Monday, March 3, 2014

Stock/Bond Asset Allocation (Part 3) - Short Duration with a mortgage! (Oh, you already are?) which I find that two wrongs may make a right....

In my previous posts, I dug into the non-normal behavior of historical stock & bond portfolios, and decided that bonds had no place in individual long-term portfolios.  Portfolios with a cash allocation will almost always do better than portfolios with bonds that have duration risk.

Below the fold, I explore that idea some more, consider the role of home ownership in these allocations, and discuss the financial semantics that result from our peculiar treatment of real estate ownership.

To revisit, here is a classic Markowitz portfolio selection model:

If we treat the mix of possible at-risk assets as a simple selection between stocks and long-duration bonds, we get the efficient frontiers shown here of diversified portfolios.  I have three versions of the efficient frontier, based on the intended holding period of the portfolio.  (These don't match the version of the graph in my previous posts exactly, because here I am using real returns instead of nominal returns.)

The Capital Allocation Line represents a simple allocation between a risk free asset (cash and cash equivalents - short term TIPS are probably the best way to think of this, and I have placed them on the graph based on the historical average real return on 1 year treasuries) and the efficient at-risk portfolio.  A risk averse investor would allocate their portfolio between cash and the stock/bond allocation given by allocation that is tangential to the most steeply sloped capital allocation line.

A short term investor would tend to hold more cash, and a long term investor would hold less cash.  In addition, we can see that the at-risk portion of a one-year portfolio would aim for about a 50/50 split between stocks and bonds, while the at-risk portion of a 20 year portfolio would hold around 90% stocks.

You could even imagine a very risky investor who wanted to invest on margin.  They might borrow 25% of their net worth, and invest 125% into the stock/bond portfolio (the leveraged investor in the graph).  The safe investor might hold 75% cash and only invest 25% in the at-risk portfolio.

....aaanyway, as I averred in the previous posts, in the binary stock vs. bond version of the efficient frontier, the risk/return curves shown above may not be accurate.  The correlation between long-duration bonds and stocks is not homogeneous over time, and the distortions seem to work against the hedging benefits of the two asset classes.

Here, I have recreated the Markowitz model, but instead of using a standard deviation based on the sum of the squared differences, I have estimated the standard deviation by using the worst case scenario for each holding period, based on 74 annual historical constructed portfolios.  This isolates the outcomes for these portfolios in the scenarios where we are most concerned with the benefits of diversification.

This is in line with my conclusions in the previous posts.  At the 1 year holding period, the at-risk bond allocation should only be 20-30% using this measure.  And the 10 & 20 year portfolios should contain no bonds at all.  If an investor is risk-averse, they should allocate some portion of their portfolio to cash, but none to bonds, except for the shortest holding periods.

In the next graph, I am comparing the stock-bond at-risk portfolios to at-risk portfolios that are instead composed of stocks and cash equivalents (here I used 1 year treasuries, not inflation protected).  I have lightened up the curves representing the stock/bond portfolios, and added curves showing the efficient frontiers using cash as the hedge.  Note that, consistent with the previous analysis, using cash moves the efficient frontiers to lower risk levels for a given return.

This is a little confusing, because I am using a cash equivalent in both the efficient frontier and the capital allocation line (CAL).  The10 and 20 year lines approximate the kind of confused result that this composition should give us.  The CAL runs basically parallel to the efficient frontier once the stock allocation reaches about 50%.  This makes sense.  An investor choosing to allocate 50% up the CAL with an at-risk portfolio that is 100% in stocks should expect to arrive at the same portfolio as an investor allocating 100% up the CAL with an at-risk portfolio that is 50% stocks and 50% in cash.  And, indeed, in the longer holding periods, this graph does provide that consistency.

But, I still think this conception of the model gives us a couple of insights.

1) Rebalancing and imperfect correlations give us some benefits when it is between cash and stocks, just like they provide benefits between stocks and bonds.  That means that, compared to a linear relationship in returns, represented by the CAL, that doesn't account for rebalancing benefits, a diversified portfolio will have slightly higher returns.  As you move from 100% cash or bonds to 100% stocks, there is a hump.  That is why the efficient frontiers don't fall exactly parallel to the CAL.  The point of tangency of the steepest CAL tends toward a 50/50 allocation as the holding period increases.  That is the allocation with the most benefit from rebalancing.  The effect of this, if one were to use this method to allocate funds, would be to pull the cash allocation slightly higher than a linear model would, since the model would be accounting for this benefit.

