Modern Portfolio Theory (MPT)

Alpha measures the relative value-added provided by an asset manager compared to a market index, given a portfolio′s market risk. A positive alpha is the extra return received by an investor for taking a risk, instead of accepting the market return. For example, an alpha of 1.0 means a portfolio produced a return 1% higher than its beta would predict. An alpha of –1.0 means a portfolio produced a return 1% lower than would be expected.

Alpha does not take into account total volatility risk and it assumes the manager holds a diversified portfolio. Diversification can be measured by R-squared. An R-squared of less than 50 makes a manager′s alpha rating virtually meaningless. Alpha can change dramatically from quarter-to-quarter.

Beta measures the performance of a portfolio′s historical returns versus a chosen benchmark. For stocks, the benchmark is usually the S&P 500 Index.

The beta of the benchmark is always 1.00. Therefore, if a portfolio has a beta of 1.00 its volatility is generally the same as the benchmark. For a fully diversified stock portfolio, a beta of 1.25 would mean that it has generally produced a 25% higher return than the S&P 500. A portfolio with a beta of 0.80 would be expected to produce a 20% lower return than the market over time and not go up as much in an up market.

Beta assumes the manager holds a totally diversified portfolio. Diversification can be measured by R-squared. An R-squared of less than 50 makes a manager′s beta rating meaningless. Beta is typically measured taking into account three to five years of historical performance.

R-squared measures how well a portfolio is diversified versus a market index (such as the S&P 500 Index). The R-squared number ranges from zero to 100. A score of 100 signifies a perfect correlation with the benchmark. For a portfolio with an R-squared 0.85, 85% of the portfolio′s risk can be attributed to being in the market, while 15% is due to other factors (i.e., security or sector selection).

Correlation measures the degree of a portfolio′s return in relation to the return of an index or other portfolios. Correlation can range from -1.00 to 1.00. A portfolio with a correlation of 1.00 means that its returns move in the same direction as the index, whereas a correlation of -1.00 means that it moves in totally the opposite direction of the index. To maintain a diversified portfolio, an investor may want to select portfolios that have varying degrees of correlation among themselves.

Sharpe ratio determines how much risk a manager assumed to achieve a portfolio′s historical return. It is calculated by taking the difference between a portfolio′s return and a risk-free return (measured by a Treasury bill) and dividing it by the portfolio′s standard deviation. For example, if a portfolio had a Sharpe ratio of 1.30 and the benchmark has a Sharpe ratio of 1.00, then the portfolio produced a 30% better return than the index versus the risk-free rate. Sharpe ratio can be an effective way to compare individual portfolios to determine the value added by an asset manager.

Standard deviation is a measurement of a portfolio′s total volatility (risk). It is calculated by measuring the disparity of a portfolio′s quarterly returns versus its total average return over the same time period. The more volatile a portfolio′s returns the greater the standard deviation. Standard deviation does not predict a portfolio′s future volatility.

This tool shows what percentage of the market′s performance—such as the S&P 500 Index—a portfolio manager captured. These ratios are calculated by dividing a manager′s performance returns by the market index′s return.

Up/down capture ratio = Manager′s return / Market index return

The up capture ratio is calculated over quarterly periods when the market index generated a positive return. The down capture ratio is for quarters when the market posts negative returns. For example, a portfolio manager with a 120% up capture ratio captured 120% of the index′s return when it appreciated (a 20% higher return than the index). A portfolio manager with a 120% down capture ratio captured 120% more than the index′s return when it declined (20% worse than the index).

Using an up/down capture ratio is just one of the tools to use to evaluate the performance of a portfolio manager. However, used in conjunction with other tools can be a useful way to determine if a particular manager and his or her portfolio are appropriate based on your risk/reward profile.

Information ratio measures the value added by a portfolio manager. The ratio shows the annualized return of a portfolio above its benchmark to annualized tracking error.

Tracking error measures how closely an asset manager′s portfolio performance is versus the market. Tracking error is calculated by taking the standard deviation of the differences in the portfolio′s returns and the market′s quarterly returns. If the portfolio tracks its benchmark closely it will have a small tracking error.

An efficient frontier is a graph representing a set of portfolios that compare returns at each level of portfolio risk (or return volatility). According to Modern Portfolio Theory, for any portfolio of assets there exists an efficient frontier, which represents variously weighted combinations of the portfolio′s assets that yield the maximum possible expected return at any given level of portfolio risk.