### Picking an investor’s preferred portfolio from the points on the efficient frontier

One’s preferred level of risk affects how one invests. Different levels of your risk coefficient will create different ideal portfolios as illustrated in the figure below. This post describes the math behind the different allocations for different risk preference levels. The classic Markowitz optimization creates a set of portfolios called the efficient frontier which returns … Continue reading

### Finding the #MinimumRisk #portfolio on a two-security #EfficientFrontier

In the #Markowitz risk-return space, there is always a portfolio which #MinimizesVolatility. In recent years this allocation scheme has become increasingly popular as the risk free rate hovers near (or below) zero. For a portfolio of two securities, there is an analytic solution which allocates capital to both securities to minimize the portfolio volatility. We … Continue reading

### The Kelly solution for one continuous distribution of possible returns

By Elliot Noma with comments from Yu Bai The Kelly criterion is usually invoked for solving the optimal bet size for a two-outcome gamble. In other posts, we have considered the three outcome solution. Here we consider the optimal bet size for a specific family of continuous distributions, a uniform distribution of outcomes over a unit interval. … Continue reading

### R code to compute beta and the Sharpe ratio for a publicly traded stock

The following R code will calculate beta and the Sharpe ratio using adjusted closing prices from Yahoo finance. A video describing the output using an earlier version of this routine is available at http://www.youtube.com/watch?v=U8rNmkFRT1M # calculate beta and the Sharpe ratio suppressPackageStartupMessages(require(quantmod)) BRCM.Quote <- getSymbols.yahoo(“BRCM”, from=”1950-01-01″, verbose=FALSE, auto.assign=FALSE) SPX.Quote <- getSymbols.yahoo(“^GSPC”, from=”1950-01-01″, verbose=FALSE, auto.assign=FALSE) Prices … Continue reading