Loan advice

Constructing an efficient portfolio based on the expected return for a portfolio (which depends on the expected return of all the asset returns in the portfolio) and the variance of the portfolio’s return (which depends on the variance of the return of all of the assets in the portfolio and the covariance of returns between all pairs of assets in the portfolio) are referred to as “mean-variance” portfolio management. The term “mean” is used because the expected return is equivalent to the “mean” or “average value” of returns. This approach also allows for the inclusion of constraints such as lower and upper bounds on particular assets or assets in particular industries or sectors. The end result of the analysis is a set of efficient portfolios—alternative portfolios from which the investor can select—that offer the maximum expected portfolio return for a given level of portfolio risk.
There are variations on this approach to portfolio construction. Mean-variance analysis can be employed by estimating risk factors that historically have explained the variance of asset returns. The basic principle is that the value of an asset is driven by a number of systematic factors (or, equivalently, risk exposures) plus a component unique to a particular company or industry. A set of efficient portfolios can be identified based on the risk factors and the sensitivity of assets to these risk factors.
With either the full mean-variance approach or the multifactor risk approach there are two variations. First, the analysis can be performed by investors using individual assets (or securities) or the analysis can be performed on asset classes.
The second variation is one in which the input used to measure risk is the tracking error of a portfolio relative to a benchmark index, rather than the variance of the portfolio return. By a benchmark index it is meant the benchmark that the investor’s performance is compared against. Tracking error is the variance of the difference in the return on the portfolio and the return on the benchmark index. When this “tracking error multifactor risk approach” to portfolio construction is applied to individual assets, the investor can identify the set of efficient portfolios in terms of a portfolio that matches the risk profile of the benchmark index for each level of tracking error. Selecting assets that intentionally cause the portfolio’s risk profile to differ from that of the benchmark index is the way a manager actively manages a portfolio. In contrast, indexing means matching the risk profile. “Enhanced” indexing basically means that the assets selected for the portfolio do not cause the risk profile of the portfolio constructed to depart materially from the risk profile of the benchmark.
At the other extreme of the full mean-variance approach to portfolio management is the assembling of a portfolio in which investors ignore all of the inputs—expected returns, variance of asset returns, and covariance of asset returns—and use their intuition to construct a portfolio. We refer to this approach as the “seat-of-the-pants approach” to portfolio construction. In a rising stock market, for example, this approach is too often confused with investment skill. It is not an approach we recommend.