FNCE10001 Chapter Notes - Chapter 11: Capital Asset Pricing Model, Expected Return, Efficient Frontier
25 May 2018
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Portfolio weights = fraction of total investment in portfolio held in each individual investment in the
portfolio
X
i
= value of investment i/ total value of portfolio
Given portfolio weights, return can be calculated
Return on portfolio, R
p
= sum of product of weight and return
Expected Return of a Portfolio
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Principles of Finance Page 1
Since prices of the stocks do not move identically, some of the risk is averaged out
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Combining stocks into a portfolio reduces risk through diversification
1.
Diversification cancels out additional risk
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Amount of risk that is eliminated in a portfolio depends on degree to which the stocks face
common risks and their prices move together
2.
Combining risks:
Determining covariance and correlation:
Positive if two stocks move together
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Negative if stocks move in opposite directions
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Large if stocks are more volatile or if stocks move closely in relation to each other
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Covariance = expected product of the deviations of two returns from their means
Same sign as covariance
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Independent risks are uncorrelated
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0 if uncorrelated (no tendency to move together or in opposition)
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Correlation = covariance of returns divided by standard deviation of each return
Stocks in same industry tend to have more highly correlated returns
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Stock returns tend to move together if affected similarly by economic events
Greatest variance if stocks have perfect positive correlation (+1)
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Computing a portfolio's variance and volatility
Volatility of a Two
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Stock Portfolio
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Principles of Finance Page 2
Additional benefits of diversification by holding more than two stocks
Large portfolio variance:
Variance of a portfolio = weighted average covariance of each stock with the portfolio = sum of
covariances of the returns of all pairs of stocks multiplied by each of their portfolio weights
Overall variability of portfolio depends on total co
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movement of stocks within it
Diversification with an equally weighted portfolio:
Equally weighted portfolio = portfolio in which same amount is invested in each stock
Variance converges to average covariance
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As number of stocks increases, variance is determined primarily by average covariance between
stocks
Benefit of diversification is most dramatic initially
Diversification with general portfolios:
Risk of portfolio < weighted average volatility of individual stocks
Volatility of a Large Portfolio
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Principles of Finance Page 3
Document Summary
Portfolio weights = fraction of total investment in portfolio held in each individual investment in the portfolio. Xi = value of investment i/ total value of portfolio. Return on portfolio, rp = sum of product of weight and return. Combining stocks into a portfolio reduces risk through diversification. Since prices of the stocks do not move identically, some of the risk is averaged out. Amount of risk that is eliminated in a portfolio depends on degree to which the stocks face common risks and their prices move together. Covariance = expected product of the deviations of two returns from their means. Large if stocks are more volatile or if stocks move closely in relation to each other. Correlation = covariance of returns divided by standard deviation of each return. 0 if uncorrelated (no tendency to move together or in opposition) Stock returns tend to move together if affected similarly by economic events.
