# Modification of CAPM for the non-diversified investor position - Investments

## CAPM modification to the non-diversified investor position

If the investor is non-diversified (does not have a portfolio, which is typical for private small companies, when all funds are invested in one business), then it is incorrect to consider compensation only for systematic risk. The investor carries all kinds of risk, including diversifiable in the portfolio. A possible algorithm for resolving this problem within the CAPM model is the recalculation of the beta coefficient (upward adjustment).

The adjusted beta coefficient, or the beta of the total risk, can be estimated from the ratio of standard deviations in the prices of shares in the industry and the market.

Recommended formula:

Beta general risk ratio = Standard deviation of shares in the industry/Standard deviation of the market = Beta coefficient average industry-free/Correlation between industry and market.

Some industry-specific values ​​of the beta coefficient for 2005 are given in Table. 19.1.

Table 19.1

Adjusted beta coefficients by industry. A measure of systematic risk for a non-diversified investor

 Industry Standard deviation of shares by industry,% Estimated value of the adjusted beta coefficient (for the non-diversified investor position) Market in general (USA) 20.00 Tobacco companies 37.23 1.85 Pharmaceutical companies 50 2.5 Food company 38 1.9 Chemical companies 42 2.1 Packing 54 2.7 Trade (network) 51 2.55

Example 1

Let's show the algorithm for calculating the adjusted coefficient for an American company with a non-licensed investor in the CAPM model. The direction of "low-alcohol drinks" is considered. food industry (calculated by the stock (regression) method leverage beta coefficient - 0.46, financial lever D/V - 0.2, income tax rate - 30%, correlation coefficient - 0.2) .

Step 1. Calculation of the lossless beta coefficient for the analogue companies (the beta-coefficient cleansing method).

Step 2. Adjustment to the non-diversified position of the investor using the formula

Beta general risk = Bezrychagovy Beta coefficient/Coefficient of correlation.

Bezrychagovy beta coefficient = 0.46/(1 + 0.25 • 0.7) = 0.39. The correlation coefficient is 0.2.

Beta total risk - 1.95.

Another indicator of the overall risk may be an assessment of the risk of the company's assets, identified with a portfolio of shares and bonds issued by the company in question. An example of calculation of the risk of assets (as a standard deviation) is shown in Table. 19.2.

Table 19.2

Assessment of the overall risk of shares and company assets by industry

 Industries Standard deviation of shares,% Share own capital,% Calculation of standard deviation by assets,% Air carriers 62.16 63.27 41.36 Biotechnology 75.66 95.63 72.44 Building Materials 45.69 73.21 34.23 Chemical companies 38.87 74.53 29.58 Diversified chemical companies 41., 70 83.75 35.22 Specialized Chemicals 44.83 75.58 34.52 Coal companies 51.17 79.39 41.16 Software 83.99 96.55 81.16 Integrated Steel Companies 53.09 67.33 37.09 Educational services 60.20 98.22 59.15 Hotel and gaming business 45.72 64.00 30.69 Manufacture of equipment 47.92 69.89 34.52 Food realization 44.47 78.94 35.59 Gas sales 24.13 53.86 14.33 Diversified gas companies 45.73 57.63 28.42 Integrated Oil Companies 39.20 85.78 33.85 Oil production 50.28 80.92 41.15 Catering 45.13 84.12 38.26 Shopping networks 60.97 91.19 55.77 Shoe industry 45.90 94.60 43.49 Tobacco industry 30.35 77.71 23.95 Hygiene products and cosmetics 51.07 89.31 45.80 Electrical Equipment 62.27 56.34 38.10 Electronics 67.30 83.68 56.79 Average US marketplace 60.55 71.59 44.51

Note: The correlation coefficient of shares and bonds is 0.3; the relative volatility of bonds is 0.25.

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