In this post, we will be diving deeper into two commonly used portfolio statistics. These terms are Alpha and Beta, are based on a statistical method called “Regression“, and are used in the Capital Asset Pricing Model (CAPM). They are calculated by fitting a “line” to a set of points.
“…alpha is the return on an investment that is not a result of general movement in the greater market”.
Description of “Alpha” from the Capital Asset Pricing Model (CAPM). Source: Investopedia
“Beta effectively describes the activity of a security’s returns as it responds to swings in the market”
Description of “Beta” from the Capital Asset Pricing Model (CAPM). Source: Investopedia
If we define the market as the S&P 500, then Beta is an indication on how sensitive a portfolio is to S&P 500 returns. Alpha indicates how returns occur independent of the S&P 500. The term Alpha is so important, that it has even spawned its own website. And, why not? It represents the return obtained without exposing an investor to (stock) market risk.
An Example of CAPM
To better illustrate how Alpha and Beta are determined, consider the last 8 months of returns for the the following data sets:
- ETFMathGuy Aggressive Portfolio Returns
- S&P 500 total returns (ticker: IVV) to represent the market
- Short-term U.S. Treasury bill returns (ticker: SHV) to represent the risk free rate
Since CAPM is based on the concept of “excess returns”, which are returns above the risk-free rate, we can visualize this relationship in a scatterplot. The horizontal axis is the “Market Returns – Risk Free Rate”, and the vertical axis is the return of our “ETFMathGuy Aggressive Risk Portfolio Returns – Risk Free Rate”.
These results look promising, with a value of Beta = 0.37 and Alpha = 2.1%. However, 8 observations are small, so analysts typically look to see if these values are “significantly different” than 0. Or, put another way, what is the chance that these value were obtained by skill, rather than luck?
Assessing Luck vs. Skill
More data or evidence is always helpful in supporting any claim using statistics. For the example we show above, we are claiming that Alpha and Beta are non-zero values. Using some fundamentals from statistics, we can determine p-values for our Alpha and Beta calculation above as 29% and 15%, respectively. (Yes, p-value is another statistical term.) These p-values are fairly easy to interpret. In this case, 29% is the probability that Alpha = 2.1% is due to random chance, and the 15% is the probability that Beta= 0.37 is due to random chance. Put another way, we can say that Alpha = 2.1% and Beta = 0.37, but there is a chance (29% and 15%) that, in fact, we are wrong and that these value should be zero. So, the smaller the p-values, the greater confidence we have that these are the correct values and have minimal estimation error.
So What?
These results show that the ETFMathGuy Aggressive Portfolio is generating positive Alpha, and isn’t overly sensitive to the market. However, more data is needed to provide stronger evidence that these results are not simply due to luck. We hope you will continue to check back to see how the ETFMathGuy portfolios perform for the rest of 2020. And, for those who are premium subscribers, the September portfolios are now available, which includes a new calculator at the bottom of the page to further aid in portfolio re-balancing decisions.
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