Download the daily prices of the S&P 500 from Quandl over the last 65 years.
Take daily log returns of the adjusted close column.
Find the standard deviation.
I.e. divide the sum by ~63.36 years (no CAGR required with logs!).
Then multiply the standard deviation by the square root of 252 days.
What do you get?
0.48 or so?
That's an OK approximation for the S&P 500's Sharpe ratio; often quoted as 0.5. Log returns lead to conservative numbers, which nice (I need to investigate this fully).
Multiply each return by the sign of the previous return, creating a new return for our 'simplified momentum strategy'.
You can create a 'sign flag' like this,
What do you see?
A ratio equal to about 1?
You have just doubled returns while keeping volatility constant.
Now you too can blog about long term Sharpe ratios higher than most can muster.
Welcome to the club.
Want to become a gold card carrying member? Send me details on how to reach a Sharpe of 2! ; )