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Paying Off the Mortgage – Risk Adjusted Analysis
Old 12-25-2018, 11:18 AM   #1
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Paying Off the Mortgage – Risk Adjusted Analysis

Sorry for the long post. But, I thought the topic required this many words. Happy holidays to all!

Summary - The forum members are routinely asked, “Should I pay off my mortgage?” The responses tend to fall into two categories. 1) From a math perspective, as long as mortgage rates are significantly below your expected portfolio return, you are better off keeping a mortgage and investing the proceeds. 2) From an emotional standpoint, some like having a paid off mortgage and being debt free. Our responses tend to be math vs. emotion.

However, the choice to pay off the mortgage or not, as it is normally depicted, does not properly account for the different risk inherent in each of the two choices. In other words, the comparison is not risk adjusted. If the two choices are risk adjusted, and expected bond portfolio returns equal mortgage rates, the risk adjusted return of both choices is identical. The only risk adjusted opportunity for arbitrage is if the bond portion of the portfolio has a higher expected yield than mortgage rates.

Detail – When a poster asks, “Should I pay off my mortgage?”, we normally explain that from a math standpoint paying off the mortgage is not the optimal choice. We base this response on the following type of analysis. Assumptions: Stock returns 9%, Bond returns 4%, (blended 60/40 return 7%), $300k Mortgage, Mortgage interest rate 4%

No Mortgage – Paid off house..... With mortgage – Invest the proceeds

Investable assets.......$2,700,000........................... ..........$3,000,000
Stocks (60%)............$1,620,000....................... .... .........$1,800,000
Bonds (40%).............$1,080,000...................... ...............$1,200,000
Portfolio return..........$ 189,000........................................$ 210,000
Mortgage interest.......$ 0.................................................-$ 12,000
Net return.................$ 189,000........................................$ 198,000

In the above analysis, the “Invest the proceeds" example provides a greater return than the “Paid off house” example. And they both appear to have a 60/40 stock/bond allocation. However, they do not have the same asset allocation. The “Invest the proceeds” example is including the value of the proceeds from the mortgaged house in the investable assets. The “Paid off house” example is not including the value of the house in the investable assets.

To make an apples to apples comparison, that would be risk adjusted, we also need to include the house value in the investable assets of the “Paid off house” example. A paid off house can be considered similar to a bond with a yield equal to the mortgage rate. The example below includes the value of the house as a bond for accurate comparison purposes.

No Mortgage – Paid off house

Investable assets.......$3,000,000
Stocks (54%)............$1,620,000
Bonds (46%).............$1,380,000 (includes house value added to bond values)
Portfolio return...........$ 201,000
House yield offset......-$ 12,000
Net return.................$ 189,000

When the house is included in both examples, the “Paid off house” example actually has a lower stock allocation of 56% compared to the 60% stock allocation of the “Invest the proceeds” example. The higher stock allocation of the “Invest the proceeds” example accounts for the out performance of this scenario. If we hold the asset allocations equal in both examples and properly account for the value of the house in both, the returns would be identical when mortgage rates and expected bond returns are the same (both are 4% in this example). As an example, the investor with the paid off house could re balance back to a 60/40 allocation by selling bonds and buying stocks. This portfolio would then have the same return as the portfolio with a mortgage and it would now have the same risk profile.

Summary – The decision to keep a mortgage or pay the house off is complicated. However, if we properly include the value of the house in both scenarios, which correctly adjusts for risk, the decision is simplified. The only arbitrage opportunity is the difference in mortgage rates and the expected bond portfolio return. Any perceived excess return, above the bond/mortgage arbitrage, is because we failed to risk adjust the two examples. This difference shows up in the increased stock allocation in the “Invest the proceeds” example or the reduced stock allocation in the “Paid off house” example.
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Old 12-25-2018, 04:41 PM   #2
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Originally Posted by flintnational View Post
Summary - The forum members are routinely asked, “Should I pay off my mortgage?” The responses tend to fall into two categories. 1) From a math perspective, as long as mortgage rates are significantly below your expected portfolio return, you are better off keeping a mortgage and investing the proceeds. 2) From an emotional standpoint, some like having a paid off mortgage and being debt free. Our responses tend to be math vs. emotion.
There is a third consideration not often mentioned: when you take out a mortgage, you invite a hostile third-party into your life. There are two scenarios where this can lead to negative results for a homeowner:
(1) if the loan originator participates in the home purchase, they can interfere with the closing in various ways (beyond the scope of this post);
(2) after origination, the mortgage servicer can screw up the servicing (sometimes in their own favor).

