## Wednesday, May 20, 2009

### Asset Pricing Models, Pt 1 - CML

One thing that I initially found confusing was the Capital Market Line (CML) and the Security Market Line (SML). At first glance, they seem to be identical graphs, but let's take a closer look at each while understanding what each is used for.

The Capital Market Line starts of with a scatter plot of all securities with the Y axis being expected return, E(R), and the X axis being standard deviation of return. After calculating the correlations and creating a variety of different portfolios, another scatter plot is super imposed onto the graph. At this point, it should naturally become obvious that there is a curved relationship between the maximum expected return for any given standard deviation (starting with economies of scope and increasing utility to a point of diminishing returns). The curve describing the upper bound of this scatter plot is called the efficient frontier.

Then, on the Y axis itself (the point of no standard deviation, no risk) we have the risk free asset which earns returns at the risk free rate (RFR) typically denoted by US Treasury securities.

The CML is created by creating a line between RFR and the point on the curve for which the CML is tangential. The reason for this is that at any given point on the CML, movement up or down the line will result in a change in the Safety First Ratio (marginal utility of risk, since we are using RFR as the basis for comparison) and therefore the utility is maximized at the point where the CML touches the efficient frontier (in theory this should happen only once). Below is the completed graph:

Because the efficient market portfolio (EMP) represents the optimal mix of securities, the optimal positions based on risk (assuming lending and borrowing at RFR) is any position along the CML. Positions with standard deviations below the EMP are lending positions (being short the EMP and long the RFA). Positions beyond the EMP are borrowing positions (being long the EMP and short the RFA). Basically, it's adjusting your risk tolerance by leveraging or deleveraging the EMP.

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