you will bid up the price of these bonds to the point where your after-tax returns on them are low.

Are you saying this applies here? But it is not the investment which is tax-advantaged, it is the loan. And that is very different, because while a rich investor can buy arbitrarily many bonds in order to drive the price up, no one can borrow arbitrarily much against their house.

Dr. T writes:

Here's a concrete example, using a set-up favorable to those who believe that it is better to take a mortgage and invest, that supports Mr. Kling's point that the strategy is bad:

You are in the top tax bracket, and your combined federal, state, and city income tax rates are 40%. You get a $500,000 mortgage at 6%, so your interest payments the first year are $30,000 (I compounded annually for simplicity.) and your interest less tax deduction is $18,000.

You use the $500,000 to buy stocks with an annual gain of 7%, and you sell them after a year. You have capital gains of $35,000 that are taxed at 20% federal but at the regular rate by state and city (12% total). Your taxes are 32% of $35,000 or $11,200. Your investment profit is $23,800.

By risking your money on the stock market, you made a net profit of $5,800 which is only 1.16% of your $500,000 nest egg. That's a small gain for a large risk. If the stock gain had been 5%, you would have lost money.

As P. Friedman notes, if you have a high probability of a larger spread between mortgage interest and stock fund performance, then you could do well by getting a big mortgage and investing the cash. The problem is that such conditions do not occur often and do not last long.

Phil Birnbaum writes:

Patri,

It's true that you don't get the dividends when you buy a call option, but the option is priced lower to compensate. So, effectively, you *do* get the dividend, just in the form of capital gains.

The long-term option choice is a good one. You buy a call and sell a put. That's the equivalent of owning the stock but not getting the dividend. By choosing an appropriate strike price, you can own this with no money down (although you need enough margin, of course).

Indeed, you can buy a way out-of-the-money call option, which makes the put option deep in-the-money. If the stock is at 20, and the strike is at 30, you'll get between $9 and $10 cash in your account ($10 minus the risk-free interest rate, I believe). You can use that to buy some other stock. Effectively, you're buying two stocks by borrowing money at the risk-free rate. Your only other cost is your commissions, and the bid-ask spread (which could be material).

Right now, GE is at $37.25. You can buy a Jan 2010 call at 60 for 54 cents. You can sell the put for $23.10. That gives you a net of about $22.50 in your account to use on other stocks. (Actually, the bid/ask spreads are about 35 cents ... factor that in, and your interest rate is the risk-free rate plus about half a point.) In January 2010, you effectively pay back the $22.50 plus interest, and receive (pay) the appreciation (price drop) on GE.

Anyway, a question for Arnold: assuming that there's no bid/ask spread, and you can effectively get the risk-free rate ... does that change your opinion on the desirability of borrowing to invest?

kebko writes:

For about 7 years, we have been using home equity so that we can max out all of our tax deferred investment options, so that we get the tax benefits on both ends - tax deductible debt & tax deferred capital gains. In addition, we have made very good returns on our targeted stock investments. Investors & professional money managers make predictably biased errors just as irrational voters do, and we have managed to take advantage of that to consistently outperform the markets. It's not possible for that many people, but for someone with economic intuition & good knowledge of accounting, there are lots of small caps with very manageable financial reports that offer lots of mispricing opportunities. The average is the average, but I think it's possible to have skill that outperforms. I've seen too many stocks that have doubled, tripled, or more, in very short order, based on performance that was previously perceivable with a reasonable amount of effort & discipline, to believe that every opportunity out there has been captured by some hedge fund stud.

Phil Birnbaum writes:

Another reason to borrow to invest (even if you have to pay more than the risk-free interest rate) is that tax policy makes it profitable.

In Canada, the interest paid on money borrowed to invest is fully deductible immediately. Capital gains are taxable only when incurred, and at exactly half the regular tax rate.

So if you can borrow at 6% to buy a stock that appreciates the same 6%, you still make money. At a 50% tax rate, you save "3%" from the interest deduction, and pay "1.5%" in capital gains, for a net profit of "1.5%".

