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Wednesday, January 26, 2011

Quantifying Investing Skill: The Information Ratio

Quick, which manager is better? Manager A who consistently beats her benchmark by a full percentage point, or Manager B who sometimes beats the benchmark by as much as five percent, but who also can underperform the same benchmark by that same five percent? It's not an easy question to answer. The difficulty lies in the chaotic and compounding nature of the market: if Manager B has a hot streak where he beat his benchmark a few months in a row, those gains can really add up compared to the first manager. But if Manager B has a cold streak for a couple of months, short-term recovery becomes difficult compared to Manager A.

At Wealthfront we want to identify the most qualified money managers across a diverse set of asset classes, and we do a lot to identify and continuously vet them. What do we mean by the best? Or what does just good mean? How can you measure it? Is it possible to compare managers who have different strategies? In this blog post I'll try to answer these questions by describing one of our most important metrics, the information ratio.

First off, implicit in my little quiz for you at the beginning is the notion of risk. If you don't want to take additional risks, you can just invest in government bonds (producing what is called the risk-free return) or buy a passive index tracking security that has marginal fees, e.g., the Vanguard 500 Index tracking the S&P 500 (producing what is called the market or benchmark return). So by definition to beat the benchmark you need to take risks, which means money managers need to "go against the grain", generally investing in what the manager considers under-valued (if holding a long position) or over-valued (if holding a short position). Risk is most commonly quantified as volatility compared to the benchmark. After all, if you don't have any differences from the benchmark you essentially are the benchmark.

The second idea embedded in my quiz is the notion of the risk-reward tradeoff, captured by the adage "greater risk offers greater rewards". Manager B could make a lot more money compared to Manager A if he beats the benchmark by five percent (a lot) more often than he loses five percent. Beating the market is hard, and most mutual funds don't beat it. (See If somebody beats the market for a couple of months, he might just be lucky, but if somebody can do it consistently then he truly shows skill.

The information ratio (IR) quantifies risk-adjusted returns, separating the skilled (those who consistently outperform) managers from the lucky. It is defined as the ratio of the (annualized) average excess return over the benchmark, divided by the (annualized) standard deviation between the manager and the benchmark. That's a quite bit to parse, so let's explore a couple of properties of this definition:
  • The benchmark has an IR of zero because the numerator would be zero.
  • If a manager has the same returns as the benchmark the IR is zero, for the same reason as above.
  • Managers who don't beat the benchmark have a negative IR, because the numerator would be negative.
  • If two managers are equally risky (volatility compared to the benchmark), the denominators of IR are equal, so the manager with the greater excess return over the benchmark has a greater IR.
  • If two managers have the same excess return, then the manager with less volatility (the denominator of IR) has a greater IR.
The information ratio rewards greater returns and less volatility, and punishes mediocre returns and excessive risk. Grinold and Kahn give the following table to judge manager's information ratios:


(Active Portfolio Management, 2nd Edition, p. 114) Thus a top-quartile manager has an information ratio of 0.5. As of Jan 25, 2011, managers available on Wealthfront have a median information ratio of 0.51 (n = 28).

You'll notice that IR is defined against "the benchmark", so it's important to note that different managers have different benchmarks. For example it doesn't make sense to judge a "value" investor against the NASDAQ, which has a high concentration of technology stocks. At Wealthfront we choose appropriate benchmarks for each kind of investment strategy, so a "small-cap" manager is judged against the small-cap benchmark Russell 2000, "emerging markets" portfolios against the iShares MSCI Emerging Markets Index ETF, etc.

One deficiency of the information ratio is that it doesn't take into account how long the managers have performed the way they do. All things being equal, a manager who has an information ratio of 0.5 for ten years is a much better manager than one who has had an information ratio of 0.5 for 3 years; the former manager has kept producing excess returns for over three times as long! To normalize information ratios over time we multiply the IR by the square root of the number of years in the manager's track record; thus the first managers time-normalized IR becomes 1.58 versus 0.86 for the second, clearly identifying the first manager as superior.

To summarize, the information ratio is one way to quantify the risk-reward tradeoff of money managers in a consistent way. Wealthfront uses the information ratio, along with a determination of whether or not the manager made his returns consistent with his investment strategy, to vet managers before listing them on our investing platform--only one in ten qualify--and we provide full access to each manager's performance, holdings, trade history, and risk metrics like the information ratio so that you, the investor, can make the most informed choices. You can view the managers, benchmarks, and information ratios at


Wealthfront does not provide personal financial planning or asset allocation services to individual investors. See full disclosure.