2) There's another twist, though.  If we consider long/short portfolios, the optimal long-term portfolio would not, in fact, be the stock/cash portfolio.  It could be a stock/bond portfolio with a short bond position, and a stock position more than 100%!  (This is estimated with the dotted green and red lines in the graph.)  Corporate bonds don't provide this level of portfolio performance.  Once the stock allocation exceeds 100%, the efficient frontier flattens out, and extra returns are related to much higher volatility.  If you look closely, you can see that I have extended the curve representing 20 year stocks/bonds up to a 130% stock position, and the curve has become horizontal at that level.  But, if allocation comes in the form of a home with a fixed long-term mortgage, then the investor gains from two tendencies:
  • The real estate position would consist of a long position in real estate and a short position in a mortgage.
  • Homes can be conceived of as long term inflation protected bonds, with lower convexity, especially in high inflation environments.  So, the long portion of this combination of positions would have less duration risk than similar bonds.  Traditionally, a home's effect on a household's comprehensive portfolio was probably like have a combination of a large amount of a near-cash asset and a small amount of long term bonds. (This is further complicated by the dual-position of the home as investment and consumption.)
  • Mortgages are bonds (not inflation protected) with lower convexity, due to the pre-payment option.  With standard fixed rate bonds, in poor economic periods where real rates are declining, a portfolio long in bonds would experience short term gains in bond values, but this would be countered over the remaining holding period by the lower realized yields.  A mortgage, held by the investor as a short bond with a pre-payment option, provides the mortgage payer (aka bond seller) with a dual benefit in this context, since the market value of the mortgage wouldn't exceed the face value, and since the mortgage payer would be able to permanently lock in that advantage by pre-paying and refinancing at a new, lower rate.

Do Two Wrongs Make A Right?

I have always seen the tendency of American households to concentrate their savings in a single, highly leveraged piece of real estate to be dangerous and inappropriate.  But, seen in this light, maybe we have stumbled into an optimal set of conventional investments.

If American households should be holding more low-risk hedges, more stocks, and be short bonds in their portfolios, highly leveraged homes are providing exactly that set of exposures.

What about the housing boom?

Ok, ok.  I can hear you all yelling from here.  "Where have you been for the past 10 years?  You can't possibly call homes a near-cash investment with a straight face!"

Hold on there, buster.  If we conceive of American household savings in this way, what we see is that in the 2000's, the combination of low inflation and low real long-term rates was making homes, as a bond representing pre-paid rent, much more convex.  (It was also making mortgages much more convex, since pre-payments risks were so small at such low rates.)  The extraordinary rise in home values in the 2000's was a product of this convexity.  And, this means that if we look at the home as an asset representing a combination of exposures (a near cash exposure and a long-duration bond exposure), what happened in the 2000's was that American households held basically optimal portfolios that they understood only in terms of heuristics and conventions, and not with conceptual sophistication.  While these heuristics remained stable, the financial environment was changing the exposure weights of those homes.  As the convexity of these assets increased, households were actually becoming more and more exposed to long-duration bond positions and less exposed to near-cash positions, simply because their homes, as financial instruments, had changed.

Baby boomers were transitioning into bonds as their prospective holding periods began to decline with retirement.  What they didn't realize was that their homes had already been transformed into long-term bonds under their noses.  Households should have seen their nominally inflated houses as an increase in their bond holdings.  The only way to re-establish the previously optimal allocations would have been to either sell their home, or to have taken out even larger mortgages, in order to establish a larger short bond position, and combine that with a large increase in cash (short term bonds) and equities.  But, at the height of the boom, homes may have been so bond-like, that it would have been impossible for households to rid their comprehensive portfolio exposures of bonds completely through a short mortgage position.  And the mortgage wouldn't have provided its usual advantages to the household portfolio either.  Selling our homes may have been the only way we could have gotten back to the efficient frontier.

All of this would be unnecessary if we bought homes like we buy firms.  If I want to be exposed to technology, all I have to do is buy one share of Microsoft.  I don't have to commit to buying the whole firm.  But, if I want exposure to real estate, I can't just buy a share in my home.  I have to expose myself to the risk of the entire property.  Could we do it a different way?

