You will notice that Fund 4 dominates Fund 3 (higher return for less standard deviation), but it is unclear whether Funds 1, 2, or 4 are the best risky choice because none of the points dominates the other. So how can you decide? The question tells us that while we can’t create a portfolios with any of the other risky assets, we CAN combine each fund with the risk-free asset. You should remember that portfolio combinations of a risky asset and a risk-free asset are determined on a line between the two portfolios. Remember that the reason it is a line is that the return of a portfolio is a simple weighted average of its individual assets. Normally, the standard deviation of a portfolio is NOT a simple weighted average because of correlations. However, when one of the assets is risk free hence its standard deviation is zero, we DO have a weighted average. We saw this in Partner’s Healthcare with combinations of the Long-Term Pool (LTP) and the Short-Term Pool (STP). The standard deviation of a portfolio with some investment in the LTP (WLTP) and some in the STP (WSTP) 2222,2pLTPLTPSTPSTPLTPSTPLTPSTPLTP STPwwwwSince the standard deviation of the risk-free asset is 0, the second and third terms above become zero and the standard deviation of the portfolio becomes a simple weighted average.

16 We saw with Partner’s that we could form portfolios of the risky assets with the risk-free assets by connecting them with straight lines, as shown below When we could ONLY invest in a risky asset, Bonds by itself seemed to be a plausible investment because, while it had lower expected return, it also had low standard deviation. However, when we could combine the risky asset with the risk-free asset, then everyone would have preferred some combination of LTP and STP. This is because no matter how much risk you wanted to take, the solid black line that represents portfolios of LTP and STP is steeper than the dotted line representing portfolios of Bonds and STP. All investors would prefer to hold LTP as their risky asset rather than Bonds. An investor’s risk tolerance wouldn’t matter for choosing the risky portfolio. It WOULD matter for where on the solid black line the investor wanted to be (i.e. how much of their money invested in LTP vs. how much in STP.) We referred to this as two-fund separation. The relevant slide is shown below

17 The best risky portfolio is the one with the highest Sharpe Ratio. The Sharpe Ratio happens to be the slope of the lines in the above graph. Thus, for our question, we need to figure out which of the four risky portfolios has the highest Sharpe Ratio, which is what the answer shows. WHY DIDN’T WE USE THE CAPM?Remember that the CAPM provides us a model of expected returns based on the beta of the asset, the MRP, and the risk-free rate. Beta is a measure of covariance with the overall market and represents the systematic risk. We would use CAPM if we were planning on adding an asset to an already diversified portfolio.