\(r_\lambda\) = levered return

\(r_u\) = unlevered return

\(\lambda\) = leverage ratio

\(i\) = interest rate

\(\pi\) = inflation

\(r_\lambda = \lambda r_u - \frac{(\lambda - 1) i}{1 + \pi}\)

set inflation = 0

\(r_\lambda = \lambda r_u - (\lambda - 1) i\)

or

\(r_\lambda = \lambda (r_u - i) + i\)

set leverage = 1

\(r_\lambda = r_u\)

ru	π	i	λ	rλ
0.10	0.00	0.00	1	0.10	no leverage
0.10	0.05	0.00	1	0.10	5% inflation
0.10	0.00	0.07	1	0.10	7% interest
0.10	0.00	0.00	2	0.20	2x leverage
0.10	0.00	0.00	6.67	0.67	leverage reflecting 15% down
0.10	0.00	0.07	6.67	0.27	7% interest and leverage
0.10	0.07	0.07	6.67	0.30	inflation = interest
0.10	0.05	0.07	6.67	0.29	inflation < interest
0.10	0.07	0.05	6.67	0.40	inflation > interest
0.10	0.07	0.15	6.67	-0.13	inflation < high interest
0.10	0.15	0.07	6.67	0.32	high inflation > interest
0.10	0.15	0.15	6.67	-0.07	high inflation = high interest