Basics Of Alpha Revisited ... For The Investor - Part 2

Includes: SPY
by: Braun Research

<< Return to Part 1

It is unfortunate that the standard performance presentations do not give clear information with regard to Alpha. The usual graphs that you see, look something like this:

It is somewhat less misleading than the first graph, which was just indicating percentage changes; but you still do not have a figure like the Alpha by which to compare in a more reliable way the two managers. The correct statistical calculation for Alpha (and Beta) is as follows:

Thus the Steady portfolio's manager achieved a higher Alpha, with a lower Beta than the manager of the High-Flyer portfolio. To better understand what is behind a correct Alpha and Beta calculation, I encourage you to take a look at the scatter plot of the two portfolios. It shows what the performance of each was compared with the benchmark performance for the same period:

The regression lines for the two portfolios tell the entire story. Note how the Steady portfolio tends to do better as the Benchmark (usually the "market") performs worse, offering thus protection, i.e. peace of mind in bad times. This is reflected by the negative Beta (yet another Greek letter that looks like this: "β" and that mathematicians enjoy to use).

You may have heard that the lower the Beta of a portfolio is, the less risk it takes. Here is why:

The higher the Beta, the steeper the slope of the regression line and the more impact the market changes have on the return. If the market goes up (or down) say 2% and you have a portfolio with a Beta of say 0.8, the portfolio performance at that point will be the Alpha, plus 0.8x2%=1.6% (or minus 1.6% if the market goes down -2%). If the Beta is negative, say -0.25 as for the Steady portfolio in our example, that would subtract from the Alpha -0.25x2%=-0.5%; or if the market happens to be down by -2%, since -0.25x-2%=+0.5%, that's what's added for that period to whatever the Alpha happens to be.

The correct, statistically calculated Alpha, is the point at which the regression line intersects the Y axis. The Steady portfolio has indeed a higher Alpha than the High-Flyer portfolio. This is the "market independent" component of the return delivered by the portfolio manager through his know-how. The total return at any given point is obtained by adding to (or subtracting from) this market-independent component (the Alpha) the market-dependent component defined by the Beta and by the market itself. In other words, the more the market goes up, the more you add and conversely, the more the market declines the more you subtract. It is the Beta that tells you by how much.

For the more mathematically inclined reader this is nothing more than a simple linear equation:

Rp = α+βRm


Rp = Return of the portfolio


Rm = Return of the market

The academics like to complicate this with a term Rf defined as "risk free return." But I hope that a humble practitioner, like me, living in the real world, will be forgiven for not going any further in this context.

In my example, the Steady portfolio tends to perform less well in a growing market than the High-Flyer portfolio. It is the price to be paid for the added performance in bad markets. It is a function of the Beta which, in turn, is a reflection of the risk a PM chooses to take through a specific stock selection. The regression line can be upward sloping for a higher Alpha too but I selected this example in an attempt to give as comprehensive a picture as possible. Beta management is as important as a high Alpha: it is the PM's job to know in what type of market s/he needs to raise the Beta (i.e. go into more risky stocks) and when to lower Beta. Not an easy task but at least you hopefully have a better understanding now of what these "mysterious" Greek letters Alpha and Beta mean. Not that big a deal to understand but very important to better evaluate a portfolio manager's performance.

So to conclude:

  • Alpha describes the contribution of the PM to the performance that a portfolio offers above and beyond the market-determined performance. It is the active management contribution for which a fee deserves to be charged over an indexer who provides passive management.
  • Beta describes the risk that a PM decides to take at any point in time as a function of the prevailing conditions. This determines to what extent the market performance influences the portfolio performance.
  • Both Alpha and Beta MUST always be defined in conjunction with a Benchmark. Simply saying that a portfolio has an Alpha of X% is meaningless unless the benchmark is specified, like for example "an Alpha of 6% vs. the S&P500 (NYSEARCA:SPY)". Specifying the index is often omitted in the day-to-day talk, and often in written materials, which can lead to substantial misunderstandings.
  • Both Alpha and Beta are variable and it must be specified for what time-span they are quoted and for what periods have they been calculated: an annual Alpha is not the same as a monthly or weekly Alpha.

Disclosure: I have no positions in any stocks mentioned, and no plans to initiate any positions within the next 72 hours.

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