# LO 64.2: Define and calculate alpha, tracking error, the information ratio, and the

LO 64.2: Define and calculate alpha, tracking error, the information ratio, and the Sharpe ratio.
Professors Note: We w ill demonstrate the calculations fo r these measures along with other performance measures later in this book (Topic 70).
Alpha is often interpreted as a measure of investor skill, but it is really just a statement of average performance in excess of a benchmark. Excess return (Rjrx ) can be seen as the difference between the return of an asset (Rt) and the return of the assets benchmark (R ^ ).
2018 Kaplan, Inc.
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Topic 64 Cross Reference to GARP Assigned Reading – Ang, Chapter 10
Excess return is also sometimes called active return. This phrase assumes that the benchmark is passive and can be achieved without investment knowledge or human intervention. The S&P 500 Index and the Russell 1000 Index are commonly used large- cap benchmarks. If the benchmark is passive, then any additional return that the investor achieves is from doing something different from the benchmark, which by definition is active.
We compute alpha (a) by finding the average excess return for T observations.
To fully understand the concept of alpha, we also need to understand tracking error and the information ratio. Tracking error is the standard deviation of excess returns. It measures the dispersion of the investors returns relative to their benchmark.
tracking error = cr = standard devation(R^x)
When a professional investment manager uses active strategies, there is often a constraint placed on the amount of tracking error permitted. Larger tracking errors indicate that the manager has more freedom in decision making.
One easy way to monitor alpha is to standardize it using tracking error. The ratio of alpha to tracking error is known as the information ratio (IR), and it is a good way to monitor risk-adjusted returns for active asset managers. Active investment choices can be ranked based on their IR scores.
O i d
Sometimes the benchmark for an asset manager is the risk-free rate (Rp). In this case, alpha is measured as the return earned on an investment (Rt) in excess of the risk-free rate.
o. Rt Rp
When the risk-free rate is the appropriate benchmark, the best way to measure risk-adjusted returns is to use the Sharpe ratio. This measure has alpha in the numerator and the standard deviation of the asset in the denominator.
Sharpe ratio
Rt – R F
a
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2018 Kaplan, Inc.
Topic 64 Cross Reference to GARP Assigned Reading – Ang, Chapter 10
Be n c h m a r k Se l e c t io n f o r Al ph a