Portfolio Risk Analysis

How to Calculate Stock Portfolios Risk.

A worked example:

Standard deviation and variability of five major portfolios over the period 1926-2000 have been:

Treasury bills Standard deviation 3.2 Variance 10.1
Government bonds Standard deviation 9.4 Variance 88.7
Corporate bonds Standard deviation 8.7 Variance 75.5
Common stocks (S&P 500) Standard deviation 20.2 Variance 406.9
Small firm common stocks Standard deviation 33.4 Variance 1,118.4

Market variability since 1981.

1981 - 1990 16.5
1991 - 2000 13.4

Diversification reduces overall risk.

Publicly traded stocks trade about a mean share price. The trading pattern is its variability and therefore each stock price yields a standard deviation of price performance measured over time.

These stocks have high variability:

Amazon.com Standard deviation 110.6
Boeing Standard deviation 30.0
Dell Computers Standard deviation 62.7
Reebok Standard deviation 58.5

Remember that the average standard deviation of the stocks trading in the US is 20.2, so all these exhibit high price variability.

Research shows quite convincingly that even a small amount of portfolio diversification up to 20 - 30 different stocks reduces the overall portfolio risk by half. The improvement becomes slight thereafter when the number of stocks in a portfolio is increased beyond 20 to 30.

Diversification works well because the prices of different stocks do not move exactly together.

Calculating Portfolio Risk

The risk of a well-diversified portfolio depends on the market risk of the securities held within the portfolio.

Market risk is provided by reviewing the beta values of each stock. See the page describing Beta.

You can retrieve beta values of stocks from Yahoo Finance.

Beta values of our sample portfolio 1996 - 2001.

Amazon.com Beta 3.25
Boeing Beta 0.56
Dell Computers Beta 2.21
ReeBok Beta 0.69


If you held a portfolio of just these four stocks, the relative portfolio risk to market can be calculated as follows:

Amazon.com Beta 3.25 Holding 25% Weighted risk 0.8125%
Boeing Beta 0.56 Holding 25% Weighted risk 0.1400%
Dell Computers Beta 2.21 Holding 35% Weighted risk 0.7735%
Reebok Beta 0.69 Holding 15% Weighted risk 0.1035% Total risk to market 1.829

This calculation indicates that the portfolio will rise 1.829% for each 1% rise in the market. The downside is that the portfolio is likely to fall by 1.829% as well for each 1% decline in the market.

Reference Pages

Measuring Risk

Portfolio ROR