Portfolio Optimization

Chapter 4

Sharpe Ratios and Implied

Risk Free Returns

The typical situation studied in Chapter 3 is illustrated in Figure 4.1.

The key quantities a r e the implied risk free return r

m

, the tangency

point o f the CML with the efficient frontier defined by µ

m

and the slope,

R, of the CML. It is apparent from Figure 4.1 that if any single one of

r

m

, µ

m

or R is changed then the other two will change accordingly. It is

the purpose of this chapter t o determine precisely what these changes

will be.

In this chapter, we will look at the following problems.

1. Given the expected return on the market portfolio µ

m

, what is

the implied risk free return r

m

?

2. Given the implied risk free return r

m

, what is the implied market

portfolio x

m

or equiva lently, what is µ

m

or t