Modern Portfolio Statistics Research Paper
Beta is a measure of a portfolio's sensitivity to market movements. The beta of the market is 1.00 by definition. Morningstar calculates beta by comparing a portfolio's excess return over T-bills to the benchmark's excess return over T-bills, so a beta of 1.10 shows that the portfolio has performed 10% better than its benchmark in up markets and 10% worse in down markets, assuming all other factors remain constant. Conversely, a beta of 0.85 indicates that the portfolio's excess return is expected to perform 15% worse than the benchmark�s excess return during up markets and 15% better during down markets.
Is a risk measure based on a comparison of the volatility of the portfolio's returns and the benchmark�s returns.
Set on a scale of 1.00. If a portfolio had a beta of 1.00, that means its returns are exactly as volatile as the benchmark�s returns. If a portfolio has a beta of 1.25, the portfolio's returns are 25% more volatile than the benchmark�s returns. If a portfolio has a beta of .68, the portfolios returns are 32% less volatile than the benchmark�s returns.
Beta is DEPENDENT ON THE BENCHMARK. So if a portfolio has a beta of 1.00, that doesn't mean that the portfolio has no volatility. It just means that the portfolio has the same volatility as the benchmark.
On a scatterplot Beta is indicated by the slope of the line.
Beta can be a useful tool when at least some of a portfolio's performance history can be explained by the market as a whole. Beta is particularly appropriate when used to measure the risk of a combined portfolio of funds.
It is important to note that a low beta does not necessarily imply a low level of volatility. A low beta signifies only that benchmark-related (market-related) risk is low. A specialty fund that invests primarily in gold, for example, will usually have a low beta, as its performance is tied more closely to the price of gold and gold-mining stocks than to the overall stock market. Thus, the specialty fund might fluctuate wildly because of rapid changes in gold prices, but its beta will remain low. R-squared is a necessary statistic to factor into the equation, because it reflects the percentage of a portfolio's movements that are explained by movements in its benchmark.
CVxy = covariance between portfolio and benchmark
Vx = variance of benchmark
Beta = CVxy /Vx
Modern Portfolio Statistics Research Paper