Alpha is a measure of the risk-adjusted return on investment. In other words, it tells us how much return we can expect from an investment after considering the level of risk associated with that investment. Alpha is often used in conjunction with beta, which is a measure of the volatility of an investment and is used to give an idea on the expected return from an investment.
Alpha quantitatively describes how much better or worse a stock performs relative to its benchmark. If the Alpha is zero, then this indicates that an investment's performance is equal to its benchmark.
It's important to know what benchmark the alpha uses for comparison. Usually, the benchmark is the stock market the stock trades on. However, there are exceptions.
For example, if a stock trading on the has an alpha of 8%, that probably means it outperformed the average of the S&P by 8%. On the other hand, if a Chinese fund had an alpha of -3%, that probably indicates that it underperformed its Shanghai (SSE) Composite by 3%. However, many stocks trade on multiple markets, so always check.
Alpha is often used to judge a fund manager's ability. A positive alpha means that the fund manager has been able to achieve returns above and beyond what would be expected given the level of risk associated with the fund. A negative alpha means that the fund manager has been unable to achieve returns commensurate with the level of risk associated with the fund.
Alpha Formula
The alpha formula is relatively simple. It is equal to the difference between the expected return on an investment and the risk-free rate of return. The expected return is the average return that investors expect to earn from an investment over time. The risk-free rate of return is the return that the investors would earn if they invested in a risk-free asset, such as a government bond.
For example, let's say that the investors expect to earn a 10% return on our investment in XYZ stock. However, they also know that XYZ stock is volatile and has a beta of 2. This means that it is twice as volatile as the market as a whole. Given this information, they can expect to earn 10% - (2 x 3%) = 4% on their investment in XYZ stock. This 4% return is the alpha.
The CAPM Formula for Alpha
The Capital Asset Pricing Model (CAPM) is a tool investors use to find the expected return on an investment. The model takes into account the risk-free rate, the expected market return, and the beta of the investment.
Beta is a measure of the volatility — or riskiness — of investment, compared to how risky the market as a whole is. For example, if a stock has a beta greater than 1, that means it's more volatile than the comparison market. For US-based investments, the comparison market is the S&P 500, which has a beta of 1. For Japanese-based investments, the Nikkei 225 Index has a beta of 1.
The higher the beta, the more volatile the investment. The beta of an investment only gives an estimate of how much risk the stock will add to your investment portfolio. Stocks with betas above 1 will tend to have more ups and downs than the S&P 500, while stocks with a beta less than 1 will have fewer ups and downs. The more a price goes up and down, the more volatile it is.
The CAPM formula for alpha is:
Alpha = Rf + beta(Rm-Rf)
How to Use the CAPM Formula to Find Alpha
To find alpha, you need to know the expected market return and the beta of your investment. You can find this information on most stock websites. For example, on Yahoo Finance you can find both beta and expected market return under the 'Key Statistics' tab. Once you have this information, plug it into the formula above to calculate your alpha.
Suppose you want to invest in Stock A. You look up Stock A on Yahoo Finance and find that its beta is 1.5 and the expected market return is 10%. Plugging these numbers into the formula gives us:
Alpha = Rf + beta(Rm-Rf)
Alpha = 0 + 1.5(10%-0)
Alpha = 15% - actual return of asset
This means that if Stock A has an actual return lower than 15%, it has a negative alpha. If Stock A has an actual return higher than 15%, it has positive alpha. This is helpful because it allows investors to benchmark their investments against others to see if they are outperforming or underperforming.
The CAPM formula is a helpful tool for investors because it tells them what kind of return they should expect from their investment (as measured by beta). By considering both risk and return, the CAPM formula gives investors a well-rounded view of their investments and how they are performing.
Alpha Interpretation and Limitation
It should be noted that alpha does have some limitations. First, alpha only considers linear relationships. This means that it might not be accurate when applied to investments with non-linear relationships (such as options). Second, alpha assumes that all risks are known and quantifiable. In reality, there are always unknown risks that could affect an investment's performance. Lastly, alpha assumes that all investors are rational and make decisions based on sound data and analysis. In reality, emotions play a role in many investment decisions.
R-squared is a number scale from 0 to 1 that practically explains the value of alpha and beta together. A high R-squared number close to 1 indicates that security details like alpha and beta work well together to describe return variations.
Despite these limitations, alpha is still considered to be an important measure by many finance professionals.
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