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Calculation of the coefficient of variation
Let’s consider the two asset portfolio with 60% of the asset A and the 40% of the asset B. Each security’s future return is considered as a random variable (RA and RB). Our portfolio is a weighed combination of assets. The return of a portfolio is also a random variable and we can calculate portfolio expected return and the variance of the portfolio.
First, let’s calculate the expected return and the variance for asset A. Assume, that the asset A has the following estimated rate of return distribution:
Rate of Return Probability
(-5%) 20%
10% 50%
20% 30%
The expected rate of return for RA
is:
rA = (-5%)*0.2 + 10%*0.5 + 20%*0.3 = 10%
The formula for variance RA is:
= (-5-10)(-5-10)*0.2 + (10-10)(10-10)*0.5 + (20-10)(20-10)*0.3 = 75
Standard deviation is simply the square root of the variance:
= 8.66%
Let us assume that the asset B has the expected value of return rB = 15%, and the standard deviation of RB is 12%.
The standard deviation reflects the degree of risk for each individual assets A and B. When we want to compare the risk of different assets with the different expected return, we need to use the relative measure - the coefficient of variation:
Hence,asset's A coefficient of variation is: 8.66/10 = 0.866
asset's B coefficient of variation is: 12/15 = 0.8
So, we can say that asset A is a riskier investment than asset B.
In the next post, we'll calculate the expected return of our portfolio, define the covariance and coefficient of correlation for two assets, and how these values affect the variance and the standard deviation of the portfolio.
Technorati Tags: Variance Expected ValueCoefficient of VariationRate of ReturnStandard Deviation
Posted by mazoo at August 17, 2006 1:50 PM
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Covariance and Calculation of Portfolio Variance Aug 23, 2006Comments
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Posted by: Daniel Pejmon Shirmard at May 29, 2007 6:32 AM
Thanks for that....very usefull.
Im doing this at uni,and nowhere was it explained that the standard deviation calculation is the risk and how its calculated. Been racking my brain for hours trying to figure out how to calculate the risk.........very helpfull
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Posted by: Jessica at January 28, 2008 4:37 PM