Some of my direct experience:
• when I bought my house a few years ago, there was no loan involved on either the buy or sell side. Boy, was that ever a clean sale! I wish everyone involved in the stressful process of buying a house could enjoy such a clean closing.
• I watched in amusement quite a few years ago as a high-net-worth relative struggled with the servicing of his jumbo mortgage. He ended up paying off the loan a year or so later, probably in disgust.

I'm not claiming this issue trumps #1 or #2 listed above in importance, but IMO it is worth considering when deciding whether to take out (or pay off) a mortgage.
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Old 12-25-2018, 04:53 PM   #3
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^^^First, thanks for reading. I know it is a long post. As you mention, there are definitely other issues. I have only addressed the financial risk/return relationship between the two examples.
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Old 12-26-2018, 01:59 PM   #4
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Quote:
Originally Posted by flintnational View Post
Sorry for the long post. But, I thought the topic required this many words. Happy holidays to all!

Summary - The forum members are routinely asked, “Should I pay off my mortgage?” The responses tend to fall into two categories. 1) From a math perspective, as long as mortgage rates are significantly below your expected portfolio return, you are better off keeping a mortgage and investing the proceeds. 2) From an emotional standpoint, some like having a paid off mortgage and being debt free. Our responses tend to be math vs. emotion.

However, the choice to pay off the mortgage or not, as it is normally depicted, does not properly account for the different risk inherent in each of the two choices. In other words, the comparison is not risk adjusted. If the two choices are risk adjusted, and expected bond portfolio returns equal mortgage rates, the risk adjusted return of both choices is identical. The only risk adjusted opportunity for arbitrage is if the bond portion of the portfolio has a higher expected yield than mortgage rates.

Detail – When a poster asks, “Should I pay off my mortgage?”, we normally explain that from a math standpoint paying off the mortgage is not the optimal choice. We base this response on the following type of analysis. Assumptions: Stock returns 9%, Bond returns 4%, (blended 60/40 return 7%), $300k Mortgage, Mortgage interest rate 4%

No Mortgage – Paid off house..... With mortgage – Invest the proceeds

Investable assets.......$2,700,000........................... ..........$3,000,000
Stocks (60%)............$1,620,000....................... .... .........$1,800,000
Bonds (40%).............$1,080,000...................... ...............$1,200,000
Portfolio return..........$ 189,000........................................$ 210,000
Mortgage interest.......$ 0.................................................-$ 12,000
Net return.................$ 189,000........................................$ 198,000

In the above analysis, the “Invest the proceeds" example provides a greater return than the “Paid off house” example. And they both appear to have a 60/40 stock/bond allocation. However, they do not have the same asset allocation. The “Invest the proceeds” example is including the value of the proceeds from the mortgaged house in the investable assets. The “Paid off house” example is not including the value of the house in the investable assets.

To make an apples to apples comparison, that would be risk adjusted, we also need to include the house value in the investable assets of the “Paid off house” example. A paid off house can be considered similar to a bond with a yield equal to the mortgage rate. The example below includes the value of the house as a bond for accurate comparison purposes.

No Mortgage – Paid off house

Investable assets.......$3,000,000
Stocks (54%)............$1,620,000
Bonds (46%).............$1,380,000 (includes house value added to bond values)
Portfolio return...........$ 201,000
House yield offset......-$ 12,000
Net return.................$ 189,000

When the house is included in both examples, the “Paid off house” example actually has a lower stock allocation of 56% compared to the 60% stock allocation of the “Invest the proceeds” example. The higher stock allocation of the “Invest the proceeds” example accounts for the out performance of this scenario. If we hold the asset allocations equal in both examples and properly account for the value of the house in both, the returns would be identical when mortgage rates and expected bond returns are the same (both are 4% in this example). As an example, the investor with the paid off house could re balance back to a 60/40 allocation by selling bonds and buying stocks. This portfolio would then have the same return as the portfolio with a mortgage and it would now have the same risk profile.

Summary – The decision to keep a mortgage or pay the house off is complicated. However, if we properly include the value of the house in both scenarios, which correctly adjusts for risk, the decision is simplified. The only arbitrage opportunity is the difference in mortgage rates and the expected bond portfolio return. Any perceived excess return, above the bond/mortgage arbitrage, is because we failed to risk adjust the two examples. This difference shows up in the increased stock allocation in the “Invest the proceeds” example or the reduced stock allocation in the “Paid off house” example.
I'm not sure you can assume the house will offer the same returns as an investment-grade bond. From what I've read, one should assume your home's appreciation will match inflation, which is always lower than a (non-gov't) bond's interest rate.

Also, your home's eventual sale probably involves a realtor's cut, which further reduces its appreciation.