Indeed, if you borrow to buy a stock that you won't be selling for 20 years or so, you can deduct the interest *every year*, but your gains compound tax-sheltered until you sell. This is a very good deal.

It may also be compatible with an efficient market because (I'm pretty sure) the lower capital gains tax rate does not apply to entities who trade for a living (such as brokerage houses). They pay full boat on their capital gains. And it's mostly those big traders who set the efficient price, isn't it? So if the break-even (after accounting for risk) is buying stocks at the risk-free rate, you probably do BETTER than breaking even buying stocks at the risk-free rate plus 1%, but getting the nice tax break.

Mike Moffatt writes:

In an efficient market, the "equity premium" is not an arbitrage opportunity.

Again, though you're ignoring the equity premium puzzle, which is the basis for why Patri's argument works.

You keep saying "well, the market is efficient!" despite 25 years worth of research to the contrary. At some point a large enough body of evidence has to trump theory.

My question to you: What body of research has convinced you that the equity premium puzzle is an artificial one?

bwv writes:

Another way to look at it is that the home has an investment component in and of itself which perhaps has some optimal amount of leverage. Why should one buy a Real Estate Investment Trust (or any company with debt for that matter)that is 50% levered at a higher rate of interest than my mortgage? The additional interest cost can be thought of as the option premium to put the property back to the bank if it falls below the mortgage amount. The cost of exercising this option should IMO be a determining factor in the trade. For a young person who can easily move into an apartment and rebuild their credit, it may have a low cost. For a middle age person with a family the cost will be prohibitive

Historicaly borrowing at fixed rates against real assets has been a good trade and will at least be an inflation hedge going forward (homeowners in the 1970's had a windfall that dwarfs the runup in home prices this decade)

Phil writes:

In an efficient market, the "equity premium" is not an arbitrage opportunity.

I agree with this, but I still don't understand Arnold's argument. Is it simply that the strategy is not "clever," just neutral, taking the risk into account? Is it that the extra point of interest on the mortgage is expensive and makes the strategy worse than it could be otherwise? I would agree with those arguments, but I don't think that's what this post is trying to say.

Mason writes:

"This is one topic where I think that untrained people are really, really out of their league making comments."

What makes this topic different from others? Is it that you consider yourself trained? *cough global warming argument* - dead horse : )

"By risking your money on the stock market, you made a net profit of $5,800 which is only 1.16% of your $500,000 nest egg."

I think you're missing the fact that I (the you of which you spoke) didn't actually invest anything. I made $5,800 on borrowed money, it wasn’t a sure thing, leveraging does increase risk, but 7% is average, so on average it should be profitable.

bwv writes:

In regards to the Separation Theorem, only in Financial Economics can a proposition be held to be true when every one of its underlying assumptions is contradicted by the available empirical evidence.

That being said, beating the financial markets is bloody difficult

Floccina writes:

IMO equity investing all boils down to dividends and expected future dividends (ok also money distributed on liquidation and stock buy backs). These are the only ways that money is paid back to the investors.

Multiples have been rising forever but at some point this must end. So that in the past equities have returned greater than bonds is not the end of the story. Much of that outperformance was due to Multiples growth not increased return (dividends).

A very interesting area of investing to me is buying energy or labor saving devices for the home that have very high paybacks. Replace that old air conditioner.

Mike Moffatt writes:

I think part of the problem we're having with this is the lack of concrete examples.

On my site I construct an example to throw some data on this debate. (Click on my name to go to the site).

I would love to hear from Kling or anyone else on the example I give.

bwv writes:

"Multiples have been rising forever but at some point this must end. "

According to the 2005 Ibbotson Yearbook, multiple expansion accounted for approximately 0.90% of annualized US Equity returns from 1926-2004. IMO the normalized earnings yield is the best expectation of future real stock returns (which would be around 6% at current valuations)

Joe Teicher writes:

I think Arnold is right. Futures are just better.
If you buy ESH8 futures you're going to be paying around 9.5 points over spot on a 1500 point item (that is a little under .7% for three months) or a little under 3% per year. The reason it is so low is that you are forgoing dividends but the dividend yield on the S&P is less than 2% so net you are still paying under 5% to own as many S&Ps as you want. That interest is tax deductible because you are paying it through the price you pay in the future and the taxes you pay are only on your profit in the future. So net you are under 4% after taxes if you want to look at it that way.

