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2011 February » The Calculating Investor

I’m a financial data junkie, so I thought I’d share some of my favorite sites for free financal and economic data.  I’ve also added links to these sites to the sidebar, and I’ll keep the sidebar list updated as I find new data sources.

  • Yahoo! Finance:  Yahoo! Finance is a great site for ETF, mutual fund, and stock data.  The site allows historical price data to be downloaded in a CSV format, and this makes it easy to calculate historical returns.  For example, the R-script I created for calculating Fama-French factor loading automatically downloads the CSV file for the target fund and converts the price data to a monthly return series..
  • Google Finance:  Google Finance is similar to Yahoo! Finance, but it lacks the historical dividend information.  This makes it less useful for analyzing historical returns.  However, Google Docs provides a “GoogleFinance” function which allows stock or fund information to be downloaded directly into a Google Docs Spreadsheet.  This is a great feature which makes it easy to setup a spreadsheet to track your portfolio.  It is possible to directly download stock information from Yahoo! Finance into Excel, but the Google Docs + Google Finance combination makes it easy.
  • Fama-French Data Library:  This site has a large amount of historical data compiled by Eugene Fama and Kenneth French.  The data is updated regularly, and the Fama-French 3-factor data is especially useful for analyzing fund and portfolio performance.
  • Robert Shiller PE10 Data: This site has Robert Shiller’s PE10 data which was used in the book “Irrational Exuberance”.   I used this data to create a regression model for forecasting future returns.  Shiller’s PE10 data is also updated regularly.
  • Federal Reserve Economic Data (FRED):  This site has a wide variety of macroeconomic data including data for unemployment, GDP, interest rates, the money supply, etc.   The site also has pretty good tools for plotting the data.
  • Treasury Yield Curve Rates: This site has historical and current data for the Treasury and TIPS yield curves.  I previously posted an Octave script which uses this data to calculate inflation expectations.
  • Statistical Abstract of the United States:  This site has a variety of U.S. and International Economic data.  I think the data on foreign stock market capitalization is especially interesting and I’m hoping to work this into a future post.

Monte Carlo Simulations using return data from 1926-2010

In 1975, Nobel laureate William Sharpe published a study titled “Likely Gains from Market Timing”. In this paper, Sharpe reportedly found that a market timer who switches between 100% stocks and 100% T-bills on an annual basis must be correct about 74% of the time (on average) to beat the market.

Unfortunately, a free copy of this paper is not available on the web, and I don’t have access to this much cited paper. However, I’ve seen a number of related analyses based on Sharpe’s approach, and I believe we can recreate a similar result through simulation.

In this post, I’ll simulate a simple market timing strategy and determine the market timing accuracy required to outperform buy-and-hold. I’ll compare market timing to buy-and-hold in terms of both total returns and risk-adjusted returns (measured by the Sharpe Ratio). I’m going to use market and T-bill returns for the years 1927-2010.

My assumptions are that an investor makes a decision at the beginning of each year to invest in either stocks or T-bills, based on his/her prediction for the coming year. The Monte Carlo simulation is run using the actual annual returns for stocks and T-bills from 1927 to 2010, and 10,000 runs of the simulation are plotted to generate a distribution.

The Monte-Carlo results for 50% prediction accuracy are shown below.  The red line represents the arithmetic average return for a buy and hold investor over the years from 1926 thru 2010, and the distribution represents the market timing outcomes for the 10,000 trials:

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How confident should you be about your investment goals?

What is the probability that your investments will fall short of a particular investment goal?  How is this probability affected by uncertainty about the equity risk premium?

In this post, I plan to look at a simple method for estimating the probability that a risky investment will fall short of a particular return goal, and I’ll then extend this analysis to allow for uncertainty about the equity risk premium.

This analysis is a very simplified example of the concept presented by Lubos Pastor and Robert F. Stambaugh in their paper “Are Stocks Really Less Volatile in the Long Run?”.

For starters, if we assume stock prices follow a random walk, then the probability of a risky investment underperforming a risk free investment, such as a T-bill, is given by this equation:

 Shortfall Probability = Prob\left ( z< \sqrt{T} \frac{r-\mu }{\sigma }\right )

r = continuously compounded (log return) t-bill rate
\mu = continuously compounded (log) equity return
\sigma = annual standard deviation of equity returns
T = number of years

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