flintnational
Thinks s/he gets paid by the 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.
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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