Advanced Portfolio Management. Giuseppe A. Paleologo

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Advanced Portfolio Management - Giuseppe A. Paleologo


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target="_blank" rel="nofollow" href="#ulink_3c8f0f81-2736-50b2-8539-ed74efbc0c62">Table 3.4 Synchrony's risk parameters for the year 2019.

Field Value (%)
Beta 1.2
Daily Market Vol (%) 0.8
Daily Idio Vol (%) 1.3
Net Market Value $10M
StartLayout 1st Row 1st Column r equals alpha plus beta times m plus epsilon 2nd Column Blank EndLayout

      Now, we can apply this formula to Synchrony. The volatility of the market term is

StartLayout 1st Row 1st Column dollar-sign 10 upper M times 1.2 times 0.8 percent-sign equals dollar-sign 96 upper K 2nd Column Blank EndLayout

      The idiosyncratic volatility is

StartLayout 1st Row 1st Column dollar-sign 10 upper M times 1.3 percent-sign equals dollar-sign 130 upper K 2nd Column Blank EndLayout

      The dollar variance of Synchrony returns is 9 6 squared plus 13 0 squared equals 26116 normal upper K squared and finally the volatility is $162K.

Schematic illustration of the variance of the sum of two independent random variables is equal to the sum to the variances of the two random variables.
Field SYF WMT SPY
Beta 1.2 0.7 1
Daily Market Vol (%) 1.4
Daily Idio Vol (%) 1.2 0.5 0.0
Net Market Value $10M $5M $10M
StartLayout 1st Row 1st Column PnL Subscript port Baseline equals 2nd Column NMV Subscript SYF Baseline times r Subscript SYF plus NMV Subscript WMT times r Subscript WMT plus NMV Subscript SPY times r Subscript SPY EndLayout

      Now, we can use Equation (3.1) to replace returns with their components, and rearrange the terms:

      (3.2)StartLayout 1st Row 1st Column PnL Subscript port Baseline equals 2nd Column left-parenthesis NMV Subscript SYF Baseline times beta Subscript SYF Baseline plus NMV Subscript WMT Baseline times beta Subscript WMT Baseline plus NMV Subscript SPY Baseline times beta Subscript SPY Baseline right-parenthesis m 2nd Row 1st Column Blank 2nd Column left-parenthesis m a r k e t c o n t r i b u t i o n right-parenthesis 3rd Row 1st Column Blank 2nd Column plus left-parenthesis NMV Subscript SYF Baseline times epsilon Subscript SYF Baseline plus NMV Subscript WMT Baseline times epsilon Subscript WMT Baseline plus NMV Subscript SPY Baseline times epsilon Subscript SPY Baseline right-parenthesis 4th Row 1st Column Blank 2nd Column left-parenthesis i d i o s y n c r a t i c c o n t r i b u t i o n right-parenthesis EndLayout

      The performance of the portfolio can be split into the contribution of two terms: a market term and an idiosyncratic one. This is a simple example of performance attribution.

      The beta of the portfolio is 1.2 times dollar-sign 10 normal upper M plus 0.7 times dollar-sign 5 normal upper M plus 1 times dollar-sign 10 normal upper M equals dollar-sign 25.5 normal upper M. The important thing to notice is that the beta of the portfolio is the sum of the betas of the individual holdings. This overall portfolio beta is expressed in dollars, and usually is called the dollar beta of the portfolio. This dollar beta, multiplied by the market return m,


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