If you think that the ability to borrow at 4% to own S&Ps is an arbitrage, then you can certainly do it for a lot more size in the futures market because you need to put up less than $5K per future (each future has a notional of $75K).

the fact that people are willing to take the other side of this trade for billions of dollars right now should indicate that it is not quite as sweet as Patri and Mike think it is.

bill shoe writes:

I look at the same issue from a different direction.

The current debate considers:
given- Patri owns a house.
question- Should he borrow money against the house to invest in the stock market?

I think it’s more relevant to consider:
given- Patri has decided to make stock market investing a priority.
question- should he rent a home or should he “own” a home with no equity and pay interest only?

The current own vs rent trade-off in Patri’s area comes down pretty dismally against owning if you look at home acquisition as an economic choice about providing shelter in the most efficient way. Owning is more expensive than renting on a monthly basis even after the tax deduction and paying interest-only. Patri is still on the hook for the principal in the long run, and there is considerable risk and lack of diversification in whether or not his house will go up or down in value in real terms.

As far as I can tell Patri is spending extra money every month to buy the extra risk associated with no-equity home ownership. Hope he likes working.

Michael Sullivan writes:

I see two potential problems with your analysis.

1. I'm not sure that step one is accurate, it's quite possible that some mortgages are available where the after-tax cost of the capital is less than the risk-free rate.

2. You may be missing a key ingredient to this decision, in that bankruptcy is much worse for institutional money and very rich investors than for Patri (or any

That puts a floor on what Patri can lose that is much smaller than his effective net worth (counting in earnings potential), which means that it may make sense for him to be more risk-seeking than the market. In a world with much harsher bankruptcy laws, you would probably be correct.

Just as tax-free bond prices provide a bit of arbitrage for people in the correct tax bracket, equities probably provide some for the class of people most suited to them, as long as that class wouldn't choose (or be able) to own the whole market at their own equilibrium price.

Bill writes:

It would work, and work well, if you do it at the right time. Mortgage 100,000 dollars, invest in a speculative interntaional fund that returns 25% or more, hold for three years, and then cash out while you're still up and pay off the mortgage. You come out ahead if the stock does well. What is so difficult to understand?

Lord writes:

Margin debt is far from comparable as it is both expensive and callable. Futures can be better, but require attention and timing. Mortgages are usually one of, if not, the best borrowing opportunities available.

Historically, the optimal investment has been 140% equities and -40% bonds. I agree the equity premium does not represent an arbitrage opportunity against bonds though, but it does present such an opportunity against other income. Income can be more or less stable and can be well traded for stocks. The only consideration is how much risk is desirable and tolerable; how far out on market line one deems reasonable for oneself.

Lord writes:

The misconception here is that EMH implies one should never borrow to buy stocks, but all EMF provides is one can accept higher risk for higher returns. No one is in the same position; they may be in a less risky position due to other assets and income, and may find more risk both acceptable and desirable. This doesn't make their position incompatible with EMH.

Lord writes:

On further reflection,

You pick the mechanism that offers the lowest interest rate, and that would not be the mortgage rate.

seems to be error. While this is theoretically possible, it would not be in practice for anyone using it and mortgage debt would typically be the lowest. Not only that, but as margin and futures are marked to market, you would be exposed to much higher risk than a fixed non-callable mortgage as well as offered less leverage. Mortgage debt is superior to anything else out there.

fundamentalist writes:
anyone who says that efficient markets theory only holds when all investors are identical clearly has never worked through the proof of the portfolio separation theorem. And unless you understand that theorem, I am not going to be convinced by what you have to say.

I understand the portfolio separation theorem, but I'm having a real hard time figuring out how it relates to EMH. Any help out there?

Arnold Kling writes:

This discussion is a mess. My conclusions are these:

1. Lots of people think they can easily outsmart the market. So the advice to act as if markets were efficient falls on deaf ears.

