Question

Assume these were the inflation rates and U.S. stock market and Treasury bill returns between 1929 and 1933:

Year	Inflation(%)	Stock Market Return(%)	T-Bill Return(%)
1929	0.5	–14.2	7.0
1930	–3.4	–31.5	2.3
1931	–9.2	–47.2	1.4
1932	–11.4	–10.4	0.9
1933	0.7	63.2	0.2

1. What was the real return on the stock market in each year?

2. What was the average real return?

3. What was the risk premium in each year?

4. What was the average risk premium?

Answer 1

Solution for a

The real return on the stock market each year = the actual stock market return - inflation that year.

Hence, real return on the stock market in 1929 = -14.2% - 0.5% = -19.2%

real return on the stock market in 1930 = -31.5% - (-3.4%) = -31.5% + 3.4% = -28.1%

real return on the stock market in 1931 = - 47.2% - (- 9.2%) = -47.2% + 9.2% = - 38.0%

real return on the stock market in 1932 = -10.4% - (-11.4%) = -10.4% + 11.4% = + 1%

real return on the stock market in 1933 = 63.2 % - 0.7% = +62.5%

Solution for b

The assumption is that the average arithmetic mean is required. Average arithmetic real stock market return = (sum of all stock market returns from 1929 to 1933)/ number of years

= (-19.2% + (-28.1%) + (-38%) + 1% + 62.5%) / 5 = -21.8%/5 = - 4.36%

Solution for c

The stock market risk premium is the return on the stock market over and above the risk-free rate.

Therefore the stock market risk premium = stock market returns for the year - T-Bill return for the year

stock market premium in 1929 = -14.2% - 7.0% = -21.2%

stock market premium in 1930 = -31.5% - 2.3% = -33.8%

stock market premium in 1931 = - 47.2% - 1.4% = - 48.6%

stock market premium in 1932 = -10.4% - 0.9% = - 11.3%

stock market premium in 1933 = 63.2 % - 0.2% = +63.0%

Solution for d

Average risk premium = (sum of risk premium from 1929 to 1933)/ number of years

= ( -21.2% - 33.8% - 48.6% - 11.3% + 63%)/5 = - 51.9% / 5 = -10.38%