Can someone explain the difference between 'Beta' and 'Standard Deviation'?

Beta is the correlation between returns on a particular security vs. the returns of the overall market. Usually "overall market" means a particular stock index but that's more for convenience than anything else.

Standard Deviation is a statistical term that applies to any data series (not just stocks). It is simply the square root of the variance. The variance of sample data from its predicted values is the sum of the squared differences between observed data points and what the model predicts.

If you aren't using a model to make predictions then sample variance is the squared difference of each observed data point from the mean.

Everything foshizzle said.

Think of standard deviation as the absolute risk you're taking on while beta as the risk relative to the total market.

That simplifies it a little to the point of convolution but it gives you a good idea. Also keep in mind they are both backwards looking so your actual risk more often than not does not equal our implied risk.

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Everything foshizzle said.

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I love it when people say that.

I'll add that there's a big distinction between variance and sample variance, but now we're getting into technical statistical stuff and all.

I never really liked the technical calculation of beta other than for equities. For fixed income I always just bucket your over or underweight duration measure in years as your beta exposure. (Index 4-years + 2-year overweight (6yr) = Beta of 1.5.) Past that security selection is just further alpha strategies.

Conceptually, top down macro shows your beta exposures then bottom up micro shows your alpha selection. I think this may be more important in the future as beta doesn't look like its going to provide the same amount of returns as in the past. Growth is just low on an aggregate level, but you can still find several asset classes that can still get high returns.

Hedge postions with derivatives and diversify the portfolio with uncorrelated asset classes.

In simple terms, standard deviation is the volatility of the investment (sometimes interpreted as risk), while Beta relates this volatility to a certain benchmark index or investment.

Mathematically,

Beta = Correlation coefficient between market and stock x (standard deviation of stock returns) / (standard deviation of market returns)

In simple terms, Beta is the combination of how volatile an investment is relative to the benchmark along with how correlated it is to the benchmark.

Correlation coefficient, often the Greek letter rho, can be negative. A negative correlation coefficient and thus Beta would mean that overall, the returns of the investment and the benchmark tend to move in opposite directions. A Beta closer to zero would be more common than a negative number, and a Beta close to zero just means that the investment returns are basically uncorrelated with the market (not necessarily that it has no volatility).

A fun thought exercise when calculating standard deviation and thus Beta is to calculate this volatility over different time windows. For example, volatility will be different if inspecting running 3 hour returns instead of running 3 month returns. So it goes for the graphical review of Beta (plotting the standard deviation of the investment returns versus the market or benchmark returns). That is a whole topic in itself with interesting conclusions.

Beta has a well-known counterpart in Alpha (of Seeking Alpha, et al.). Think of this directly as slope and intercept line fit of the investment returns in comparison with a benchmark (i.e. the market). Beta represents the slope of the line, while Alpha represents the y-intercept - or the intrinsic incremental return outside of the volatility relationship itself.

In Excel you can literally solve for Alpha and Beta with the linear Slope() and Intercept() functions comparing a series of investment returns with a series of market/benchmark returns. ETA: I am 90% sure of this paragraph but not 100%, and don't recall if additional manipulations are needed. It's been a VERY long time.

Although their rating system may use Beta as a factor, I don't think there is any significant correlation between Beta and a certain number of stars. Beta simply measures how much a security moves compared to the market. For example if the market goes up 10% and Stock A goes up 15%, that stocks beta is 1.5. If the stock only went up 5%, it's beta would be 0.5.