Testing the Semi Strong form of Market Efficiency

• The Sharpe Ratio
  

The Sharpe ratio is also known as the reward to risk ratio, this ratio was introduced by William F. Sharpe in 1966 (Sharpe, 1994), and enables the comparison of portfolios with different risk or standard error. The Sharpe ratio is commonly represented by the following formulae.


Which is simply the mean return of a portfolio divided by the standard error, the resulting Sharpe ratios from the data are shown in table 6.


It can be clearly shown in table 6, that the estimated negative residual properties or under priced properties out perform the over priced properties. These results indicate that the hedonic pricing model can on average identify properties with a higher return for the equivalent risk.

But these results only show the returns and risk of the properties that are collectively purchased at the same time, but in reality only a small percentage is available for investors at each time interval. To truly confirm the performance of this trading rule we need to compare the performance of the selected properties with the total sample of properties throughout time.

In order to do this, properties from each portfolio were assigned to the month of purchase, and the excess returns gained from that month was averaged to get a time series of returns for the separate portfolios.
The statistics show that the means and the standard deviations are different from the previous results; this is because different weightings are placed on returns relative to the amount of properties in each month. The average monthly Sharpe ratio still show that estimated under priced properties still out perform the entire portfolio of properties and also the over priced properties throughout time, again confirming the effectiveness of the trading rule in identifying abnormal excess returns.