The Capital Market Line
Given the preceding conclusion that the single efficient fund of risky assets is the market portfolio, we can label this fund on the T~a diagram with an M for market. The efficient set therefore consists of a single straight line, emanating from the risk-free point and passing through the market portfolio. This line, shown in Figure 7 1, is called the capital market line.
This line shows the relation between the expected rate of return and the risk of return (as measured by the standard deviation) for efficient assets or portfolios of assets. It is also referred to as a pricing line, since prices should adjust so that efficient assets fall on this line.
The line has great intuitive appeal. It states that as risk increases, the corresponding expected rate of return must also increase Furthermore, this relationship can be r
FIGURE 7 1 Capital market line. Efficient assets must all lie on the line determined by the risk-free rate and the market portfolio
described by a straight line if risk is measured by standard deviation In mathematical terms the capital market line states that where Tm and am are the expected value and the standard deviation of the market rate of return and r and a are the expected value and the standard deviation of the rate of return of an arbitrary efficient asset
The slope of the capital market line is K — (/>/ — rf)/a\t, and this value is frequently called the price of risk. It tells by how much the expected rate of return of a portfolio must increase if the standard deviation of that rate increases by one unit.
Example 7.1 {The impatient investor) Mr Smith is young and impatient He notes that the risk-free rate is only 6% and the market portfolio of risky assets has an expected return of 12% and a standard deviation of 15%, He figures that it would take about 60 years for his $1,000 00 nest egg to increase to $1 million if it earned the market rate of return He can't wait that long. He wants that $1 million in 10 years.
Mr. Smith easily determines that he must attain an average rate of return of about 100% per year to achieve his goal (since $1,000 x 2l° = $1,048,000). Correspondingly, his yearly standard deviation according to the capital market line would be the value of a satisfying
12-06
or <7 = 10 This corresponds to a — 1,000%. So this young man is certainly not guaranteed success (even if he could borrow the amount required to move far beyond the market on the capital market line).
Example 7.2 (An oil venture) Consider an oil drilling venture The price of a share of this venture is $875 It is expected to yield the equivalent of $1,000 after 1 year, but due to high uncertainty about how much oil is at the drilling site, the standard deviation of the return is a = 40%. Currently the risk-free rate is 10% The expected rate of return on the market portfolio is 17%, and the standard deviation of this rate is 12%,
Let us see how this venture compares with assets on the capital market line Given the level of a, the expected rate of return predicted by the capital market line is
However, the actual expected rate of return is only 7 — 1,000/875 — 1 = 14%. Therefore the point representing the oil venture lies well below the capital market line. (This does not mean that the venture is necessarily a poor one, as we shall see later, but it certainly does not, by itself, constitute an efficient portfolio.)
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