2. Unless you are a borderline deadbeat, paying off your mortgage is an arbitrage opportunity for you. If you are not going to default on your mortgage, then you are being charged a risk premium which you can earn by paying off the debt. The arbitrage opportunity that you forego by not paying off your mortgage is larger than any arbitrage opportunity that you can finance with the mortgage. But not if you believe you can outsmart the market. Which takes me back to (1).

fundamentalist writes:
Lots of people think they can easily outsmart the market..

Or you can invest with someone who has a record of outsmarting the market.

fundamentalist writes:

There is a lot of research that shows that most mutual funds under perform the market, but is that evidence that no one can beat the market? I don’t think so for several reasons. There is also a lot of research on the psychological factors involved in investing. The herd mentality in mutual fund management is very strong. That’s partly because managers know the cost/benefits ratio of being wrong with the crowd is much greater than being right against the crowd. If you’re right when the crowd is wrong, you’re called lucky. If you’re wrong when the crowd is right, you’re fired. But if you’re wrong and the crowd is wrong, that’s just business as usual.

In addition, mutual funds have to diversify 1) because they’re so large and don’t want to affect any particular stock and 2) because they believe in EMH and diversification is the gospel.

Finally, very few investment managers have the psychological make-up to be contrarian investors. It takes a rare personality to be a contrarian; most people can’t do it. Yet that is where the market-beating returns exist. Entrepreneurs tend to be contrarians, which is why they make the big bucks.

All the above are reasons to join an investing club if you have contrarian tendencies and want to share the workload with like-minded people. Many investment clubs beat the market on a regular basis.

A simple way to beat the market is to invest in the Dow dogs on a regular basis. There are web sites to explain it in detail, but the essence is to shift your money into the Dow stocks with the lowest PE ratios once or twice a year. That strategy has consistently outperformed market indices for decades.

Tom writes:

I though there was a lot of research that people are too risk adverse. Would this not just be taking advantage of this fact? Investing, long term, generates 10% while a mortgage cost 6%. Risk is there but is overstated, as we are too risk adverse.

I see where people who have a long horizon can profit at the expense of the risk adverse, and those who cannot afford to stay in the market long enough.

BWV writes:

One other thing, no one has brought up the real reason why the interest rates on mortgages (conforming ones at least) are significantly higher than treasuries - which is the prepayment option. The government cannot call its debt at par if rates drop while the mortgage holder can.

Michael Sullivan writes:

2. Unless you are a borderline deadbeat, paying off your mortgage is an arbitrage opportunity for you. If you are not going to default on your mortgage, then you are being charged a risk premium which you can earn by paying off the debt. The arbitrage opportunity that you forego by not paying off your mortgage is larger than any arbitrage opportunity that you can finance with the mortgage. But not if you believe you can outsmart the market. Which takes me back to (1).

In general I agree, but you haven't addressed either of my points about why there may be exceptions to this rule within an efficient market.

Michael Sullivan writes:

I though there was a lot of research that people are too risk adverse. Would this not just be taking advantage of this fact? Investing, long term, generates 10% while a mortgage cost 6%. Risk is there but is overstated, as we are too risk adverse.

The likelihood that this arbitrage is very large is small. Remember that an efficient market does not represent some kind of mean average of risk-taking across the market. The market becomes efficient because risk-takers bid up the prices of risky assets, and risk-avoiders bid up the prices of safer assets until there is an equilibrium somewhere in between the risk-seeker's equilibrium and the risk-avoider's equilibrium.

In an efficient market, we don't get arbitrage on risky investments just by being more risk-seeking than average. We have to be at least as risk-seeking as the most risk-seeking $N in the market, where $N is enough to buy all of the best risk-seeking assets. Since most professional money managers appear to operate with utility functions that are very risk-comfortable, that's a lot of risk-seeking you have to do to be in the class that might get an arbitrage.

I don't doubt that Patri and some others might qualify, but most people surely don't. You need to be young, high-income but not already very wealthy, *and* have the right (basically advantage gambler's) temperament.

