# 1. What is the Difference Between Alpha and Beta?¶

## 1.1. Alpha and Beta for Beginners¶

In finance, alpha and beta are two of the most commonly used measurements, to gauge how successful portfolio managers performs, relative to their peers. Simply defined, alpha is the excess return (also known as the active return), an investment or a portfolio of investments ushers in, above and beyond a market index or benchmark that represent the market’s broader movements.

Beta is a measurement of the volatility, or systematic risk of a security or portfolio, compared to the market as a whole. Often referred to as the beta coefficient, beta is a key component in the capital asset pricing mode (CAPM), which calculates the theoretically appropriate required rate of return of an asset, to make it worth incorporating into an investment portfolio.

Alpha and beta are standard technical risk calculations that investment managers use to calculate and compare an investment’s returns, along with standard deviation, R-squared, and the Sharpe ratio.

- FAST FACT：
- Both alpha and beta are historical measures.

### 1.1.1. Alpha¶

Although the Alpha figure is often represented as a single number (like 3 or -5), it actually describes a percentage that measuring how a stock of mutual fund performed compared to a benchmark index. The numbers mentioned would mean the investment respectively fared 3% better and 5% worse than the broader market. Therefore, an alpha of 1.0 means the investment outperformed its benchmark index by 1%, while conversely, an alpha of -1.0 means the investment underperformed its benchmark index by 1%.

Alpha, one of the most commonly quoted indicators of investment performance, is defined as the excess return on an investment relative to the return on a benchmark index. For example, if you invest in a stock, and it returns 20% while the S&P 500 earned 5%, the alpha is 15. An alpha of -15 would indicate that the investment underperformed by 20%.

Alpha is also a measure of risk. In the above example, the -15 means the investment was far too risky given the return. An alpha of zero suggests that an investment has earned a return commensurate with the risk. Alpha of greater than zero means an investment outperformed.

Alpha is one of the five major risk management indicators for mutual funds, stocks, and bonds and, in a sense, tells investors whether an asset has performed better or worse than its beta predicts.

When hedge fund managers talk about high alpha, they’re usually saying that their managers are good enough to outperform the market. But that raises another important question: when alpha is the “excess” return over an index, what index are you using? For example, a fund manager might say that she or he generated a 20% return when the S&P returned 15%, an alpha of 5. But is the S&P an appropriate index to use? Consider a manager who has invested in Apple Inc. (AAPL) on Aug. 1, 2014. Compared to the S&P 500, the alpha would look quite good: Apple returned 18.14%, while the S&P 500 returned 6.13%, for an alpha of about 12.

But few experts would consider the S&P a proper comparison for Apple, given the differing levels of risk. Perhaps the NASDAQ would be a more appropriate measure. The NASDAQ in that same yearlong period returned 15.51%, which pulls the alpha of that Apple investment down 2.63. So when judging whether a portfolio has a high alpha or not, it’s useful to ask just what the baseline portfolio is.

### 1.1.2. Alpha Examples¶

Alpha is essential to gauging an investment manager’s true success. For example, an 8% return on a mutual fund seems impressive when equity markets as a whole are returning 4%. But that same 8% return would be considered underwhelming if the broader market is earning 15%.

With the CAPM （ capital asset pricing model ）, alpha is the rate of return that exceeds the model’s prediction. Investors generally prefer investments with high alpha. For example, if the CAPM analysis indicates that the portfolio should have earned 5%, based on risk, economic conditions and other factors, but instead the portfolio earned just 3%, the alpha of the portfolio would be therefore be a discouraging -2%.

Formula for Alpha:

Alpha = End Price + DPS − Start Price / Start Price where: DPS = Distribution per share

Portfolio managers seek to generate alpha by diversifying portfolios to eliminate unsystematic risk. Because alpha represents the performance of a portfolio relative to a benchmark, it represents the value that a portfolio manager adds or subtracts from a fund’s return. The baseline number for alpha is zero, which indicates that the portfolio or fund is tracking perfectly with the benchmark index. In this case, it can be extrapolated that investment manager has neither added or lost any value.

### 1.1.3. Beta¶

Beta fundamentally analyzes the volatility of an asset or portfolio in relation to the overall market, to help investors determine how much risk they’re willing to take to achieve the return for taking on said risk. The baseline number for beta is one, which indicates that the security’s price moves exactly as the market moves. A beta of less than 1 means that the security will be less volatile than the market, while a beta greater than 1 indicates that the security’s price will be more volatile than the market. If a stock’s beta is 1.5, it is considered to be 50% more volatile than the overall market.

Unlike alpha, which measures relative return, beta is the measure of relative volatility. It measures the systematic risk of a security or a portfolio in comparison to the market as a whole. A tech stock such as that mentioned in the example above would have a beta in excess of 1 (and probably rather high), while a T-bill would be close to zero because its prices hardly move relative to the market as a whole.

Beta is a multiplicative factor. A stock with a beta of 2 relative to the S&P 500 goes up or down twice as much as the index in a given period of time. If the beta is -2, then the stock moves in the opposite direction of the index by a factor of two. Some investments with negative betas are inverse exchange-traded funds (ETFs) or some types of bonds.

What beta also tells you is when risk cannot be diversified away. If you look at the beta of a typical mutual fund, it’s essentially telling you how much risk you’re adding to a portfolio of funds.

