When discussing the risk-return diagram, the risk component is often perceived theoretically. In this note, I will mathematically demonstrate how financial leverage and risk are essentially the same (all else being equal), how leveraging real estate affects the expected return on average, and how it proportionally influences the range of uncertainty around that expected return.
Below is a table:
- The first section presents the basic assumptions.
- The second section illustrates how leverage changes the return on real estate.
The first column shows a scenario where I purchase real estate, rent it out, and sell it after one year. As a result, I achieve a 10% return, of which 8% comes from rental income and 2% from property appreciation.
The second column depicts the same operation, but in this case, 60% of the real estate purchase is financed with an 8% loan. My return increases to 13%. However, this does not come without a cost—risk increases as well.
Now, let’s assume that instead of renting for $800, I rent for $700 or $900, and instead of a 2% price increase, the property value drops by 8% or rises by 12% (a 10% deviation from expectations). What happens then?
The upper two tables below show the range of return uncertainty when buying real estate without leverage, while the lower two tables show the return uncertainty when purchasing real estate with 2.5x leverage.
Notice that dividing the bottom right table by the top right table results exactly in 2.5:
Ultimately, this results in the following risk-return diagram:
If we take this a step further and acknowledge that debt is not risk-free—meaning returns may not even be sufficient to cover loan payments—then we can add the risk-free interest rate to the diagram and increase the slope of the risk premium.
Excel File – RE Risk & Leverage
Adapted from:
Commercial Real Estate Analysis and Investments – D. M. Geltner, N. G. Miller, J. Clayton, P. Eichholtz