February 19, 2004
A Statistical View of Risk
We can use the expected value, variance, and standard deviation of the outcome to characterize the expected return and risk of an asset.
An examaple shows that using the standard deviation to characterize risk makes sense.
A "proof" of the "aX+b" rules:
We will stick to one risky asset and one risk-free asset because working with two or more risky assets requires consideration of covariances, which makes the budget constraint nonlinear.
Three possible covariances:
From the "variance of a sum" formula, we learn that negative covariances lower the risk of a portfolio.