Alpha v Beta
Filed in: Alpha | Beta | Standard Deviation | R-Squared | Sharpe Ratio | Treynor Ratio | Banking | Finance
Measuring the performance of a fund or portfolio is really a measure of how well that fund is performing verses how well the overall market is performing.
One of the main measures is Alpha. This is why you always hear people going on about wanting high Alpha. However you must bear in mind that with higher Alpha you are also going to get higher risk.
Alpha is the rate of return that exceeds what the what the model would normally predict. The formula is generally
(end price + distributions + dividends )/start price
If you take your fund or portfolio and calculate the Alpha you should at least be making more than what the market is making. A lot of times people compare the Alpha of a fund / portfolio against CAPM ( Capital Pricing Asset Model ) or against the s&P 500 or if you are truly global you should have an Alpha greater than the Alpha of MSCI world index. The argument here is why do all the effort of a fund or portfolio if your returns are less than just buying the MSCI over the same time period. Note when we talk about effort this implies actively managed and when we talk about just investing simply in one thing this is passive investment.
I should also throw out a note of caution here, the sage of Omaha, Warren Buffet has said that the S&P 500 will outperform any actively managed Hedge fund. He bet a large sum of money over a 10 year time period and it looks like he will be proved correct.
Beta measures the volatility of your fund or Portfolio over a time period compared to the market. The Beta coefficient is how does your volatility compare to the market volatility. If your Beta is 1 your vol moves as the market moves. Less than 1 your volatility is less severe than the market and conversely greater than 1 your vol moves more than the market volatility.
Using Alpha and Beta you can compare your fund or Portfolio to the market, with the aim of achieving high Alpha with low Beta.
Other statistical evaluations that are used for measuring performance.
Standard Deviation is the dispersion of data from the mean or the square root of the variance. This is done by looking at the variance to the mean and the further the point is from the mean the higher the variance. Volatile stocks have higher Standard Deviation and larger price ranges compared to Blue Chip stocks that tend to have lower standard deviation.
R-Squared - this is a statistical measure that measures as a percentage how the fund or portfolio moves compared to a benchmark index like MSCI or S&P 500. The higher the value the more the fund/portfolio moves in line with benchmark moves. The lower the value the less likely moves in the benchmark will move the fund/portfolio.
Sharpe Ratio - measure the risk adjusted return and is
(Mean Portfolio return - Risk Free Rate )/Portfolio standard Deviation
Treynor Ratio is the reward to volatility Ratio. It measures returns that are greater than those that would have been gained on a risk less investment per unit of market risk. It is defined as:
(Average return of the portfolio - Average return of the risk free rate )/ Beta of the Portfolio.
This is similar to the sharp but uses Beta ( Market Risk ) to measure volatility as opposed to standard deviation.
People who enjoyed this article also enjoyed the following:
Naive Bayes classification AI algorithm
K-Means Clustering AI algorithm
Equity Derivatives tutorial
Fixed Income tutorial
And the following Trails:
C++Java
python
Scala
Investment Banking tutorials
HOME
