The Alpha Beta Soup

Posted on: March 5th, 2013

A primer on portfolio statistics

The analysis and reporting of returns on investments frequently involves a number of statistical measures that we do not encounter elsewhere in our daily lives. The following is an effort to demystify some of those measures,

Return. The total return of an investment or portfolio of investments is the price appreciation or depreciation of the portfolio plus any dividends or interest earned during the reporting period. The annual return of a portfolio is the average return that would have been earned during each of the years in a multi-year reporting period. Annual returns can mask significant fluctuations of returns within a multi-year period. Annual Returns typically assume the reinvestment of all dividends and interest earned. Returns can be reported gross or net of fees. Returns on mutual funds are reported net of the internal fees of the funds, but may not include any external advisory fees. Returns on portfolios of stocks and bonds can be reported either net or gross of management fees. Returns are frequently compared to benchmarks or indexes and these never include any offset for management fees, since they are not managed portfolios. Excess return is the difference between a portfolio return and a benchmark return.

Yield. The Yield on an investment is the income earned in the form of dividends or interest. The Dividend Yield of a stock or stock portfolio is value of the annual dividends divided by the price of the stock or value of the stock portfolio. Bonds have four yields: coupon yield (the bond interest rate at par), current yield (the bond interest rate as a percentage of the current price of the bond), and yield to maturity (an estimate of what an investor will receive if the bond is held to its maturity date). Yield-to-call is the yield calculated to a call date. Yield-toworst is the lowest yield-to-call possible in a bond series.

Standard Deviation. Standard deviation is a measure of the variability of the returns of a portfolio around the average return of that portfolio. It is indicative of the volatility of an asset or portfolio. For example, a portfolio with a return of 9% and a standard deviation of 5% would have less volatility than a portfolio with the same return and a standard deviation of 20% over the same period. In a “normal” or “bell-shaped” distribution of returns, 95% of the returns will fall within two standard deviations of the average (of course, the other 5% can include unusually good results or the rare, but devastating, disaster). The distribution of returns for an asset or portfolio is not always “normal” in the statistical sense, but standard deviation is a useful indicator of the volatility of a portfolio. Standard deviation is often cited as a measure of risk, and it is a reasonably accessible measure of volatility risk in a portfolio, but volatility risk is only one type of risk among many that a portfolio might present.

Beta. Beta is a measure of the sensitivity of a portfolio to movements in the broader market, usually represented by an index. The index (say the S&P 500) has a beta of 1.0. A portfolio with a beta of 1.15 magnifies the volatility of that index by 15%; a portfolio with a beta of 0.80 tends to dampen the up and down movements of the market by a factor of 20%.

Alpha. Alpha is a measure of the return of a portfolio once beta (the influence of the market) is subtracted. It is the return generated by active management that is independent of moves in the broad market. It can be positive or negative. When it is positive it is evidence that an active manager is earning a return that is independent of broad market moves. It is evidence of manager skill. In order for alpha and beta to be meaningful they should be calculated using a benchmark that is relevant to the portfolio. The S&P 500 may be appropriate for a diversified portfolio of large cap domestic stocks; other benchmarks should be used for other types of portfolios.

Portfolio statistics are not intuitive. If you have any questions about these measures or how they might be calculated for a given portfolio, please do not hesitate to contact us.

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