Again, similar caveats to alpha apply: it’s important to know what you’re using as your benchmark for volatility. Morningstar, Inc. (MORN), for example, uses U.S. Treasuries as its benchmark for beta calculations. The firm takes the return of a fund over T-bills and compares that to the return over the markets as a whole and using those two numbers comes up with a beta. There are, though, a number of other benchmarks one could use.

Beta is a statistical measure of the volatility of a stock versus the overall market. It’s generally used as both a measure of systematic risk and a performance measure. The market is described as having a beta of 1. The beta for a stock describes how much the stock’s price moves in relation to the market. If a stock has a beta above 1, it’s more volatile than the overall market. As an example, if an asset has a beta of 1.3, it’s theoretically 30% more volatile than the market. Stocks generally have a positive beta since they are correlated to the market.

If the beta is below 1, the stock either has lower volatility than the market or it’s a volatile asset whose price movements are not highly correlated with the overall market. The price of Treasury bills (T-bills) has a beta lower than 1 because it doesn’t move very much in relation to the overall market. Many consider stocks in the utility sector to have betas less than 1 since they’re not very volatile. Gold, on the other hand, is quite volatile but has at times had a tendency to move inversely to the market. Lower beta stocks with less volatility do not carry as much risk, but generally provide less opportunity for a higher return.

The beta coefficient is calculated by dividing the covariance of the stock return versus the market return by the variance of the market. Beta is used in the calculation of the capital asset pricing model (CAPM). This model calculates the required return for an asset versus its risk. The required return is calculated by taking the risk-free rate plus the risk premium. The risk premium is found by taking the market return minus the risk-free rate and multiplying it by the beta.

The market against which to measure beta is often represented by a stock index. The most commonly used stock index is the S&P 500. The S&P 500 is used as the measure because of the high number of large-cap stocks included in the index, as well as the broad number of sectors included. The Dow Jones Industrial Average has also previously been the main measure of the market, but it has fallen out of favor since it only includes 30 companies and is very limited in its breadth.

Beta is an important concept for the analysis of hedge funds. It can show the relationship between a hedge fund’s returns and the market return. Beta can show how much risk the fund is taking in certain asset classes and can be used to measure against other benchmarks, such as fixed income or even hedge fund indexes. This measure can help investors determine how much capital to allocate to a hedge fund or whether they would be better off keeping their exposure in the equity market or even cash.

### 1.1.4. Beta Examples¶

Here are the betas (at the time of writing) for three popular stocks:

Micron Technology Inc. (MU): beta = 1.26 Coca-Cola Company (KO): beta = .37 Apple Inc. (AAPL): beta = .99

We can see that Micron is seen as 26% more volatile than the market, while Coca-Cola is 37% as volatile as the market, and Apple is more in line with the market or 0.01% less volatile than the market.

Betas vary across companies and sectors. For example, while many utility stocks have a beta of less than 1, many high-tech, Nasdaq-listed stocks have a beta of greater than 1. This means that the latter groups of stocks offer the possibility of higher rates of return, but generally pose more risk.

While a positive alpha is always more desirable than a negative alpha, beta isn’t as clear-cut. Risk averse investors such as retirees seeking a steady income are attracted to lower beta. On the other hand, risk-tolerant investors who seek growth, are often willing to invest in higher beta stocks, whose higher volatility often generate superior returns.

Investors must distinguish short-term risks, where beta and price volatility are useful, from long-term risks, where fundamental, big picture risk factors are more prevalent.

Investors looking for low-risk investments might gravitate to low beta stocks, whose prices will not fall quite as much as the overall market drops during downturns. However, those same stocks will not rise as much as the overall market during upswings. Investors can use beta figures to determine their optimal risk-reward ratios for their portfolios.

Formula for Beta

Her is a useful formula for calculating beta:

Beta = CR / Variance of Market’s Return where: CR = Covariance of asset’s return with market’s return

Covariance is used to measure the correlation in price moves of two different stocks. Covariance measures how two stocks move in relation to one another. A positive covariance means the stocks tend to move in lockstep, while a negative covariance conveys stocks move in opposite directions. On the other hand, variance refers to how far a stock moves relative to its mean, and is frequently used to measure the volatility of an individual stock’s price over time.

Past Performance

Both alpha and beta are backward-looking risk ratios and it is important to remember that past performance is no guarantee of future results.

Investors use alpha to measure a portfolio manager’s performance against a benchmark while also monitoring the risk or beta associated with the investments that comprise the portfolio. Some investors might look for either a high beta or low beta depending on their risk tolerance and expected rate of return.

关键要点

Alpha and beta are common measurements that gauge the performance of portfolio managers compared to their peers. Alpha is the excess return or active return of an investment or a portfolio. Beta measures volatility of a security or portfolio compared to the market. Both alpha and beta are backward-looking and can’t guarantee future results.

Alpha is the excess return on an investment relative to the return on a benchmark index. Beta is the measure of relative volatility. Alpha and beta are both risk ratios that calculate, compare, and predict returns.

The Bottom Line

Alpha and beta are both risk ratios that investors use as a tool to calculate, compare, and predict returns. They’re very important numbers to know, but one must check carefully to see how they are calculated.