Question on alpha and beta

Hi,
Recent college graduate and new here to WSO, very excited to learn more about Finance. I have recently started creating an investing sort of tool in excel and I have a question regarding alpha and beta.

As I understand (correct me if I'm wrong), it is a widely debated topic, whether it is better practice, to maximize alpha or to minimize beta. Alpha equals the return of a stock over what it's risk warrants (as depicted by CAPM for example).

Putting this together I realized, by choosing to minimize beta, you are inadvertently maximizing alpha, since alpha is a function of beta (indirectly). Am I right in this theory and if so, should we direct our attention primarily towards stocks' betas?

Thanks!

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Comments (18)

Mar 28, 2011 - 4:48am

that's not necessarily true. alpha is defined as returns above the rate of return predicted by the CAPM model. as such, alpha does not necessarily depend on the beta of your portfolio.

CAPM:

excess return = alpha + risk free + beta(market- risk free)
so alpha = excess - risk free - beta
(market-risk free) * this is calculated ex-post

however this equation can be misleading, since this is calculated ex-post (vs. ex-ante like your question) and since your alpha should by definition be generated by an abnormal return above what is expected based on your beta. since alpha is the "abnormal return," there shouldn't be a clear inverse relationship such as minimizing beta --> maximizing alpha.

correct me if im wrong, but thats mostly what i remember from a class on MPT i took a few years ago

Mar 28, 2011 - 10:32am

This is the backward-looking form of re-arranging CAPM to arrive at Beta:
Beta = -(alpha + rf - returns) / (market returns - Rf)

To figure out how to minimize our expected beta, we arrive at the following:
E(Beta) = -(E(alpha) + Rf - E(r)) / (E(Rm)-Rf)

Here, we can see that to minimize expected beta, we need to either minimize E(r), this is the risk-return relationship or we can maximize E(alpha). However, by definition, alpha is the component of a stock's returns that are unpredictable and therefore E(alpha) = 0 and so we're left with only being able to minimize E(r).

Alpha = returns - Rf - (Beta*(Rm-Rf))

To maximize E(alpha), we get the following:
E(alpha) = E(r) - Rf - (E(Beta)*(Rm-Rf))

However, since E(r) = Rf + Beta*(Rm-Rf) then,
E(alpha) = E(r) - E(r) = 0

Mar 28, 2011 - 10:32am

This is the backward-looking form of re-arranging CAPM to arrive at Beta:
Beta = -(alpha + rf - returns) / (market returns - Rf)

To figure out how to minimize our expected beta, we arrive at the following:
E(Beta) = -(E(alpha) + Rf - E(r)) / (E(Rm)-Rf)

Here, we can see that to minimize expected beta, we need to either minimize E(r), this is the risk-return relationship or we can maximize E(alpha). However, by definition, alpha is the component of a stock's returns that are unpredictable and therefore E(alpha) = 0 and so we're left with only being able to minimize E(r).

Alpha = returns - Rf - (Beta*(Rm-Rf))

To maximize E(alpha), we get the following:
E(alpha) = E(r) - Rf - (E(Beta)*(Rm-Rf))

However, since E(r) = Rf + Beta*(Rm-Rf) then,
E(alpha) = E(r) - E(r) = 0

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Mar 28, 2011 - 1:26pm

Beta is how much a security will move in price in relation to how the market moves in price. It is used to derive the "expected" return.

Alpha is how much more the security returns above the "expected" amount. In short, there is no correlation between beta and alpha. You simply need the beta in order to calculate alpha.

"It is hard to fail, but it is worse never to have tried to succeed." Theodore Roosevelt
  • 1
Mar 28, 2011 - 1:32pm

So, using the beta, a PM would calculate the expected return. Once the trade has been placed and returns start flowing in, the alpha is everything above this expected value?

Mar 28, 2011 - 2:25pm

No. A PM would value a security using whatever method best fits his investment style (possibly CAPM). The beta is simply the securities volatility in relation to the market. It's how much it is expected to move compared to the market. A security with a beta of 2 and a market return of 100 should return 200. If there is no risk free rate (or it's 0) and the above scenario holds, then there is zero alpha. If the security returns 250 b/c of some news or something else, then the alpha is 50. It's just judging your stock picking ability in selecting securities that return better than expected.

