A Hitchhiker's Guide to Equity Portfolio Management & Risk Measurement - Part I
Team Latte
Dec 07, 2002

The above table shows that most of the constituent stocks exceed the volatility of the Hang Seng index and thereby are more risky than the index itself. An investor is much better off investing in the index, perhaps, through futures or index funds, than investing either in individual stocks or creating a customized portfolio of these stocks.

A big problem with volatility is that it changes from period to period and is not a static concept. Therefore a 37.96% volatility number for HSBC stock may change in a month's time or a quarter's time. It is therefore always better to work with volatility ranges.

Shown below is a chart of historical volatility (annualized) for Hang Seng index for a period of six years (1996 - 2002). It shows that the historical volatility for the index is mostly bounded between 20% and 40%. There are rare spikes above 40% - times of severe turbulence like the Asian financial crisis of 1997-98 and some leak below 20% - times of relative quite.

It must be emphasized though that given this six year period the volatility of the index has remained high. Even a 20% annualized volatility is a high number given the global stock market history of some 75 years.

Fig 1.0

Tracking Error: Tracking error measures risk by computing the annualized standard deviation of the difference between the portfolio return and the benchmark return. It provides a relevant performance measure for the fund manager and is more useful for evaluating passive portfolios.

A useful way to decompose risk of a portfolio is to look at the Capital Asset Pricing Model (CAPM) equation that is used to price risk assets, such as equity. This was the pioneering model developed by William Sharpe and is now an accepted technique of asset pricing. The CAPM states that the return on a risk asset, such as equity is given by:

From the above equation Total Risk of a portfolio can be estimated by looking at individual risk components for an asset such as an equity share. It is clear from the above that the total risk is a combination of the Risk Free, that is zero risk of a government security and the excess risk. Therefore Excess Risk is the true risk of an asset - and thereby that of a portfolio - and is further a combination of the Systematic risk as measured by beta and the residual risk which is the component of risk uncorrelated with the market portfolio. Beta is the sensitivity of an asset or a portfolio to a benchmark, such as a market index. Residual Risk is the annualized standard deviation of the residual return, i.e. the difference between the market portfolio return and the risk free return.

From the above equation Total Risk of a portfolio can be estimated by looking at individual risk components for an asset such as an equity share. It is clear from the above that the total risk is a combination of the Risk Free, that is zero risk of a government security and the excess risk. Therefore Excess Risk is the true risk of an asset - and thereby that of a portfolio - and is further a combination of the Systematic risk as measured by beta and the residual risk which is the component of risk uncorrelated with the market portfolio. Beta is the sensitivity of an asset or a portfolio to a benchmark, such as a market index. Residual Risk is the annualized standard deviation of the residual return, i.e. the difference between the market portfolio return and the risk free return.

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