There are a large number of statistical measures available for looking at a mutual fund, ETF, stock or a combination of these in the total portfolio.

So what are the important measures and what do they mean?

I dove into this topic yesterday with a discussion of two important measures: Volatility and Beta. Today I’ll add six more to watch.

### Alpha

To understand Alpha, an investor must first master Beta.

The description of Beta in my post yesterday explains why investors need to look beyond a fund’s average annual returns when judging its performance. A high-Beta fund that out-performs the S&P 500 needs to be judged relative to the level of Beta. A fund manager who looks to be racking up a great record, may be doing so by choosing investments that carry more market risk. If that’s the case, when the market turns south, that fund will likely drop even more quickly.

Alpha is the amount of annual return that cannot be explained by Beta and other factors. In short, Alpha is the out-performance that investors are looking for.

The simplest measure of Alpha is determined by the amount of annual return after subtracting the annual return due to the degree to which an investment follows the market (the Beta effect). This is called single-factor Alpha, but is often simply referred to as Alpha.

There are more complex formulations of Alpha that correct for performance factors other than Beta.

Investors need to be careful about looking at historical “Alphas” as a decision point in investing. It is often impossible to determine whether the historical Alpha of a portfolio is due to skill or luck, and past performance, as they say, does not predict future results.

Using a measure of Alpha for portfolio performance is superior to simply looking at trailing performance, although both total return and Alpha are valuable.

### Correlation

Correlation is a statistic that measures the degree to which assets move together. In finance, the correlation is always measured between returns rather than price. Correlation ranges from 100% (two assets always move together) to -100% (two assets always move in opposite directions). A correlation of 0% means that there is no relationship between the movements of one asset to another. Two assets with zero correlation may sometimes move together, sometimes in opposite directions.

Correlations between assets are key statistics in modern financial theory. Investors typically seek to combine assets in their portfolios which have fairly low correlations to one another so that when one is declining, others may not be.

This is the key driver of a diversified portfolio.

Many investors intuitively understand that combining different assets in their portfolios will help to insulate the portfolios from a big loss in any single asset class. Unfortunately, these same investors often do not know which assets have high correlations, and which have relatively low correlations. For example, holding emerging market stocks, international developed market stocks, and U.S. stocks during the crash of 2008 provided very little protection because these three asset groups were, in fact, highly correlated—and this was true well before the crash occurred.

### Judging Correlation Correctly

Identifying the asset class that is most correlated to a mutual fund will help you judge the performance of the fund. For example, the Fairholme Fund (FAIRX) is officially classified as a ‘Large Cap Value’ fund by Morningstar and has substantially out-performed the S&P 500. However, the returns on FAIRX are more highly correlated to a Mid Cap Value index than to either a Large Cap Value index or to the S&P 500.

There are a variety of ways to see this type of disconnect between the stated style and the apparent style of a mutual fund. Morningstar, for example, shows that the ‘Best Fit Index’ for FAIRX is the Mid Cap Value, rather than the S&P500 Index. The performance of FAIRX is very similar to that of a Mid Cap Value index fund (JKI). This result suggests that the Fairholme Fund’s substantial out-performance in recent years may largely be due to the fact that it is a mid-cap fund that is being compared (somewhat questionably) to a large cap benchmark. This is important because it gives an accurate sense of how well the fund has performed. It also would help an investor constructing a portfolio that includes Fairholme to understand which asset class the fund truly exposes them to, and which ones (a.k.a., large cap value) they still need to fill.

### R-Squared

R-squared (also written as R2) measures the degree to which all of the return from a portfolio, fund, or stock can be explained by the S&P 500. R-squared is related to correlation and to Beta. If the R-squared of an actively managed mutual fund is very high (greater than 95%) the fund is tracking the S&P 500 so closely that the active management is having little or no impact on the performance. When a fund hugs this closely to its benchmark index, it is often referred to as a ‘closet index fund.’

### Average Annual Return

Average Annual Return (AAR), more formally referred to as the Arithmetic Annual Return, is the average of the return from holding an asset for a 12-month period. An investment that has a 20% return in one year, followed by a 0% return in the next year, and a -20% return in the third year has an AAR of 0% (the average 20%, 0%, and -20%).

### Compound Annual Return

Compound Annual Return, also known as Compound Annual Growth Rate (CAGR), is the annual return that accrues to an investor who holds an investment over multiple years. CAGR differs from AAR in that the relative impacts of gains and losses compound through the years.

The three-year CAGR for the example in the AAR definition above, is -4% (as compared to the AAR of 0%).

Here’s how that works: If you started with $100, at the end of year one you made 20% on that and have $120. After year two, you haven’t made any more or lost any money, and are left with $120. Year three’s 20% loss costs you $24, leaving you with $96.

An investor who held the hypothetical investment in that example for the three year period ends up with less money than he started with: an amount equal to what he would have had if he had simply lost 4% over the three year period.

CAGR is always less than the AAR for investments that carry any level of risk. This effect is referred to as “volatility drag”.

### Total Return

Total return is the annual return from an investment after you account for the expenses associated with that investment (management fees, trading costs, etc.) and assuming that any dividends or income produced by that investment are reinvested.

### Using Portfolio Statistics

The statistical measures that we have covered are all widely available and very useful. Every MBA learns about these statistics in his or her first year, but a number of these statistics are not commonly used by investors. These measures should be the financial equivalent of the Body Mass Index (BMI)—metrics that can be used to easily assess the characteristics of an investment or total portfolio.

(photo: aussiegall)

business dailyNet asset values NAVs and distributions from dividends and capital gains are used to perform these calculations.The simpler of the two computes the return from the beginning of the year to the date that the first distribution is made then from each distribution to the next and from the last distribution to the end of the year. ..There are a few things you should be aware of here Computing returns under the assumption that distributions occur at the end of the month will produce returns that are incorrect to varying degrees in all cases when distributions are made on some day other than the last trading day of the month.