You can manipulate alpha by being levered though, and thats why it's never used alone to gauge a PM. if you take the same trade and use 2X leverage, then your return would be 500 and your alpha 300, but you would probably have a really low sharp ratio showing your risk.

Yes, alpha is everything above the expected value/return including the risk free rate (beta*market return + RFF= alpha)

Edit: You don't really see it for one security, it's usually the sum of an entire portfolio where every security adds a little bit or detracts a little bit from the overall portfolio alpha.

"It is hard to fail, but it is worse never to have tried to succeed." Theodore Roosevelt
  • 3
Mar 29, 2011 - 5:58pm
Something Creative:
No. A PM would value a security using whatever method best fits his investment style (possibly CAPM). The beta is simply the securities volatility in relation to the market. It's how much it is expected to move compared to the market. A security with a beta of 2 and a market return of 100 should return 200. If there is no risk free rate (or it's 0) and the above scenario holds, then there is zero alpha. If the security returns 250 b/c of some news or something else, then the alpha is 50. It's just judging your stock picking ability in selecting securities that return better than expected.

You can manipulate alpha by being levered though, and thats why it's never used alone to gauge a PM. if you take the same trade and use 2X leverage, then your return would be 500 and your alpha 300, but you would probably have a really low sharp ratio showing your risk.

Yes, alpha is everything above the expected value/return including the risk free rate (beta*market return + RFF= alpha)

Edit: You don't really see it for one security, it's usually the sum of an entire portfolio where every security adds a little bit or detracts a little bit from the overall portfolio alpha.

Thank you.

Mar 31, 2011 - 10:55pm

If there were a "method" to trade with alpha rather than beta, everyone would do it. TL;DR version: Beta is just getting a market return adjusted for volatility, alpha is getting returns in excess of what the beta of your portfolio implies, suggesting idiosyncratic factors at work.

Before answering your question, lets do a quick refresher on CAPM. The return of any asset is describable as:

Ri = Rf + B(Rm - Rf) + a

Ri = asset return
Rf = Risk-free rate (say 10-yr govt bond for simplicity sake)
Rm = expected market return - depending on what market you're in, this is the S&P or the index of the country
a = alpha

If you are driving returns with Beta, all it means is that you are timing the market (which is fine but not that differentiated). In other ways, if your portfolio consists of high-beta assets in a rising market, you will outperform the market nominally, but it's just because you have volatile assets. Likewise, if your portfolio consists of high-beta assets in a falling market, your losses will be greater than those of the market.

On the other hand, if your returns are based more on alpha, it implies that you are driving returns via stock (or other asset) selection, on idiosyncratic / company-specific factors. The process behind that is generally higher quality / more repeatable.

  • 4
Mar 31, 2011 - 10:56pm

I've never heard the alpha and beta used in the exact way you used them. The poster above you basically answered the question. If his response seemed too technical, however, I'll try to give a nontechnical answer for you.

A very short answer is that alpha is a product of manager skill, and beta is a product of the broader returns of the market.

A basic rule of financial theory is that greater reward requires greater risk. Someone who generates unusually high returns might be doing so simply by borrowing money to invest, or investing in companies that have themselves borrowed money (and are thus riskier) or investing on other risky assets that promise high returns.

Taking on more risk to get higher returns might be the correct course of action for some people in some situations, but such producing returns by taking on greater risk isn't a sign of an investment manager's skill. Returns, high or low, that are not due to a money manager's skill, but instead are due to taking on greater or lesser amounts of risk, are a product of beta, a measure of market risk. Such returns are the reward that investors demand in order to take on "exposure" to the risks inherent in investing in a given market.

Alpha is, in essence, returns due to manager skill. It is the out-performance that remains after adjusting for the riskiness of an investor's decisions. Alpha is worth paying an investment manager for; beta is not. You can get beta-driven returns by buying a low-cost, "mindless" index fund. Alpha requires a skilled investor, and is rare.

The distinctions between alpha and beta are not quite as clear-cut as I made them seem above. One can attempt to generate a form of alpha by taking on different exposure to different betas at different times, for instance, moving between broad indexes of stocks, bonds, real estate, commodities, etc. To some extant, this is what some "macro" traders do, and is also what asset allocator funds do as well. There are other issues, empirical and theoretical, with the alpha/beta divide as well. For instance, low beta (in theory, low risk) portfolios tend to do better than the model of low risk-low return/high risk-high return would suggest they should.

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