Risk and Return: Making Sense of Alpha and Beta


Alpha and beta are risk and return measures of the investment. Alpha represents the unsystematic risk while beta is used to measure systematic risk. In broader terms, the total risk is the combination of unsystematic risk and systematic Risk. 

Unsystematic Risk (Alpha)


Unsystematic risk is specific to the company and/or the specific industry. Following are examples of unsystematic risks:

  • Company specific financial risk: i.e., a company taking on too much debt, increasing debt-to-equity ratio
  • Sale and/or profit deterioration due to competition or change in consumer behavior or government policy
  • Issues with company specific labor force or supply chain
  • Poor management decisions leading to business risk for a specific company

Systematic Risk (Beta)


Systematic risk typically affects the entire market or entire segment of the market. Following are examples of systematic risks:

  • Inflation risk or deflation risk affecting purchasing power
  • Interest rate changes affecting the market
  • Market risk resulting in volatility and uncertainty (Example: 2008 financial crisis, March 2020 Pandemic)
  • Geopolitical Risk
  • Trading Policy Changes

So the combination of unsystematic risk (alpha) and systematic risk (beta) gives you perspective of the total risk of an investment. 

Now let’s dig in.

Alpha 𝛂


Alpha is one of the statistical measures in Modern Portfolio Theory (MPT).

Simply put, alpha is the difference between the actual return of an investment over its expected return based on its beta. In other words, alpha is used to measure the performance of an investment on a risk adjusted basis. 

The base alpha score is “zero” meaning investment return matched return of the benchmark index. So in general,

  • If 𝛂 = 0, investment return is inline with the return of the benchmark index
  • If 𝛂 = + number, investment is outperforming the benchmark index
  • If 𝛂 = – number, investment is underperforming the benchmark index

For example, if a fund returns 10% and its benchmark index return 8%, the fund’s alpha score is +2. Conversely, if a fund returns 7% and its benchmark index return 8%, the fund’s alpha score is -1. 

The goal of the active fund managers and hedge fund managers is to “seek” the alpha. In other words, active managers expect to outperform the benchmark index. Hence, the “value” added by the fund manager. 

However, it is a challenge to consistently outperform the market over a long period of time. According to this CNBC article, almost 92% of active managers underperform S&P 500 over a 15 years period.

Beta (𝞫)


Beta is another statistical measure in Modern Portfolio Theory (MPT).

It represents systematic risk. It is the measure of the sensitivity of an investment relative to the benchmark index. In other words, beta is a measure of volatility relative to the benchmark index.

The beta of the benchmark index is 1.0. So in general,

  • If 𝞫 = 1, investment moves in tandem with the benchmark index
  • If 𝞫 < 1, investment is less volatile than the benchmark index
  • If 𝞫 > 1, investment is more volatile than the benchmark index

Let’s look at some examples of Beta. You can get beta of a stock from morningstar.com or finance.yahoo.com.

Wells Fargo (WFC)

  • WFC’s beta is 1.06, meaning Wells Fargo’s stock is 6% more volatile than the S&P 500 Index. So if the S&P 500 rises 10%, WFC is expected to rise 10.6%. Conversely, if the S&P Index drops 10%, WFC is expected to fall 10.6%.

Johnson and Johnson (JNJ)

  • Johnson’s and Johnson’s beta is 0.69, meaning JNJ is less volatile than the S&P 500 Index. So if the S&P 500 index rises 10%, JNJ is expected to rise 6.9%. Conversely, if the S&P 500 Index drops 10%, JNJ is expected to fall 6.9%.

Similarly, you can find the beta for mutual funds. 

Vanguard Total Stock Market Index Fund (VTSAX) 

  • VTSAX beta is 1.04, meaning VTSAX is 4% more volatile than the S&P 500 Index. Hence, it would closely track the performance of the benchmark index. 

Vanguard Small Cap Index Fund (VSMAX)

  • VSMAX beta is 1.21, meaning VSMAX is 21% more volatile than the S&P 500 Index.

Smart Beta


You may have heard the term “smart beta”. Smart beta combines the principle of active and passive investing approach based on certain rules. One of the rules is to use an equal-weighted approach instead of a market-cap-weighted approach. 