I don't know if there is a regulatory barrier to this, but some entrepreneur would do us all a huge favor if he started selling homes this way.  Instead of taking out a mortgage to buy our entire homes, we could enter into partnerships where we buy shares in the properties over time.  A public policy that encouraged this kind of arrangement would produce a much more robust outcome than the current mortgage interest deduction policy.  The resulting lack of autonomy by the homeowner over investments in the property probably make that sort of system a non-starter.

But, conceptually, this makes me sanguine about worries of excessive consumer debt.  So much of that debt is based on real estate.  If our tradition was for banks and investors to hold real estate, as equity, and then sell shares in that equity to the residents, all of that debt would go away, but the systemic risks wouldn't be substantially different than they are now.

Now, when a house is bought, with mortgage funding, the bank debits cash and credits a receivable.  The homeowner credits real assets and debits a loan payable.  Conceptually, the same transaction could be recorded with no debt - the bank could debit cash and credit real assets.  As the homeowner paid for the home, the bank would credit cash and debit real assets, while the homeowner would do the opposite.  There are some complexities in the details, but, in either case, if the value of the real estate plunges as part of a systemic crisis, the bank is going to take the asset and the write-off.

The systemic risk doesn't necessarily come from the presence of the mortgage receivables on the banks' balance sheets, it comes from the relationship between the real assets themselves and the banks' liabilities and capital.

Follow up posts.


  1. You can get limited exposure to real estate by buying a share in a REIT.

    1. Thanks for the input, Philo. I wonder if we didn't have the mortgage interest deduction (and maybe some regulations / conventions in home financing), if we would tend to have more institutional ownership of real estate, and households would gain exposure to real estate through REITS, or maybe even some sort of proportional owner-occupant ownership.

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  3. I am sorry, I really have to weigh in here. Kevin, your analysis (like most others I know of) assumes that market prices capture the investment returns to housing. Based on my analysis when I was a Level 1 Candidate for CFA Charterholder, in most cases they do not. Specifically, they ignore the costs of holding the asset ("maintenance").

    Let's take an example (figures not exact). My father bought a house with his own money in 1955 for $60,000 (nominal). It was sold in 2009 for $10 million minus transaction costs (leaving out tax effects), or about $9.5 million - about 8%/year growth/year in real terms. Great, huh? Except that maintenance averaged 2-4% of house value over that period, including a whopping $400,000 in deferred maintenance plus more than $100,000 in ongoing maintenance costs the year of the sale. These costs grow faster than inflation because maintenance costs are for larger items like electrical over longer periods of time and because tastes change. Therefore I conclude that investment returns average actually 2-4% lower.

    This, in turn, places housing between stocks and bonds in return over time, with actually higher volatility than stocks -- after all, effectively, you are never going to lose the entire value of an S&P index fund.

    A proxy for housing investments is a REIT stock, which does take account of costs. However, a REIT is a business with returns to scale -- trying to compare the great mass of the individual housing market to REITs is like trying to compare a pizza-parlor owner to Domino's.

    1. It is true that you shouldn't take this analysis too literally. I couldn't figure out how to model the owner-occupied home strictly as an investment, because it is also a form of consumption. So, increasing its size in your portfolio increases your consumption of housing services. That gets complicated fast.

      So, this analysis can serve as a conceptual starting point, but it can't really get you to a marginal buy or rent decision.

      That said, you haven't mentioned rent. If I buy a bond at $100 which will mature in 10 years at $100, is that bond a good buy? We can't know. The whole point of owning a bond is the yield. The whole point of owning a house is the rental income (either in cash or imputed). A house could be a good investment with zero capital gains. Nobel Prize winners make this mistake.

    2. I haven't mentioned rent because the whole point of owning a house is not typically to rent it, but to live in it. To put it another way, there is not a sharp dichotomy between investments in profit and investments in survival/living: a car is an investment that yields negative returns over time (resale value), making it a little akin to an expense and a little akin to an investment. In the same way, housing for living in, while it actually does typically make a profit, is partly akin to a pure investment and partly akin to an expense. The proper way to treat that is not as a pure investment without expenses, but as investment minus expense, i.e., like a car. A rented house (many middle-class folks are landlords, cf a study just quoted in delong's blog) should be viewed as more akin to a REIT.

