FIN560 - Chapter 7 - Mean Variance Analysis

What are some ways to form the best diversified portfolio through mean variance math?

• put more weight on assets with higher expected returns; • put less weight on assets with higher variance; and • put less weight in assets with higher covariance.

What does the Sharpe Ratio measure?

The Sharpe ratio measures the amount of reward we get (expected return) per unit of risk taken (standard deviation): Sharpe Ratio = Reward / Risk = E(RA)−Rf / σ(RA) *What we care about is the Sharpe ratio of our total investments, not the Sharpe ratio of individual assets. We value individual assets for how they contribute to our overall portfolio to increase the Sharpe ratio of our total portfolio.

What is the capital allocation line?

The capital allocation line is the line that connects (and extends past on either end) the risk free asset and the tangency portfolio.

How is the highest sharpe ratio of a portfolio represented on a graph?

The portfolio with the highest Sharpe ratio will be the one at the tangency point between our total investment opportunity set and a line originating from the risk free rate. That tangency point gives us as steep of a line as we can get.

How do we measure the relationship between risk and the sharpe ratio?

We measure this interaction by the covariance of the movement between two securities. The larger the covariance the more they move together and consequently the less diversification benefit we get from combining them. Covariance numbers can be difficult to digest at times, so we often talk about correlations between assets. Correlations between assets also measure how they move together but are normalized to lie between −1 and 1.