I've always assumed any monies invested in a personal residence to be a sunk cost, not yielding any real returns over my lifetime. Or am I missing something?
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Old 12-26-2018, 03:47 PM   #5
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Originally Posted by El Magnifico Loco View Post
I'm not sure you can assume the house will offer the same returns as an investment-grade bond. From what I've read, one should assume your home's appreciation will match inflation, which is always lower than a (non-gov't) bond's interest rate.

Also, your home's eventual sale probably involves a realtor's cut, which further reduces its appreciation.

I've always assumed any monies invested in a personal residence to be a sunk cost, not yielding any real returns over my lifetime. Or am I missing something?
Yes, it is hard to follow. I hope I can explain it adequately.

The "invest the proceeds" example assumes the house is mortgaged and the money is then invested. So, to equate the two examples, we need to determine the investment value of not having a mortgage. Otherwise we cannot make a head to head comparison between the two choices. The example is not assuming the house appreciation will match a bond return. It is assuming the bond return is equal to the mortgage rate so that we can compare the (no mortgage/mortgage) examples on an apples to apples basis. In other words, what would the return be on a bond that would offset the mortgage interest payment? It would be equal to the mortgage interest rate.

Regarding your second point about a house being sunk cost. I agree. But, keep in mind when someone asks "Should I keep a mortgage and invest the proceeds" they are in fact moving the house value (equity) into the investment column. So, if we want to compare the two choices (mortgage or no mortgage), since one example already includes the house equity as an investment, we need to include it in both. Otherwise, it gives the false impression that returns are greater by keeping a mortgage. They are only greater because the "invest the proceeds" decision has a higher stock allocation. I am not suggesting that we count a paid of house as an investment. I am using the example to show why the "the invest the proceeds" example has higher returns. Once someone understands that the out performance of the "invest the proceeds" example is only due to a higher stock allocation, they could then adjust their stock allocation and keep a paid off house. Both choices would then provide the same return with the same risk.
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Old 12-26-2018, 04:36 PM   #6
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I think a better way of looking at it is if the funding of the payoff comes from bonds... arguably the retiree can comfortably assume a bit more risk if they don't have a mortgage. Expanding on your example, if the mortgage was paid with proceeds from the sale of bonds then you would get:
No Mortgage – Paid off house

Investable assets.......$2,700,000

Stocks (67%)............$1,800,000

Bonds (33%).............$ 900,000

Portfolio return...........$ 198,000

House yield offset......-$ 0

Net return.................$ 198,000

I have long said that IF someone changed their AA to correspond with paying off their mortgage that one would be indifferent.... however, very few poster intend to increase their allocation to stocks if they pay off their mortgage... or take the payoff from bonds.
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Old 12-26-2018, 04:38 PM   #7
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I'm comparing paying off a mortgage as equivalent to the return of a tax-free municipal where the risk is zero. I checked and a mortgage is available today for about 4.5% so a tax free muni, for me, would have to yield 4.5% to be equal. Oh, and free of risk.
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Old 12-26-2018, 04:57 PM   #8
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Originally Posted by pb4uski View Post
I think a better way of looking at it is if the funding of the payoff comes from bonds... arguably the retiree can comfortably assume a bit more risk if they don't have a mortgage. Expanding on your example, if the mortgage was paid with proceeds from the sale of bonds then you would get:
No Mortgage – Paid off house

Investable assets.......$2,700,000

Stocks (67%)............$1,800,000

Bonds (33%).............$ 900,000

Portfolio return...........$ 198,000

House yield offset......-$ 0

Net return.................$ 198,000

I have long said that IF someone changed their AA to correspond with paying off their mortgage that one would be indifferent.... however, very few poster intend to increase their allocation to stocks if they pay off their mortgage... or take the payoff from bonds.
Perfect! Thanks. I was about to post the reserve view as you have done. And, yes it may be clearer since many do not want to count the house in the investment column.
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Old 12-26-2018, 05:38 PM   #9
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Another way of looking at is how much income the investment needs to generate to service the debt.

A $300,000 loan requires over $20,436 in monthly payments to service the debt @5%. Assuming only a 12% tax rate takes you up to $22,888 at 22% tax rate you need to earn more than $24,931 gross income from your investment to make it worth it. That is assuming you still owe the entire $300,000.

That would require an 8% return on the $300,000. If you had been making payment and only owed $200,000 you would need to earn a return of 12.4%.

The debt no longer has a tax deductible advantage, but the income to service it still requires a tax payment.


I'm all ears for people who can show me safe investments showing income returns in 2018 that can hold a candle to those outlined above.
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Old 12-26-2018, 05:46 PM   #10
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however, very few poster intend to increase their allocation to stocks if they pay off their mortgage... or take the payoff from bonds.

