Читать книгу Advanced Portfolio Management - Giuseppe A. Paleologo - Страница 15

1 Compute the dollar betas for the individual positions;

2 Compute the dollar portfolio beta as the sum of the individual betas;

3 Compute the market component of the volatility as (portfolio beta) (market volatility);

4 Compute the dollar idio volatility as the square root of the sum of the squared dollar volatilities.

Table 3.6 Portfolio example, with increasing number of stocks. Each stock has unit beta. The daily stocks' idio vol and market vol are both 1%.

# Stocks	Idio Vol ($)	Market Vol ($)	Idio Var (% tot)
1	1M	1M	50
10	316K	1M	9.09
100	100K	1M	0.99
1000	31.6K	1M	0.01

Say that you consider four long-only portfolios, each one with $100M of market value. The first one has one stock, the second one has ten stocks, the third has 100 stocks, the fourth one has 1000 stocks. Each stock has beta 1, and a daily idio vol of 1%. The market also has a daily vol of 1%. These are made-up numbers of course, but they simplify the calculation, and real portfolios are not that far from these values. What are the idio and market components of these portfolios? Table 3.6 has the numbers.⁷

Given this example, you can now understand better why SPY has zero percentage idio volatility in Table 3.5. The SPY is a long-only portfolio of 500 stocks. Each stock in the portfolio has a positive beta. As a percentage of the total risk, the idiosyncractic risk is very small, and is usually approximated to zero.