Tag: risk

The information ratio is one component of the Fundamental Law of Active management and is a measure of risk adjusted returns relative to a stated benchmark.

The Information Ratio can be calculated using the following formula:

where:

Let’s assume an investor wants to compare two large cap value managers. Manager A & B’s portfolios have the following characteristics:

	Manager A	Manager B	Benchmark
Return	8.00%	9.00%	7.00%
Std Dev	11.00%	13.00%	10.00%

Given the numbers above, let’s calculate the information ratio for Manager A:

Next, we’ll calculate the information ratio for Manager B:

On the surface, it would appear that Manager B’s portfolio is superior to Manager A’s portfolio based solely on the absolute level of investment returns; however, Manager A’s portfolio is superior if looking at absolute returns on a risk adjusted basis.

Since Manager A’s information ratio of 1.00 is greater than Manager B’s information ratio of 0.667, we can make the determination that Manager A has better risk adjusted returns, all else being equal, since both of these managers are creating portfolios with a large cap value mandate and their returns are adjusted using the same benchmark.

Generally speaking, information ratios near one are good, above one are great, and above zero are passable. It is important to note, that no information can be gleaned from information ratios that are negative.

The Sharpe Ratio is used to help investors calculate the risk adjusted return relative to the risk free rate of return, the formula is as follows:

where:

Let’s assume that an investor purchases a security that has a project rate of return of 7%, if the risk free rate of return is 3% and the standard deviation of the asset is 15%, what is the Sharpe Ratio of the asset?

We can calculate the Sharpe Ratio as follows:

A Sharpe Ratio of 0.266 can be interpreted as the amount of return the asset produces for each given unit of risk. In other words, for each 1% increase in standard deviation, this particular asset produces 0.26% in return. If you multiple the standard deviation of 0.15 by 0.266, the resulting product of the two numbers is 0.07, which is asset’s assumed rate of return.

Portfolio managers typically compare the Sharpe Ratios of different portfolios and assets in order to determine which portfolio or asset has a higher risk adjusted rate of return. If two portfolios have similar investment characteristics, the portfolio with the higher Sharpe Ratio should be considered over the one with the lower ratio, all else equal.