The Mathematics of Financial Modelingand Investment Management

23-RiskManagement Page 751 Wednesday, February 4, 2004 1:13 PM

Risk Management 751

ability Ratio.” The Sharpe ratio is to evaluate expected returns in a risk-

weighted framework. Given a portfolio, the ex ante Sharpe ratio is

defined as the ratio between the expected excess return (measured rela-

tive to the risk-free rate) and volatility:

Expected return – Risk-free rate

Sharpe ratio = ----------------------------------------------------------------------------------

Standard deviation of return

A number of other measures similar to the Sharpe ratio have been

introduced, in particular the Sortino ratio^13 which uses only downside

volatility.

A variant of the Sharpe ratio commonly used to assess the perfor-

mance of a portfolio manager is the information ratio. The information

ratio is the ratio of the excess return over a designated benchmark

divided by the tracking error, the standard deviation of the difference

between portfolio return and the benchmark market (see Chapter 19).

The excess return over the benchmark is referred to as the “alpha” or

“active return.” The information ratio is typically calculated on an ex

post basis as follows:

Portfolio return – Benchmark return

Information ratio = ---------------------------------------------------------------------------------------------

Tracking error

RISK MANAGEMENT IN ASSET AND PORTFOLIO MANAGEMENT

Risk has different facets in asset and portfolio management. In particu-

lar, risk can be characterized as (1) market risk; (2) risk of underperfor-

mance relative to a benchmark; or (3) business risk. Ultimately, risk is

market risk. The question is: Who bears it? Asset management firms

define their risk as the risk of underperformance relative to a bench-

mark: the client assumes the market risk implicit in the portfolio; the

asset manager assumes the benchmark risk. However, the asset manage-

ment function is concerned essentially with market risk.

Some nuance is required. If a firm manages the assets of the parent

company (e.g., an insurance company or investment bank), it is exposed

to market risk as an investor. Also, volatility of returns or a loss of cap-

ital might be unacceptable to some institutional or retail investors, forc-

(^13) See Frank Sortino and Robert Van Meer, “Downside Risk,” Journal of Portfolio
Management (Summer 1991), pp. 27–32.