This is key. A mortgage is a negative bond from an AA perspective. When paid off the money SHOULD come from bonds and AA STAYS THE SAME as the mortgage and bond reduction cancel each other out.
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Old 12-26-2018, 06:07 PM   #11
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This is key. A mortgage is a negative bond from an AA perspective. When paid off the money SHOULD come from bonds and AA STAYS THE SAME as the mortgage and bond reduction cancel each other out.
I would agree with that view. Good way to look at it. Your mortgage payments are directly offsetting your bond interest payments.
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Old 12-26-2018, 06:17 PM   #12
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Originally Posted by flintnational View Post
Sorry for the long post. But, I thought the topic required this many words. Happy holidays to all!

Summary - The forum members are routinely asked, “Should I pay off my mortgage?” The responses tend to fall into two categories. 1) From a math perspective, as long as mortgage rates are significantly below your expected portfolio return, you are better off keeping a mortgage and investing the proceeds. 2) From an emotional standpoint, some like having a paid off mortgage and being debt free. Our responses tend to be math vs. emotion.

However, the choice to pay off the mortgage or not, as it is normally depicted, does not properly account for the different risk inherent in each of the two choices. In other words, the comparison is not risk adjusted. If the two choices are risk adjusted, and expected bond portfolio returns equal mortgage rates, the risk adjusted return of both choices is identical. The only risk adjusted opportunity for arbitrage is if the bond portion of the portfolio has a higher expected yield than mortgage rates.

Detail – When a poster asks, “Should I pay off my mortgage?”, we normally explain that from a math standpoint paying off the mortgage is not the optimal choice. We base this response on the following type of analysis. Assumptions: Stock returns 9%, Bond returns 4%, (blended 60/40 return 7%), $300k Mortgage, Mortgage interest rate 4%

No Mortgage – Paid off house..... With mortgage – Invest the proceeds

Investable assets.......$2,700,000........................... ..........$3,000,000
Stocks (60%)............$1,620,000....................... .... .........$1,800,000
Bonds (40%).............$1,080,000...................... ...............$1,200,000
Portfolio return..........$ 189,000........................................$ 210,000
Mortgage interest.......$ 0.................................................-$ 12,000
Net return.................$ 189,000........................................$ 198,000

In the above analysis, the “Invest the proceeds" example provides a greater return than the “Paid off house” example. And they both appear to have a 60/40 stock/bond allocation. However, they do not have the same asset allocation. The “Invest the proceeds” example is including the value of the proceeds from the mortgaged house in the investable assets. The “Paid off house” example is not including the value of the house in the investable assets.

To make an apples to apples comparison, that would be risk adjusted, we also need to include the house value in the investable assets of the “Paid off house” example. A paid off house can be considered similar to a bond with a yield equal to the mortgage rate. The example below includes the value of the house as a bond for accurate comparison purposes.

No Mortgage – Paid off house

Investable assets.......$3,000,000
Stocks (54%)............$1,620,000
Bonds (46%).............$1,380,000 (includes house value added to bond values)
Portfolio return...........$ 201,000
House yield offset......-$ 12,000
Net return.................$ 189,000

When the house is included in both examples, the “Paid off house” example actually has a lower stock allocation of 56% compared to the 60% stock allocation of the “Invest the proceeds” example. The higher stock allocation of the “Invest the proceeds” example accounts for the out performance of this scenario. If we hold the asset allocations equal in both examples and properly account for the value of the house in both, the returns would be identical when mortgage rates and expected bond returns are the same (both are 4% in this example). As an example, the investor with the paid off house could re balance back to a 60/40 allocation by selling bonds and buying stocks. This portfolio would then have the same return as the portfolio with a mortgage and it would now have the same risk profile.

Summary – The decision to keep a mortgage or pay the house off is complicated. However, if we properly include the value of the house in both scenarios, which correctly adjusts for risk, the decision is simplified. The only arbitrage opportunity is the difference in mortgage rates and the expected bond portfolio return. Any perceived excess return, above the bond/mortgage arbitrage, is because we failed to risk adjust the two examples. This difference shows up in the increased stock allocation in the “Invest the proceeds” example or the reduced stock allocation in the “Paid off house” example.
Simple answer -YES , pay off your home

My situation

1993 Bought new home , 20% down, 30 year fixed mortgage
2005 Paid off home . Still own and live in home.
1993-2005 monthly auto invest to mutual index funds
2005-2018 $$$ that would have gone to monthly mortgage payments went to monthly auto invest to mutual index funds and maxing out 401K to increase monthly investments
2018 Early retired and loving it.
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Old 12-27-2018, 10:30 AM   #13
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Interesting rational in basis for conclusions. Insightful.
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