      Capital gains has nothing to do with my analysis (I am sorry if my comparison of Domino's to pizza parlors misled you; the rented house is indeed like a pizza parlor). Although tax effects might slightly alter this picture, the fact that today's capital gains taxes are effectively halved in the long run by intergenerational/estate lack of taxes tends to suggest that stocks actually have an advantage over real estate in that respect.

      Btw, the same study notes that the rich are typically not landlords and earn higher returns. It doesn't say if they invest in REITs beyond the market.

      P.S. I am only doing this anonymously because your site keeps telling me my OpenID doesn't pass muster. Sincerely, Wayne Kernochan (

    3. I prefer to look at it somewhat differently. Expenses (including depreciation) certainly should be accounted for. But, I think it is best to see the owner as having two roles - owner and tenant. As a tenant they are a consumer. As an owner they are an investor. Even though they don't write themselves a check each month, there is still an implied transaction. The value of that rent is the most important determinant in the value of the home.

    4. All right, let's play this game. As an owner, I charge myself as consumer rent, paid to me as owner. Suppose I charge $1 rent. Then I am no better or worse off than before, since what I have gained as investor I have lost as consumer. Second case: I charge the entire market value of the house as rent. I have no difficulty paying myself that sum. I am no better or worse off than before.

      Now here's the point: to the outside world, the two cases are indistinguishable. The market has no way of knowing what rent I charged, and the results in terms of home market value at the end of the rental period are identical. The amount of "owner-rent" has zero effect on the market value of the home.

    5. Follow-on: Now suppose we separate the two roles: I am renting to someone else. If I successfully charge $1 rent and value-of-the-house rent, my profit and thus the market value of the house are quite different between the two cases: property yielding 100% return per period has a much higher value than profit yielding 0.1% return. The explanation in these cases is that return does not compensate for expenses in the first case, while it earns windfall profits over expenses for the second case.

    6. It is the market rent that is important. That is what you would pay if you were renting the home from someone else. Maybe it would be easier if you thought of it in terms of opportunity costs. I own the home. How much would I spend each month to have a similar dwelling if I didn't own this home?

    7. Sigh. I covered that case from the landlord's point of view. We are trying to determine if housing prices, which are dominated by self-owned houses, give an accurate picture of ROI/yr. If you want to use cost/yr of an equivalent rental as a proxy for expenses, fine (it's distorted because of imbalance of power between landlord and renter). But that means that your ROI (percentage terms) should not be [market price of house (end of year) minus market price (start of year)]/[market price (start of year), but [MP (EOY) - MP (SOY) - yearly rental cost]/[MP(SOY)].

      I repeat: Changes in home price values in this case do not show you the real ROI, the real return to the investor in most cases, i.e., the investor in a self-owned house. You need to add in a proxy for maintenance costs. Or, you need to separate out returns to landlords and use them as a guesstimate of maintenance costs.

      If you want to put it in your terms, the opportunity cost of rental of a similar dwelling is change in market price minus maintenance costs, since if I own it I cover maintenance costs while if I don't own it I don't cover those costs.

    8. As I mentioned, I couldn't figure out how to model this with changing portfolio shares of an owner-occupied house because increasing the housing share also would increase the household's consumption of housing. So, the part of these posts that considers housing as an asset class should only be regarded at a conceptual level. I really made no attempt at comparing ROI on the house to ROI on other assets because I didn't consider the income part of the house at all. Since rent is generally stable and changing home values are more volatile, I limited my analysis to the covariance of the house with the other asset classes.

      Actually, I would probably even walk back some of my conceptual discussion, too, because I was still thinking of the housing boom as a national phenomenon, and work I have done since then has led me to conclude that the US housing market has become too bifurcated to be able to treat it as a single aggregate market. I don't think homes really became that much more bond-like any more. Some homes rose in value because of unexpected increases in their persistent rental values, and other homes didn't really have much of a regime shift at all.

    9. Thank you for this last informative reply; I learned a lot :) I suspect that now that my caveat has been honored, you know way more than I do about the rest. I have to sign off at this point because I know I won't spend any more time in the near future on this fascinating subject. Thanks again, and all the best - Wayne