And then the question Arnold asks is still key -- is *that* arbitrage greater than what you'd get by simply paying down the mortgage? Unless your mortgage rate is at or below current market rates and you are in a high tax bracket, it's doubtful.

Lord writes:

Well, if your mortgage rate is above current rates, you must be a bad risk, and if you are in a low tax bracket, this doesn't make much sense, so for most people it probably doesn't, but they probably aren't using this strategy or reading this blog either. What is debt but another risky asset that people bid up or down to the value deemed worth?

Patri Friedman writes:

I don't understand why Arnold thinks I am trying to outsmart the market. I don't see how that is implied by anything I am doing. The source from which I am borrowing is one only available to US homeowners, and only in limited amounts. Thus this cannot be arbitraged away. As others have pointed out, this loan source is cheaper than all the other options. Hence the fact that other options (like options, futures, etc.) represent opportunities to arbitrage is irrelevant to the question of whether borrowing from your home to buy stocks is profitable.

As Michael pointed out, the tax-adjusted interest rate of borrowing against your home can be less than the risk-free rate. And if, instead of buying a bond with regular payments, you buy a bond that pays a lump-sum on maturation, your effective tax rate may be low enough to make this a profitable move. Nothing that Arnold has says disproves this possibility. Nor does the EMH, because the pool of money available to arbitrage this away is limited.

Patri Friedman writes:

Dr. T says: By risking your money on the stock market, you made a net profit of $5,800 which is only 1.16% of your $500,000 nest egg.

If we take as a given that you own a house, which I was, then this 1.16% is a phantom number. It means nothing at all, since you are exposed to price movements on the $500,000 regardless of where you put your money. Your arbitrage made you a free $5,800 is the right way to look at it. Or "you make money if stock returns are above 6%". Which they are more than half the time.

Joe - in the method you describe for putting up 4% to own the S&P, don't you only capture the S&P return without dividends? Which is several percent below the full return.

bill shoe - I have a pretty unusual housing situation which required buying (various custom changes to the property), so the choice you describe is not actually relevant to me.

fundamentalist writes:

I have to agree with Friedman on this. If you have half you mortgage paid for on a $500,000 house, then your equity will grow in value at about 1-2% per year. Not a very happy scenario. You don't have the money to pay off the other half or you would, which means that you don't have the spare money to invest in stocks or bonds. But if you borrow the equity in your home at 6% and invest in the stock market, you can make the equity in you home grow at a faster rate.

I don't understand why Dr. T chose 7% as the rate of appreciation for a stock market investment when the market has averaged about 12% growth for almost a century. The 6% difference between the second mortage and the returns from the stock market cause the equity in my house to grow by 7-8% per year instead of 1-2%. But even if I earn just 1% on stocks, that doubles the growth rate of the equity in my home.

fundamentalist writes:

I have to agree with Friedman on this. If you have half you mortgage paid for on a $500,000 house, then your equity will grow in value at about 1-2% per year. Not a very happy scenario. You don't have the money to pay off the other half or you would, which means that you don't have the spare money to invest in stocks or bonds. But if you borrow the equity in your home at 6% and invest in the stock market, you can make the equity in you home grow at a faster rate.

I don't understand why Dr. T chose 7% as the rate of appreciation for a stock market investment when the market has averaged about 12% growth for almost a century. The 6% difference between the second mortage and the returns from the stock market cause the equity in my house to grow by 7-8% per year instead of 1-2%. But even if I earn just 1% on stocks, that doubles the growth rate of the equity in my home.

And as Friedman points out, no one is trying to beat the market, they're simply taking greater risk in order to earn greater returns.

fundamentalist writes:
Step 2 is a risk-return trade-off. In an efficient market, the "equity premium" is not an arbitrage opportunity. It is compensation for taking more nondiversifiable risk.

I would think that investing in the stock market is a more diversified investment than keeping the money in the house. In the stock market you can own multiple companies in multiple industries, even real estate via REIT's. With equity in a home, you're not diversified at all; you're stuck with all of your money in one investment, the value of which is subject to the volatility of the economy and interest rates, among many other things. You also have to pay a lot for maintenance and insurance, neither of which an investment in the stock market requires.

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