Long-Run Equity Returns and Economic Growth
In January 2000, Alena Bjornsdottir, CFA, was updating her firm’s projections for US equity returns. The firm had always used the historical average return with little adjustment. Bjornsdottir was aware that historical averages are subject to large sampling errors and was especially concerned about this fact because of the sequence of very high returns in the late 1990s. She decided to examine whether US equity returns since World War II had been consistent with economic growth. For the period 1946–1999, the continuously compounded (i.e., logarithmic) return was 12.18% per annum, which reflected the following components:
Real GDP Growth Inflation EPS/GDP (Chg) P/E (Chg) Dividend Yield
3.14% 4.12% 0.00% 0.95% 3.97%
Question
1 What conclusion was Bjornsdottir likely have drawn from this analysis?
Can anyone help me as to how to approach the question and the rationale behind the guideline answer. this has been taken from distribution.
This has been taken from Reading 10 :Capital Market Expectations, Part 1: Framework and Macro Considerations
The excerpt says that we have assumed the continuosly compounded returns from 1946 to 1999 to be 12.18% p.a.
This means that 1 rupee invested in 1946 is assumed to have become 1*e^[0.1218*54] in 1999.
In this we have taken a P/E change component of 0.95% which is likely not going to be the case in future. In the long run P/E growth approaches 0. This means that for this 54 year period we have taken an extra component of 0.95% in the return calculation. Without this the return should have been 12.18-0.95 = 11.23%. So, 1 rupee in 1946 should accumulate to 1*e^[(0.1218-0.0095)*54].
This means the returns for the future is overstated by 1*e^[0.1218*54] / 1*e^[(0.1218-0.0095)*54] = e^[0.0095*54] = 1.67.
This means actual returns is 67% lesser than the return calculated based on the period 1946-1999’s data.