Information Ratio - What is it and why is it important?

hat differentiates a 'good' manager from one who is not as good? One of the earliest measures proposed and still one of the most popular is called the Sharpe Ratio , and it is defined as follows:

            Sharpe Ratio    =         (R_p  –  r ) / σ_p

where:

            R_p        =          the return of the portfolio,         

            r           =          the risk-free rate, usually chosen as a 1 month T-Bill,

            σ_p         =          the volatility of the portfolio , usually calculated as the standard deviation of returns.

The basic idea is that an investment with a higher Sharpe ratio is a better investment. A higher ratio indicates more return per unit of risk assumed by the manager. But by better, do we mean that the manager has more skill? Not necessarily, because the investments could be in completely unrelated types of securities. In an environment where stocks are outperforming bonds, most stock managers will have a higher Sharpe ratio than the fixed income counterparts. So it is necessary to compare these ratios on some type of level playing field, which is usually done by comparing to a relevant index.

To provide some meaning to this ratio, it is best to compare it the Sharpe Ratio for the investment benchmark. Consider the following example.

The S&P 500 is characterized as a Large Cap index with blended style. Blended means that it is evenly balanced between the value and growth sectors of the market. Tabled below is the annualized return and volatility for this index (as represented by the index fund VFINX), for the five year period ending March 31, 2005. Table 1 lists these values for several of the top performing mutual funds in this category.[2]

Table 1

These funds are listed in order of returns from highest to lowest, and with only one small exception, their Sharpe ratios are in the same order. So if one wanted to order these funds from better to best, either return or Sharpe would give approximately the same result.

Another popular measure of skill is called alpha, α, and is defined as follows. The returns, usually monthly, of the fund are regressed on the returns of the benchmark. The slope of the regression line is referred to as beta, β, and the intercept is called alpha.

Beta represents the manager’s relative sensitivity to the market. A beta of 1.0 indicates that a manager’s performance will tend to match the market. If the Beta is greater than 1.0, then the fund will tend to appreciate by more than the benchmark, when the benchmark has a positive return, and decline by more than the benchmark, when the benchmark has a negative return.

Alpha represents the average performance of the fund taking into account the funds general sensitivity to the market, and as such measures the skill of the manager.

Mathematically, the regression equation is of the form:

                                    (R_p-r) = α + β (R_i-r)

where

            R_p        =          the return on the portfolio,

            R_i         =          the return of the benchmark

            r           =          the risk free rate.

The scatter-plot below illustrates this for the fund VADDX, with the regression line drawn in.

For this fund the beta, as represented by the slope of the regression line, is .83; and the intercept term represents approximately 84 basis points of alpha per month. On an annualized basis, the alpha would be 10.1%. Table 1 is updated to include this measure as well:

Table 1 (Updated)

Again we notice that one minor exception, this measure of performance, alpha, seems to be consistent with the other measures we have calculated.

A closely related concept that also measures ‘beta-adjusted’ performance is the Jensen Alpha[3]. Its definition is similar to the above, but incorporates long term returns rather than the individual monthly returns.

Jensen’s Alpha is defined as:

            Jα         =          R_p  -  r - β(R_i-r).

Modigliani & Modigliani[4] propose a measure of added value that depends only on the relative risks of the funds and does not incorporate correlation, as the beta does. In their approach, any excess performance is modified by how much volatility the portfolio assumed relative to the benchmark. Their risk-adjusted measure is defined as:

            M²       =          (R_p – R_i) * σ_i / σ_p.

Our table, with these new values, continues to show the same basic ranking of funds.

The measure that we now discuss is called the information ratio, IR, and is perhaps the most important[5]. IR attempts to measure not just the excess return to a benchmark, but also how consistent is that performance. Is a manager beating the benchmark by a little every month, or a lot in a few particular months? Most investors would prefer the former, and the IR measures this degree of consistency.

To define the IR we first have to define a related concept called the tracking error. The tracking error is defined as the volatility, or standard deviation, of monthly excess returns. The IR is then defined as the excess performance divided by the tracking error.

Mathematically:

tracking error                =          σ_p-i

information ratio             =         (R_p-R_i) / σ_p-i

When the benchmark for an investment is taken as cash, the information ratio is the same as the Sharpe ratio.

We now illustrate for our funds the tracking error and information ratios:

The VADDX fund which ranked close to the bottom for the other performance measures now has the highest value. Even though it’s return and risk-adjusted return is not as high as those of the other funds. The lower tracking error actually causes it to have the highest information ratio.

The point of this article is not to confuse the reader with all of these measures, but to provide a rationale for why the information ratio is so important. A manager with a higher information ratio can ‘leverage’ their investment process to produce additional return more efficiently than another manager with a lower information ratio. In other words, for taking on additional risk, a higher information ratio manager can provide greater additional return (and alpha as well). An example would be helpful, but first let us explain what we mean by leveraging an investment process.

Suppose I represents the benchmark, a collection of stocks (or bonds for that matter) and P represents the manager’s portfolio. We can form a portfolio,  P-βI , which refers to an investment that shorts beta dollars of I for every dollar long held in P. This portfolio is not ‘dollar-neutral’, but it is ‘beta-neutral’ and as such has less risk than a dollar neutral portfolio. To lever the investment process, an investor would then hold I + k(P-βI), for any value of k. The higher the value of k, the more leveraged the portfolio.

This idea is sometimes referred to as portable alpha. Rather than investing in an active portfolio management style P, one can invest in a passive benchmark investment I, and also a beta-neutral portfolio P-βI. The former portfolio I typically has a very low management fee, while the latter piece provides the Alpha of the investment. The leverage factor k allows an investor to earn higher returns commensurate with the desired level of risk.

Now we turn to the question of what affect the information ratio of a process has on these leveraged portfolios.

 Suppose the benchmark has the following statistics:

                                    R_i = 10%         σ_i = 15%.        

We now examine two managers with the following statistics:

            Manager A:      R_p = 10%         σ_p = 15%                     IR = 0.5,

            Manager B:      R_p = 10%         σ_p = 15%                     IR = 1.0.

In this example, each manager has the same risk as the benchmark, the same return as each other, but Manager B has a higher information ratio. The chart below illustrates the risk-return of portfolios created with progressively greater values of k, for each of these managers.

For the value of k equal to 0, both of these lines start at the index statistics of 15% for risk, and 10% for return, but as k increases the manager with a higher information ratio is generating more return for comparable risk. Alternatively, the chart below illustrates the alpha of these leveraged portfolios, with the same results.

For both of these measures, we see, that a higher information ratio will allow a manger to leverage into a better investment.

If we wanted to use different managers to leverage I into a portfolio with a volatility of 20%, we would be creating portfolios with different returns, and performance measures. Illustrated below are the returns and alphas of the portfolios for these managers.  As the information ratio of the management process increases, so do the returns and alphas for their respective portfolios. The Sharpe ratio of these portfolios would exhibit the same features, since they all have the same volatility.

It is also possible to leverage I using different IR processes but maintain a constant tracking error. In this manner, we create a range of leveraged portfolios that have higher volatility than the portfolio we start out, but the tracking error remains the same. As the chart below illustrates, both the returns and alphas improve as the information ratio of the process being leveraged increases.

While there are many measures of risk-adjusted performance, and they all have their strengths and weaknesses, the information ratio is very informative as it highlights which managers can improve their performance most with the least disruption to their existing risk.