# Alpha

Alpha is a measure of the performance of an investment in relation to a benchmark index. Often specified as a percentage, an alpha of 1% means that the return on investment was 1% better than the benchmark.

Alpha will often be expressed in basis point terms, where 1 basis point is equal to one-hundredth of one percent (i.e., 0.01%). 100 basis points (often abbreviated bps) of alpha is the same as 1% of alpha. It can also be regularly seen as a whole number – e.g., 2 – which would express an annual excess return of 2% versus a benchmark.

Alpha is frequently used to compare the performance of various ETFs, mutual funds, and other investment vehicles against a measure considered “the market” and typically done to gauge the talent level of a trader or investment manager.

For a mutual fund that invests in stocks, the S&P 500 or its most popular ETF equivalent, SPY, is a typical benchmark. For a mutual fund that invests in mostly investment grade bonds, an aggregate bond index or associated ETF (e.g., AGG, BND) would be more suitable.

A close cousin of alpha, beta, is designed to measure systematic risk or volatility. Beta can be measured with respect to a single security – namely, its volatility relative to the broader market – or as it relates to an entire portfolio. Total return is equal to the sum of alpha, beta, and whatever one returns on any cash holdings (i.e., the “risk-free” rate).

## Alternative Definitions of Alpha

There are also different calculations for alpha, typically to adjust for risk performance.

For example, Jensen’s alpha takes into account performance over or under a theoretical benchmark using the following formula:

Portfolio Return – [Risk-free rate + Portfolio beta * (Return of market benchmark – Risk-free rate)]

If we assume that the risk-free rate is a 3-month US Treasury (10-year US Treasury is also common) and equal to 1.50%, the portfolio beta is 1.60 (60% more systematic risk or volatility than the benchmark), the benchmark has returned 10% annualized, and the portfolio return is 20%, we have:

20% – [1.5% + 1.6 * (10% – 1.5%)] = 4.9% or 490 bps

This means that despite a 10% outperformance over the benchmark (20% vs. 10%), a more accurate estimation of the portfolio’s alpha when adjusting for the risk taken on by the portfolio is about half that.

Alpha generation can also vary wildly depending on the business cycle. Portfolios invested exclusively in one type of asset class will disproportionately do well – even add alpha – in a specific type of market environment, but do poorly in another.

For example, stocks will do when the economy is running smoothly and generally lose value quickly when there’s a contraction. Safe bonds are typically mediocre investments when the economy is doing well and perform well when the economy underperforms.

Therefore, understanding a portfolio’s long-term viability or a trader or manager’s talent is best done when looking at an entire market cycle. If that’s not an option due to an insufficiently long track record, risk-reward metrics, such as the Sharpe ratio, Sortino ratio, or a risk-adjusted alpha measurement should be looked at to view return as it relates to the amount of risk taken on to achieve it.

## Obtaining Alpha and Its Use in Day Trading

While one is likely to generate positive returns over time investing in “the market” or a broad benchmark via beta, alpha is considered a zero-sum game and is dependent on managers deviating from the betas. This is where the concept of day trading and active asset management comes into play; namely, the desire to beat the market and achieve outsized returns.

Despite the allure of obtaining alpha in a portfolio, most active managers nonetheless fail to achieve it. Not only is achieving alpha a zero-sum game, one could reasonably consider it a negative-sum game when taking into account fees and commissions.

This has led to the widespread proliferation of low-cost index funds (ETFs), which follow specific stock and bond indices or provide an equity product equivalent to investing in a certain commodity or currency. The cheapest ETFs cost less than 0.10% in expense fees per year – e.g., \$10 per year per every \$10,000 invested – versus around 1.00% for many mutual funds and financial advisors.

Going out even further over the spectrum, investment vehicles such as hedge funds, private equity, and venture capital, which are open only to high net worth individuals, charge even higher fees.

Naturally, the greater the demanded fee compensation, the better an investment vehicle must perform in order to justify the cost. The general trend of the more expensive vehicles struggling to generate alpha has led to cheaper passive alternatives beginning to take market share.