Is Your Portfolio Beating Its Benchmark?

By Edward Aw AAA

Believe me, no: I thank my fortune for it,
My ventures are not in one bottom trusted,
Nor to one place; nor is my whole estate
Upon the fortune of this present year:
Therefore my merchandise makes me not sad.
Antonio, in William Shakespeare's "The Merchant of Venice", Act 1, Scene 1.

Like Shakespeare's Antonio, most people understand that it is not in their best interest to put all of their eggs in the same basket. The same people might also agree that the different baskets of eggs should not be placed right next to each other. Unfortunately, investments aren't as simple as a basket of eggs. In this article, we'll show you how the information ratio can help you measure the expected rewards from your investments while monitoring their relative placement in your portfolio.

Background to Modern Portfolio Theory
Today, investors have a wide range of investment choices, which are differentiated by assets class, market capitalization, investment styles, geography etc. Each of these investments has unique return and risk expectations. Let's take a look at two investment choices, A and B, in the efficient frontier chart in Figure 1 along with the combined payoff scenario from holding these investments.

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Figure 1

If you plot all the investment choices that you have at your disposal (stocks, bonds, portfolios of stocks and bonds) in Figure 1, the resulting chart will be bounded by an upward sloping curve known as the efficient frontier.

The unique reward and risk expectations of investments A and B are shown on the efficient frontier chart in red. One possible payoff from holding investment A and B is shown in green. The interaction between A and B could result in a payoff that is less risky with superior reward. Applying this same diversification concept to multiple investment choices can lead to a superior payoff that approaches the efficient frontier.

In the asset allocation decision process, it is common to use a market proxy or a benchmark that defines a particular investment class. If investment A represents a U.S. large cap equity as defined by the S&P 500, a typical investor can invest in many passive and active portfolios that use the S&P 500 as a benchmark.

A passive strategy mimics the returns of its benchmark, while an active strategy is expected to return some additional returns beyond its benchmark. Thus, a passive strategy can be represented by A and an active strategy will be represented by investments scattered around A.

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Figure 2

Considering Tracking Error
A statistical dispersion, or an indication of how far away an investment's performance is from its benchmark, is called a tracking error. The tracking error by itself does not indicate whether a portfolio is outperforming or underperforming its benchmark. However, a zero tracking error portfolio will have a risk profile that is identical to its benchmark.

In Figure 2, portfolios on the blue dotted line represent the zero tracking error portfolios. Numerically, a tracking error of 3% indicates that there is a 95% probability that portfolio returns will be within plus or minus 6% of the targeted benchmark.

Why should investors care about tracking error? In order for an assets allocation strategy to work effectively (investment baskets in their general area on the efficient frontier), each of the assets class managers must stay true to his or her stated objectives. A portfolio manager with high tracking error - or one that's too far away from the portfolio's stated benchmark - can become too close to another manger's benchmark, thereby increasing correlation between two assets classes in the same overall portfolio. Higher correlation leads to an inferior overall payoff.

The Information Ratio
The information ratio (IR) is designed to measure how many units of return an investor can achieve over a predefined benchmark for each unit of tracking error risk taken. A common mathematical definition of the information ratio for a portfolio is the excess returns of the portfolio over the predefined benchmark divided by the standard deviation of those excess returns, or the tracking error.

Figure 3

As shown in the formula, the IR will penalize the excess returns by any addition of tracking error risk. The ratio is best used in evaluating portfolio managers of the same asset class with the same benchmark. The information ratio allows the investor to look at a portfolio manager's returns versus his or her peers on a tracking-error-risk-adjusted basis. Going back to our investment choice A (S&P 500 market proxy), a portfolio with the highest IR compared to the S&P 500 will deliver superior rewards compared to the S&P 500 while maintaining all the reward and risk expectation of the S&P 500 and keeping your assets uncorrelated with other investments.

The Bottom Line
There have been many ratios used by proponents of modern portfolio theory, but the information ratio is one of the best for comparing one manager's returns versus his or her peers. Penalizing excess returns because of an addition of tracking error is one of the key reasons why this ratio is gaining popularity among industry professionals and students of portfolio analysis.

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