Stock Market History
a. What was the average rate of return on large U.S. common stocks from 1900 to 2001?
b. What was the average risk premium on large stocks?
C. What was the standard deviation of returns on the market portfolio?
a. Which index? Inflation adjusted or not?
b. Which large stocks?
c. Which portfolio?
You need to be more specific in your question, and should make an attempt to find this some of the data yourself.
I only came up with the following. I thought the questions was kinda vague too.
A. T-bills = 4.1%
TBonds = 5.1 %
Common stocks = 11.8 %
B. I was not sure if a formula was the answer.. if so
interest rate on T-bills + market risk premium
C.??
As you said, I still have some work to do on this one.
A. The stock and T-bill rates you listed look about right for that period, but I thought T-Bonds (10-year) averaged more like 7%.
(See http://research.stlouisfed.org/fred2/data/GS10.txt for a list of rates)
B. The "risk premium" is the difference between the stock market appreciation rate and the Treasury Bond rate (assume ten-year bonds). Using your figures, it would be 6.7%.
C. To calculate the standard deviation of returns on the market portfolio, you would need historical data on the returns of the market portfolio. This could be represented by a broad market index such as the S&P 500 or the Dow Jones Industrial Average. You would then calculate the annual returns of the market portfolio for the desired time period (in this case, from 1900 to 2001) and then use those returns to calculate the standard deviation.
To calculate the standard deviation, follow these steps:
1. Calculate the average return of the market portfolio by summing up all the annual returns and dividing it by the number of years.
2. Calculate the difference between each annual return and the average return, square those differences, and sum them up.
3. Divide the sum of the squared differences by the number of years minus one (this is known as the degrees of freedom).
4. Take the square root of the result from step 3.
This will give you the standard deviation of the returns on the market portfolio for the given time period.
Note: To find the historical returns of the market portfolio, you can use financial websites, databases, or historical stock market data providers. Examples include Yahoo Finance, Google Finance, or the St. Louis Federal Reserve Economic Data (FRED) website.