S&P 500 is a market-cap-weighted index meaning the weight of each stock in the S&P 500 index is solely based on its market cap. Hence, a company with a larger market cap will have the larger weight in the index. Since technology stocks have performed better in recent years, it represents 25% in S&P 500. An equal-weight approach would reduce technology exposure and increase weight to the undervalued stocks potentially resulting in over performance.

Caution with Alpha (𝛂) and Beta (𝞫)


Firstly, alpha and beta are based on past performance. As you know past performance is not a guarantee for future results. 

Secondly, alpha and beta are appropriate statistical measures when it is calculated against relevant benchmarks. For example, the “S&P 500 TR (Total Return)” is the calculation benchmark for most US stock funds. While “MSCI ACWI ex USA” is the calculation benchmark for international stock Funds. And “Bloomberg Barclays US Aggregate Bond” is the calculation benchmark for the US bond funds.

Thirdly, in general, beta is not a reliable measure of an investment when it is far off from the base value of 1.0. 

Fourth, alpha is a performance of an investment on a risk adjusted basis (dependent on beta). So if the value of beta is not reliable, then the value of alpha is not reliable either.

Making Sense of Alpha (𝛂) and Beta (𝞫)


How do we use alpha and beta in analyzing our investments? 

Let’s look at a hypothetical portfolio of the following funds.

  • US Total Market Index Fund – Fund 1
  • Small Cap Index Fund – Fund 2
  • Total International Market Fund – Fund 3
  • Total Bond Market Index Fund – Fund 4

The following table lists funds’ alpha and beta over the last 10-year period. You can get the fund specific values from Morningstar.com under “risk” tab.

FundAlphaBetaBenchmark
Fund 1: Total US Market Index-0.871.04S&P 500 Total Return
Fund 2: Small Cap Index-4.631.21S&P 500 Total Return
Fund 3: Total International Market Index0.221.00MSCI ACWI Ex USA
Fund 4: Total Bond Market Index-0.141.03BBgBarc US Agg Bond TR


Keep in mid that the base value of alpha and beta for the benchmark index is 0 and 1.0, respectively. 

What does alpha and beta of each fund mean to us as an investor?

Observation 1:

  • Fund 1 is the Total US Stock Market Index Fund with a negative alpha, indicating underperformance compared to its relevant benchmark, S&P 500. You would expect the fund’s alpha to be close to zero, matching the return of S&P 500.
  • What could be the reasons for the fund’s underperformance if it closely follows the S&P 500 Index? 
    • Is the underperformance due to higher fund fees? 
    • Is the fund risk level higher relative to its benchmark? 

Consideration 1: Should you swap fund 1 with another total stock market index fund with alpha 0 and beta 1.0?

Observation 2:

  • In comparison to Fund 1 (beta = 1.04), fund 2 is a much more volatile fund (beta = 1.21). 
  • So fund 2 needs to generate higher than the benchmark return to produce positive alpha. However it is not the case here as Fund 2 alpha is negative.
  •  Fund 2 (alpha = -4.63) has been underperforming the market over the last 10 years.

Consideration 2: Should you abandon a small cap index fund? Read more in this article.

Observation 3:


Fund 3 Total International Market Fund closely follows its relevant benchmark index; marginal over performance (alpha +0.22) and the same volatility (beta 1.00).

Observation 4:


Fund 4 Total Bond Market Index Fund closely follows its relevant benchmark index; marginal underperformance (alpha -0.14) and the slightly higher volatility (beta 1.03).

So there you have it. Besides alpha and beta other three common indicators of investment risk are R-Squared, Sharpe ratio and standard deviation. Read about it in this post.

Summary


Investors can enhance the return of the portfolio by “seeking” alpha. However per CNBC.com article, a very few (less than 8%) of active managers outperform the market over the last 15 years. If you decide to “seek” alpha, pay attention to the fees, review the active manager’s track record, and check your appetite for taking risk

Average investor like you and I cannot control the systematic risk (beta) but we can manage unsystematic risk (alpha) with diversification. Investing in a broadly diversified index fund is one of the ways to manage unsystematic risk.




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