Sunday, 18 December 2016

The Art of Leverage

Borrowing to invest in an asset will not simply multiply your returns.
It is more accurate to say that leverage multiplies the difference between the returns on the asset and the cost of borrowing.

Short Form Calculation

Return on Equity = Interest Rate Differential x Debt to Equity Multiple + Asset's Return

For example:
8:1 Debt to Equity at 4% debt interest with an asset return of 5%:

1 x 8/1 + 5 = 13%


Visualisation looks a little something like this:
ROE Alpha (Y-axis) by Return-Borrowing Differential (Z-axis) by Borrowing (X-axis)

Notes

  • I was overly pessimistic about leverage here. While more leverage will increase your borrowing costs, it will also increase the effect that changes in asset value has on your returns.
  • We focus on stories of riches or ruin, but there is also a wide band of mediocrity masquerading as success. Let's say you borrow 80% to buy a property at 4.5% interest. Net appreciation plus yield is 4%.
    -0.5% x (80/20) + 4% = 2%
    You've made 2% on your investment despite interest greater than appreciation. Win, right? But you would have been better off putting your down payment in a term deposit at 2.75%.
  • You only benefit if the asset return is greater than the debt interest rate.
  • Don't bet on your ability to pick those assets. Annual percentage increases in Australia's real property index was on average 1.68% lower than the standard variable home loan rate, for every quarter between September 2003 to September 2015 (similarly covered here).
  • You can't say this post title was misleading, though sorry if you were expecting a manual on how to gear your way to riches.
  • Here is a great treatment of the effects of leverage on your return on equity.

Data Table


ROE Alpha
by Return-Borrowing Differential
by Borrowing
10%20%30%40%50%60%70%80%90%
-5.00%-0.56%-1.25%-2.14%-3.33%-5.00%-7.50%-11.67%-20.00%-45.00%
-4.50%-0.50%-1.13%-1.93%-3.00%-4.50%-6.75%-10.50%-18.00%-40.50%
-4.00%-0.44%-1.00%-1.71%-2.67%-4.00%-6.00%-9.33%-16.00%-36.00%
-3.50%-0.39%-0.88%-1.50%-2.33%-3.50%-5.25%-8.17%-14.00%-31.50%
-3.00%-0.33%-0.75%-1.29%-2.00%-3.00%-4.50%-7.00%-12.00%-27.00%
-2.50%-0.28%-0.63%-1.07%-1.67%-2.50%-3.75%-5.83%-10.00%-22.50%
-2.00%-0.22%-0.50%-0.86%-1.33%-2.00%-3.00%-4.67%-8.00%-18.00%
-1.50%-0.17%-0.38%-0.64%-1.00%-1.50%-2.25%-3.50%-6.00%-13.50%
-1.00%-0.11%-0.25%-0.43%-0.67%-1.00%-1.50%-2.33%-4.00%-9.00%
-0.50%-0.06%-0.13%-0.21%-0.33%-0.50%-0.75%-1.17%-2.00%-4.50%
0.00%0.00%0.00%0.00%0.00%0.00%0.00%0.00%0.00%0.00%
0.50%0.06%0.13%0.21%0.33%0.50%0.75%1.17%2.00%4.50%
1.00%0.11%0.25%0.43%0.67%1.00%1.50%2.33%4.00%9.00%
1.50%0.17%0.38%0.64%1.00%1.50%2.25%3.50%6.00%13.50%
2.00%0.22%0.50%0.86%1.33%2.00%3.00%4.67%8.00%18.00%
2.50%0.28%0.63%1.07%1.67%2.50%3.75%5.83%10.00%22.50%
3.00%0.33%0.75%1.29%2.00%3.00%4.50%7.00%12.00%27.00%
3.50%0.39%0.88%1.50%2.33%3.50%5.25%8.17%14.00%31.50%
4.00%0.44%1.00%1.71%2.67%4.00%6.00%9.33%16.00%36.00%
4.50%0.50%1.13%1.93%3.00%4.50%6.75%10.50%18.00%40.50%
5.00%0.56%1.25%2.14%3.33%5.00%7.50%11.67%20.00%45.00%
 

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