Question

preadsheet/output. · Portfolio Separation a. What is two-fund portfolio separation and why is it important? b. What are the assumptions that need to hold in order for two-fund separation to apply

Answer 1

a. what is two fund portfolio separation?

It is a theory stating that under conditions in which all investors borrow and lend at the riskless rate, all investors will either choose to possess a risk-free portfolio or the market portfolio.

The two-fund separation theorem tells us that an investor with quadratic utility can separate her asset allocation decision into two steps: First, find the tangency portfolio (TP), i.e., the portfolio of risky assets that maximizes the Sharpe ratio (SR); and then, decide on the mix of the TP and the risk-free asset, depending on the investor’s attitude toward risk.

Importance

The extension tells us that when the uncertainty model is convex, an investor with quadratic utility and uncertainty aversion can separate her investment problem into two steps: First, find the portfolio of risky assets that maximizes the worst-case SR (over all possible asset return statistics); and then, decide on the mix of this risky portfolio and the risk-free asset, depending on the investor’s attitude toward risk. The risky portfolio is the TP corresponding to the least favorable asset return statistics, with portfolio weights chosen optimally.

b. Assumptions

The two-step asset allocation process is based on the assumption that there is no model uncertainty or model mis-specification, i.e., the input data or parameters (the mean vector and covariance matrix of asset returns) are perfectly known. These input parameters are typically empirically estimated from historical data of asset returns, or from extensive analysis of various types of information about the assets and macro-economic conditions.