Torturing portfolios to give different volatilities between a factor model and Ledoit-Wolf shrinkage. Previously There have been posts on: “What the hell is a variance matrix?” factor models Ledoit-Wolf shrinkage Question Two of the several ways to produce an estimate of the variance matrix of asset returns is a statistical factor model and Ledoit-Wolf shrinkage.  Can we learn anything about what is happening when the two estimates give different answers for a portfolio? We can manufacture such portfolios by generating random portfolios that satisfy some constraints including...

What’s that thing about arithmetic and geometric returns and the variance? Previously An introduction to the difference between simple and log returns is: A tale of two returns Issue Suppose you are predicting the mean annual return of an asset for some number of years.  To simplify the discussion, let’s buy into the fantasy that the observed returns are a good (unbiased) estimate of future returns.  If you take the mean of the historical simple returns, you will be over-estimating the mean return — call this “Amean” (as in arithmetic mean).  Better is to take...

Most popular posts in 2013 April A practical introduction to garch modeling (posted in 2012) A tale of two returns (posted in 2010) Stock-picking opportunity and the ratio of variabilities A pictorial history of US large cap correlation The top 7 portfolio optimization problems (posted in 2012) garch and the distribution of returns Alternative equity indices and random portfolios Predicted correlations and portfolio optimization The distribution of financial returns made simple (posted in 2012) Slouching towards simulating investment skill The number 1 novice quant mistake (posted in 2011)...