Understanding The Statistics ?
How do they work?
A positive "Alpha" of 1.0 means the fund or stock has outperformed its benchmark index by 1 percent. A similar negative alpha of 1.0 would indicate an underperformance of 1 percent. A "Beta" of less than 1 means that the security will be less volatile than the market. A beta of greater than 1 indicates that the security's price will be more volatile than the market. For example, if a stock's beta is 1.2, it's theoretically 20 percent more volatile—subject to big swings in prices or sales—than the market.
Stock Beta and Alpha as an Example
Let’s assume XYZ’s stock has a return on investment of 12% for the year and a beta of + 1.5. Our benchmark is the S&P500 which was up 10% during the period. Is this a good investment?. A beta of 1.5 implies volatility 50% greater than the benchmark; therefore the stock should have had a return of 15% to compensate for the additional volatility risk taken by owning a higher volatility investment. The stock only had a return of 12%; three percent lower than the rate of return needed to compensate for the additional risk. The Alpha for this stock was -3 and tells us it was not a good investment even though the return was higher than the benchmark.
What's R-squared
An R-squared of 100 indicates that all movements of a portfolio can be explained by movements in the benchmark. Thus, index funds that invest only in S&P 500 stocks will have an R-squared very close to 100. Conversely, a low R-squared indicates that very few of the portfolio's movements can be explained by movements in its benchmark index. An R-squared measure of 35, for example, means that only 35% of the portfolio's movements can be explained by movements in the benchmark index. R-squared can be used to ascertain the significance of a particular beta or alpha. Generally, a higher R-squared will indicate a more useful beta figure If the R-squared is lower, then the beta
is less relevant to the fund's performance.
Sharpe Ratio
The Sharpe Ratio calculates the difference between risk-free and a risky asset, you divide the difference by the Standard Deviation ( the value of risk) of the stock / portfolio. The Sharpe Ratio is a strategy to maximize the reward to risk relationship. It is a measure which can be used to compare two or more investments to show which one earned the most excess return given the least amount of extra risk. Two Stocks or Portfolios that generate the same return over a certain period might not be the same in terms of the risk taken to invest in each of them. One of them might have been more volatile during that period, meaning that our risk for that stock / portfolio was greater. To give you some insight, a ratio of 1 or better is considered good, 2 and better is very good, and 3 and better is considered excellent.
Treynor Ratio
Ultimately, the Treynor ratio attempts to measure how successful an investment is in providing investors compensation, with consideration for the investment’s inherent level of risk. The Treynor ratio is reliant upon beta – that is, the sensitivity of an investment to movements in the market – to judge risk. The Treynor ratio is based on the premise that risk inherent to the entire market (as represented by beta) must be penalized, because diversification will not remove it. When the value of the Treynor ratio is high, it is an indication that an investor has generated high returns on each of the market risks he has taken. The Treynor ratio allows for an understanding of how each investment within a portfolio is performing. It also gives the investor an idea of how efficiently capital is being used.
The Manager, Fidelibus Lucrum, Pooled Investment Club.
